summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/latex/latex-web-companion/ch4
diff options
context:
space:
mode:
Diffstat (limited to 'Master/texmf-dist/doc/latex/latex-web-companion/ch4')
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.aux29
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.css45
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.dvibin0 -> 73912 bytes
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.html1510
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.idvbin0 -> 14276 bytes
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.lg121
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.log285
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.otc13
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.tex549
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.toc12
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.xref81
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/phys332-1.eps419
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/phys332-2.eps556
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/tex4ht.env70
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/tex4ht.tmp2
-rw-r--r--Master/texmf-dist/doc/latex/latex-web-companion/ch4/tmp.ps542
16 files changed, 4234 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.aux b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.aux
new file mode 100644
index 00000000000..96bb466013e
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.aux
@@ -0,0 +1,29 @@
+\relax
+\ifx\rEfLiNK\UnDef\gdef \xRef#1#2{#2}\fi
+\newlabel{fg:phys332-1}{{\rEfLiNK{1-10061}{1}}{\rEfLiNK{1-10061}{6}}}
+\citation{bib-LAND}
+\citation{bib-TALM}
+\newlabel{sec:phys332-1}{{\rEfLiNK{1-20002}{2}}{\rEfLiNK{1-20002}{7}}}
+\citation{bib-VAVI}
+\citation{bib-SCH1}
+\newlabel{vavref}{{\rEfLiNK{1-40003}{3}}{\rEfLiNK{1-40003}{9}}}
+\citation{bib-SELT}
+\newlabel{urban}{{\rEfLiNK{1-60005}{5}}{\rEfLiNK{1-60005}{10}}}
+\newlabel{fg:phys332-2}{{\rEfLiNK{1-60012}{2}}{\rEfLiNK{1-60012}{12}}}
+\newlabel{eq:sigex}{{\rEfLiNK{1-6003r2}{2}}{\rEfLiNK{1-6003r2}{13}}}
+\newlabel{eq:sigion}{{\rEfLiNK{1-6004r3}{3}}{\rEfLiNK{1-6004r3}{13}}}
+\newlabel{eq:fisum}{{\rEfLiNK{1-6005r4}{4}}{\rEfLiNK{1-6005r4}{14}}}
+\newlabel{eq:flnsum}{{\rEfLiNK{1-6005r5}{5}}{\rEfLiNK{1-6005r5}{14}}}
+\newlabel{eq:phys332-5}{{\rEfLiNK{1-7001r13}{13}}{\rEfLiNK{1-7001r13}{17}}}
+\newlabel{eq:phys332-1}{{\rEfLiNK{1-7004r16}{16}}{\rEfLiNK{1-7004r16}{17}}}
+\newlabel{eq:phys332-2}{{\rEfLiNK{1-7004r17}{17}}{\rEfLiNK{1-7004r17}{17}}}
+\newlabel{eq:phys332-3}{{\rEfLiNK{1-7005r18}{18}}{\rEfLiNK{1-7005r18}{18}}}
+\newlabel{eq:phys332-4}{{\rEfLiNK{1-7005r19}{19}}{\rEfLiNK{1-7005r19}{18}}}
+\newlabel{eq:phys332-6}{{\rEfLiNK{1-7008r22}{22}}{\rEfLiNK{1-7008r22}{18}}}
+\newlabel{eq:phys332-7}{{\rEfLiNK{1-7008r23}{23}}{\rEfLiNK{1-7008r23}{18}}}
+\newlabel{eq:phys332-8}{{\rEfLiNK{1-7008r24}{24}}{\rEfLiNK{1-7008r24}{19}}}
+\bibcite{bib-LAND}{1}
+\bibcite{bib-SCH1}{2}
+\bibcite{bib-SELT}{3}
+\bibcite{bib-TALM}{4}
+\bibcite{bib-VAVI}{5}
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.css b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.css
new file mode 100644
index 00000000000..333d950a156
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.css
@@ -0,0 +1,45 @@
+
+/* start css.sty */
+.cmsy-7{font-size:70%;}
+.emr-17{font-size:170%;}
+.emr-12{font-size:120%;}
+.emtt-10{font-family: monospace;}
+.emr-7{font-size:70%;}
+.emr-5{font-size:50%;}
+.emmi-7{font-size:70%;}
+.emmi-5{font-size:50%;}
+.emti-10{font-style: italic;}
+.small-caps{font-variant: small-caps; }
+p.noindent { text-indent: 0em }
+p.indent{ text-indent: 1.5em }
+.sub, .sup {font-size:110%}
+.Canvas { position:relative; }
+img.mathdisplay{ margin-top: 1em; margin-bottom: 1em; }
+li p.indent, li p.indent{ text-indent: 0em }
+p.bibitem { text-indent: -2em; margin-left: 2em; }
+.quote {margin-bottom:0.25em; margin-top:0.25em; margin-left:1em; }
+DIV.td00{ margin-left:0; margin-right:0; }
+DIV.td01{ margin-left:0; margin-right:5; }
+DIV.td10{ margin-left:5; margin-right:0; }
+DIV.td11{ margin-left:5; margin-right:5; }
+.hline hr, .cline hr{ height : 1px; }
+.verbatim {margin-bottom:0.5em; margin-top:0.5em; }
+span.footnotetext{ font-size:75%; font-style:italic; }
+span.TEX {letter-spacing: -0.125em; }
+span.TEX span.E{ position:relative;top:0.5ex;left:-0.0417em;}
+a span.TEX span.E {text-decoration: none; }
+span.LATEX span.A{ position:relative; top:-0.5ex; left:-0.4em; font-size:85%;}
+span.LATEX span.TEX{ position:relative; left: -0.4em; }
+.marginpar {width:20%; float:right; text-align:left; margin-left:1em; margin-top:0.5em; font-size:85%; text-decoration:underline;}
+.equation TD{text-align:center; }
+.obeylines-h,.obeylines-v {white-space: nowrap; }
+span.pmatrix img{vertical-align:middle;}
+.underline{ text-decoration:underline; }
+.overline{ text-decoration:overline; }
+td.caption{white-space: nowrap; }
+h2.titleHead{text-align:center;}
+div.maketitle{ margin-bottom: 2em; }
+h1.partHead{text-align: center}
+.paragraphHead, .likeparagraphHead { margin-top:2em; font-weight: bold;}
+.subparagraphHead, .likesubparagraphHead { font-weight: bold;}
+/* end css.sty */
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.dvi b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.dvi
new file mode 100644
index 00000000000..49e057e59c8
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.dvi
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.html b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.html
new file mode 100644
index 00000000000..7461e32259f
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.html
@@ -0,0 +1,1510 @@
+
+
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html
+><head><!--latexexa.html from latexexa.tex (TeX4ht, 1999-03-31 09:15:00)-->
+<title>Simulation of Energy Loss Straggling</title><link
+rel="stylesheet" type="text/css" href="latexexa.css"></head><body
+> <div align="center" class="maketitle">
+<h2 class="titleHead">Simulation of Energy Loss Straggling</h2>
+<div class="author" align="center"><span
+class="emr-12">Maria Physicist</span></div>
+<br>
+<div class="date" align="center"><span
+class="emr-12">March 31, 1999</span></div>
+ <span class="thanks"></span></div>
+ <h2 class="sectionHead">1 <a
+ name="1-10001"></a><a
+ name="QQ1-1-1"></a>Introduction</h2>
+<!--16--><p class="noindent">Due to the statistical nature of ionisation energy loss, large fluctuations can occur in
+the amount of energy deposited by a particle traversing an absorber element.
+Continuous processes such as multiple scattering and energy loss play a
+relevant role in the longitudinal and lateral development of electromagnetic and
+hadronic showers, and in the case of sampling calorimeters the measured
+resolution can be significantly affected by such fluctuations in their active
+layers. The description of ionisation fluctuations is characterised by the
+significance parameter <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"></span>, which is proportional to the ratio of mean energy loss to
+the maximum allowed energy transfer in a single collision with an atomic
+electron
+ <center>
+<img
+src="latexexa0x.gif"alt=" q
+k = E----
+ max"class="mathdisplay"></center> <span
+class="emmi-10">E</span><span
+class="emr-7">max</span>
+is the maximum transferable energy in a single collision with an atomic
+electron.
+ <center>
+<img
+src="latexexa1x.gif"alt=" 2m b2g2
+Emax = ----------e----------2-,
+ 1 +2gme/mx + (me/mx)"class="mathdisplay"></center> where
+<span
+class="emmi-10"><img
+src="emmi10-d.gif"alt="g"class="10--d"> </span>= <span
+class="emmi-10">E/m</span><sub ><span
+class="emmi-7">x</span></sub> , <span
+class="emmi-10">E </span>is energy and <span
+class="emmi-10">m</span><sub ><span
+class="emmi-7">x</span></sub> the mass of the incident particle, <span
+class="emmi-10"><img
+src="emmi10-c.gif"alt="b"class="emmi-10--c"align="middle"></span><sup ><span
+class="emr-7">2</span></sup> = 1 <span
+class="cmsy-10">- </span>1<span
+class="emmi-10">/<img
+src="emmi10-d.gif"alt="g"class="10--d"></span><sup ><span
+class="emr-7">2</span></sup> and
+<span
+class="emmi-10">m</span><sub ><span
+class="emmi-7">e</span></sub> is the electron mass. <span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle"> </span>comes from the Rutherford scattering cross section and is
+defined as: <div align="center" class="eqnarray"><a
+ name="1-1001r1"></a>
+<table
+class="eqnarray-star"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle"> </span>= 2<span
+class="emmi-10"><img
+src="emmi10-19.gif"alt="p"class="10--19">z</span><sup ><span
+class="emr-7">2</span></sup><span
+class="emmi-10">e</span><sup ><span
+class="emr-7">4</span></sup><span
+class="emmi-10">N</span><sub ><span
+class="emmi-7">Av</span></sub><span
+class="emmi-10">Z<img
+src="emmi10-1a.gif"alt="r"class="emmi-10--1a"align="middle"><img
+src="emmi10-e.gif"alt="d"class="10--e">x</span>
+ <span
+class="emmi-10">m</span><sub ><span
+class="emmi-7">e</span></sub><span
+class="emmi-10"><img
+src="emmi10-c.gif"alt="b"class="emmi-10--c"align="middle"></span><sup ><span
+class="emr-7">2</span></sup><span
+class="emmi-10">c</span><sup ><span
+class="emr-7">2</span></sup><span
+class="emmi-10">A</span> = 153<span
+class="emmi-10">.</span>4 <span
+class="emmi-10">z</span><sup ><span
+class="emr-7">2</span></sup>
+<span
+class="emmi-10"><img
+src="emmi10-c.gif"alt="b"class="emmi-10--c"align="middle"></span><sup ><span
+class="emr-7">2</span></sup> <span
+class="emmi-10">Z</span>
+<span
+class="emmi-10">A</span><span
+class="emmi-10"><img
+src="emmi10-1a.gif"alt="r"class="emmi-10--1a"align="middle"><img
+src="emmi10-e.gif"alt="d"class="10--e">x</span> keV<span
+class="emmi-10">,</span></td><td
+align="center"nowrap
+class="eqnarray2"></td><td
+align="left"nowrap
+class="eqnarray3"></td></tr></table>
+</div>where
+ <div align="center"><table class="tabular"
+cellspacing="0pt" cellpadding="0"
+frame="void" ><colgroup><col
+id="TBL-2-1"><col
+id="TBL-2-2"></colgroup><tr
+valign="baseline" id="TBL-2-1-"><td align="left"nowrap id="TBL-2-1-1"
+><div class="td11"><span
+class="emmi-10">z </span></div></td><td align="left"nowrap id="TBL-2-1-2"
+><div class="td11">charge of the incident particle </div></td>
+</tr><tr
+valign="baseline" id="TBL-2-2-"><td align="left"nowrap id="TBL-2-2-1"
+><div class="td11"><span
+class="emmi-10">N</span><sub ><span
+class="emmi-7">Av</span></sub></div></td><td align="left"nowrap id="TBL-2-2-2"
+><div class="td11">Avogadro's number </div></td>
+</tr><tr
+valign="baseline" id="TBL-2-3-"><td align="left"nowrap id="TBL-2-3-1"
+><div class="td11"><span
+class="emmi-10">Z </span></div></td><td align="left"nowrap id="TBL-2-3-2"
+><div class="td11">atomic number of the material</div></td>
+</tr><tr
+valign="baseline" id="TBL-2-4-"><td align="left"nowrap id="TBL-2-4-1"
+><div class="td11"><span
+class="emmi-10">A </span></div></td><td align="left"nowrap id="TBL-2-4-2"
+><div class="td11">atomic weight of the material </div></td>
+</tr><tr
+valign="baseline" id="TBL-2-5-"><td align="left"nowrap id="TBL-2-5-1"
+><div class="td11"><span
+class="emmi-10"><img
+src="emmi10-1a.gif"alt="r"class="emmi-10--1a"align="middle"> </span></div></td><td align="left"nowrap id="TBL-2-5-2"
+><div class="td11">density </div></td>
+</tr><tr
+valign="baseline" id="TBL-2-6-"><td align="left"nowrap id="TBL-2-6-1"
+><div class="td11"><span
+class="emmi-10"><img
+src="emmi10-e.gif"alt="d"class="10--e">x </span></div></td><td align="left"nowrap id="TBL-2-6-2"
+><div class="td11">thickness of the material </div></td>
+</tr><tr
+valign="baseline" id="TBL-2-7-"><td align="left"nowrap id="TBL-2-7-1"
+><div class="td11"> </div></td> </tr></table>
+</div>
+<!--57--><p class="indent"> <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"> </span>measures the contribution of the collisions with energy transfer close to <span
+class="emmi-10">E</span><span
+class="emr-7">max</span>.
+For a given absorber, <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"> </span>tends towards large values if <span
+class="emmi-10"><img
+src="emmi10-e.gif"alt="d"class="10--e">x </span>is large and/or if <span
+class="emmi-10"><img
+src="emmi10-c.gif"alt="b"class="emmi-10--c"align="middle"> </span>is
+small. Likewise, <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"> </span>tends towards zero if <span
+class="emmi-10"><img
+src="emmi10-e.gif"alt="d"class="10--e">x </span>is small and/or if <span
+class="emmi-10"><img
+src="emmi10-c.gif"alt="b"class="emmi-10--c"align="middle"> </span>approaches
+1.
+<!--63--><p class="indent"> The value of <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"> </span>distinguishes two regimes which occur in the description of
+ionisation fluctuations :
+ <ol type="1"class="enumerate1"
+>
+ <li class="enumerate"><a
+ name="1-1003x1"></a>A large number of collisions involving the loss of all or most of the incident
+ particle energy during the traversal of an absorber.
+ <!--70--><p class="noindent">As the total energy transfer is composed of a multitude of small energy
+ losses, we can apply the central limit theorem and describe the fluctuations
+ by a Gaussian distribution. This case is applicable to non-relativistic
+ particles and is described by the inequality <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"> &gt; </span>10 (i.e. when the mean
+ energy loss in the absorber is greater than the maximum energy transfer
+ in a single collision).
+ </li>
+ <li class="enumerate"><a
+ name="1-1005x2"></a>Particles traversing thin counters and incident electrons under any
+ conditions.
+ <!--81--><p class="noindent">The relevant inequalities and distributions are 0<span
+class="emmi-10">.</span>01 <span
+class="emmi-10">&lt; <img
+src="emmi10-14.gif"alt="k"class="10--14"> &lt; </span>10, Vavilov
+ distribution, and <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"> &lt; </span>0<span
+class="emmi-10">.</span>01, Landau distribution.</li></ol>
+<!--83--><p class="noindent">
+<!--85--><p class="indent"> An additional regime is defined by the contribution of the collisions with low
+energy transfer which can be estimated with the relation <span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle">/I</span><sub ><span
+class="emr-7">0</span></sub>, where <span
+class="emmi-10">I</span><sub ><span
+class="emr-7">0</span></sub> is the mean
+ionisation potential of the atom. Landau theory assumes that the number of these
+collisions is high, and consequently, it has a restriction <span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle">/I</span><sub ><span
+class="emr-7">0</span></sub> <span
+class="cmsy-10">» </span>1. In <span
+class="emtt-10">GEANT </span>(see URL
+<span
+class="emtt-10">http://wwwinfo.cern.ch/asdoc/geant/geantall.html</span>), the limit of Landau
+theory has been set at <span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle">/I</span><sub ><span
+class="emr-7">0</span></sub> = 50. Below this limit special models taking into account
+the atomic structure of the material are used. This is important in thin layers and
+gaseous materials. Figure <a
+ href="#1-10061">1</a> shows the behaviour of <span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle">/I</span><sub ><span
+class="emr-7">0</span></sub> as a function of the layer
+thickness for an electron of 100 keV and 1 GeV of kinetic energy in Argon, Silicon
+and Uranium.
+<a
+ name="1-10061"></a>
+ <hr class="float"><div align="center" class="float"
+><table class="float"><tr class="float"><td class="float"
+>
+<img
+src="latexexa2x.gif"alt="PIC">
+<br><div align="center"class="caption"><table class="caption"
+><tr valign="baseline" class="caption"><td class="id">Figure 1</td><td
+class="content">The variable <span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle">/I</span><sub ><span
+class="emr-7">0</span></sub> can be used to measure the validity range of the
+Landau theory. It depends on the type and energy of the particle, <span
+class="emmi-10">Z </span>, <span
+class="emmi-10">A </span>and the
+ionisation potential of the material and the layer thickness. </td></tr></table></div>
+ </td></tr></table></div><hr class="endfloat">
+<!--110--><p class="indent"> In the following sections, the different theories and models for the energy loss
+fluctuation are described. First, the Landau theory and its limitations are discussed,
+and then, the Vavilov and Gaussian straggling functions and the methods in the thin
+layers and gaseous materials are presented.
+ <h2 class="sectionHead">2 <a
+ name="1-20002"></a><a
+ name="QQ1-1-3"></a>Landau theory</h2>
+<!--119--><p class="noindent">For a particle of mass <span
+class="emmi-10">m</span><sub ><span
+class="emmi-7">x</span></sub> traversing a thickness of material <span
+class="emmi-10"><img
+src="emmi10-e.gif"alt="d"class="10--e">x</span>, the Landau
+probability distribution may be written in terms of the universal Landau function
+<span
+class="emmi-10"><img
+src="emmi10-1e.gif"alt="f"class="10--1e"></span>(<span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span>) as[<a
+ href="#Xbib-LAND">1</a>]: <div align="center" class="eqnarray"><a
+ name="1-2001r1"></a>
+<table
+class="eqnarray-star"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10">f</span>(<span
+class="emmi-10"><img
+src="emmi10-f.gif"alt="e"class="10--f">, <img
+src="emmi10-e.gif"alt="d"class="10--e">x</span>)</td><td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3">1
+ <span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle"></span> <span
+class="emmi-10"><img
+src="emmi10-1e.gif"alt="f"class="10--1e"></span>(<span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span>)</td></tr></table>
+</div>where <div align="center" class="eqnarray"><a
+ name="1-2002r1"></a>
+<table
+class="eqnarray-star"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-1e.gif"alt="f"class="10--1e"></span>(<span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span>)</td><td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"> 1_
+2<span
+class="emmi-10"><img
+src="emmi10-19.gif"alt="p"class="10--19">i</span> <span
+class="cmex-10"><img
+src="cmex10-5a.gif"alt=" integral "class="cmex-10--5a"align="middle"></span>
+ <sub> <span
+class="emmi-10">c </span><span
+class="cmsy-10">- </span><span
+class="emmi-10">i</span><span
+class="cmsy-10"><img
+src="cmsy10-31.gif"alt=" oo "class="10--31"></span></sub><sup><span
+class="emmi-10">c </span>+ <span
+class="emmi-10">i</span><span
+class="cmsy-10"><img
+src="cmsy10-31.gif"alt=" oo "class="10--31"></span></sup> exp <img
+src="latexexa3x.gif"alt="(u ln u+ cu)"class="left" align="middle"> <span
+class="emmi-10">du</span><span
+class="emmi-10"> </span><span
+class="emmi-10"> </span><span
+class="emmi-10"> </span><span
+class="emmi-10"> </span><span
+class="emmi-10"> </span> <span
+class="emmi-10">c </span><span
+class="cmsy-10"><span
+class="underline">&gt;</span> </span>0</td></tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span></td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"><span
+class="emmi-10"><img
+src="emmi10-f.gif"alt="e"class="10--f"> </span><span
+class="cmsy-10">-</span> <img
+src="latexexa4x.gif"alt="e"class="bar" >
+ <span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle"></span> <span
+class="cmsy-10">- </span><span
+class="emmi-10"><img
+src="emmi10-d.gif"alt="g"class="10--d"></span><span
+class="cmsy-7">'</span> <span
+class="cmsy-10">- </span><span
+class="emmi-10"><img
+src="emmi10-c.gif"alt="b"class="emmi-10--c"align="middle"></span><sup ><span
+class="emr-7">2</span></sup> <span
+class="cmsy-10">-</span> ln <span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle"></span> ___
+<span
+class="emmi-10">E</span><span
+class="emr-7">max</span> </td> </tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-d.gif"alt="g"class="10--d"></span><span
+class="cmsy-7">'</span></td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3">0<span
+class="emmi-10">.</span>422784 <span
+class="emmi-10">. . .</span> = 1 <span
+class="cmsy-10">- </span><span
+class="emmi-10"><img
+src="emmi10-d.gif"alt="g"class="10--d"></span></td> </tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-d.gif"alt="g"class="10--d"></span></td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3">0<span
+class="emmi-10">.</span>577215 <span
+class="emmi-10">. . .</span> (Euler's constant)</td> </tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><img
+src="latexexa5x.gif"alt="e"class="bar" ></td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3">average energy loss</td> </tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-f.gif"alt="e"class="10--f"></span></td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3">actual energy loss</td> </tr></table>
+</div>
+ <h3 class="subsectionHead">2.1 <a
+ name="1-30002.1"></a><a
+ name="QQ1-1-4"></a>Restrictions</h3>
+<!--140--><p class="noindent">The Landau formalism makes two restrictive assumptions :
+ <ol type="1"class="enumerate1"
+>
+ <li class="enumerate"><a
+ name="1-3002x1"></a>The typical energy loss is small compared to the maximum energy loss in
+ a single collision. This restriction is removed in the Vavilov theory (see
+ section <a
+ href="#1-40003">3</a>).
+ </li>
+ <li class="enumerate"><a
+ name="1-3004x2"></a>The typical energy loss in the absorber should be large compared to the
+ binding energy of the most tightly bound electron. For gaseous detectors,
+ typical energy losses are a few keV which is comparable to the binding
+ energies of the inner electrons. In such cases a more sophisticated approach
+ which accounts for atomic energy levels[<a
+ href="#Xbib-TALM">4</a>] is necessary to accurately
+ simulate data distributions. In <span
+class="emtt-10">GEANT</span>, a parameterised model by L. Urb&aacute;n
+ is used (see section <a
+ href="#1-60005">5</a>).</li></ol>
+<!--153--><p class="noindent">
+<!--155--><p class="indent"> In addition, the average value of the Landau distribution is infinite. Summing the
+Landau fluctuation obtained to the average energy from the <span
+class="emmi-10">dE/dx </span>tables, we
+obtain a value which is larger than the one coming from the table. The
+probability to sample a large value is small, so it takes a large number of steps
+(extractions) for the average fluctuation to be significantly larger than zero. This
+introduces a dependence of the energy loss on the step size which can affect
+calculations.
+<!--164--><p class="indent"> A solution to this has been to introduce a limit on the value of the variable
+sampled by the Landau distribution in order to keep the average fluctuation to 0.
+The value obtained from the <span
+class="emtt-10">GLANDO </span>routine is:
+ <center>
+<img
+src="latexexa6x.gif"alt="ddE/dx = e- e = q(c -g'+ b2 + ln--q-)
+ Emax"class="mathdisplay"></center> In
+order for this to have average 0, we must impose that:
+ <center>
+<img
+src="latexexa7x.gif"alt="c = -g'- b2 -ln -q---
+ Emax"class="mathdisplay"></center>
+<!--177--><p class="indent"> This is realised introducing a <span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span><sub ><span
+class="emr-7">max</span></sub>(<img
+src="latexexa8x.gif"alt="c"class="bar" >) such that if only values of <span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"> </span><span
+class="cmsy-10"><span
+class="underline">&lt;</span> </span><span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span><sub ><span
+class="emr-7">max</span></sub> are
+accepted, the average value of the distribution is <img
+src="latexexa9x.gif"alt="c"class="bar" >.
+<!--181--><p class="indent"> A parametric fit to the universal Landau distribution has been performed, with
+following result:
+ <center>
+<img
+src="latexexa10x.gif"alt="cmax = 0.60715+ 1.1934c + (0.67794+ 0.052382c)exp(0.94753 +0.74442c)"class="mathdisplay"></center>
+only values smaller than <span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span><sub ><span
+class="emr-7">max</span></sub> are accepted, otherwise the distribution is
+resampled.
+ <h2 class="sectionHead">3 <a
+ name="1-40003"></a><a
+ name="QQ1-1-5"></a>Vavilov theory</h2>
+<!--197--><p class="noindent">Vavilov[<a
+ href="#Xbib-VAVI">5</a>] derived a more accurate straggling distribution by introducing the
+kinematic limit on the maximum transferable energy in a single collision, rather than
+using <span
+class="emmi-10">E</span><span
+class="emr-7">max</span> = <span
+class="cmsy-10"><img
+src="cmsy10-31.gif"alt=" oo "class="10--31"></span>. Now we can write[<a
+ href="#Xbib-SCH1">2</a>]: <div align="center" class="eqnarray"><a
+ name="1-4001r1"></a>
+<table
+class="eqnarray-star"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10">f</span><img
+src="latexexa11x.gif"alt="(e,ds)"class="left" align="middle"></td><td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3">1
+ <span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle"></span> <span
+class="emmi-10"><img
+src="emmi10-1e.gif"alt="f"class="10--1e"></span><sub ><span
+class="emmi-7">v</span></sub><img
+src="latexexa12x.gif"alt="( )
+ cv,k,b2"class="left" align="middle"></td></tr></table>
+</div>where <div align="center" class="eqnarray"><a
+ name="1-4002r1"></a>
+<table
+class="eqnarray-star"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-1e.gif"alt="f"class="10--1e"></span><sub ><span
+class="emmi-7">v</span></sub><img
+src="latexexa13x.gif"alt="(cv,k,b2)"class="left" align="middle"></td><td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"> 1_
+2<span
+class="emmi-10"><img
+src="emmi10-19.gif"alt="p"class="10--19">i</span> <span
+class="cmex-10"><img
+src="cmex10-5a.gif"alt=" integral "class="cmex-10--5a"align="middle"></span>
+ <sub> <span
+class="emmi-10">c </span><span
+class="cmsy-10">- </span><span
+class="emmi-10">i</span><span
+class="cmsy-10"><img
+src="cmsy10-31.gif"alt=" oo "class="10--31"></span></sub><sup><span
+class="emmi-10">c </span>+ <span
+class="emmi-10">i</span><span
+class="cmsy-10"><img
+src="cmsy10-31.gif"alt=" oo "class="10--31"></span></sup><span
+class="emmi-10"><img
+src="emmi10-1e.gif"alt="f"class="10--1e"></span><img
+src="latexexa14x.gif"alt="(s)"class="left" align="middle"> <span
+class="emmi-10">e</span><sup ><span
+class="emmi-7"><img
+src="emmi7-15.gif"alt="c"class="7--15">s</span></sup><span
+class="emmi-10">ds</span><span
+class="emmi-10"> </span><span
+class="emmi-10"> </span><span
+class="emmi-10"> </span><span
+class="emmi-10"> </span><span
+class="emmi-10"> </span> <span
+class="emmi-10">c </span><span
+class="cmsy-10"><span
+class="underline">&gt;</span> </span>0</td></tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-1e.gif"alt="f"class="10--1e"></span><img
+src="latexexa15x.gif"alt="(s)"class="left" align="middle"></td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3">exp <img
+src="latexexa16x.gif"alt="[ 2 ]
+ k(1+ b g)"class="left" align="middle"> <span
+class="emmi-10"> </span> exp <img
+src="latexexa17x.gif"alt="[y(s)]"class="left" align="middle"> <span
+class="emmi-10">,</span> </td> </tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-20.gif"alt="y"class="10--20"></span><img
+src="latexexa18x.gif"alt="(s)"class="left" align="middle"></td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"><span
+class="emmi-10">s</span> ln <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"> </span>+ (<span
+class="emmi-10">s </span>+ <span
+class="emmi-10"><img
+src="emmi10-c.gif"alt="b"class="emmi-10--c"align="middle"></span><sup ><span
+class="emr-7">2</span></sup><span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"></span>)<img
+src="latexexa19x.gif"alt="[ln(s/k)+ E1(s/k)]"class="left" align="middle"> <span
+class="cmsy-10">- </span><span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14">e</span><sup ><span
+class="cmsy-7">-</span><span
+class="emmi-7">s/<img
+src="emmi7-14.gif"alt="k"class="7--14"></span></sup><span
+class="emmi-10">,</span></td> </tr></table>
+</div>and <div align="center" class="eqnarray"><a
+ name="1-4003r1"></a>
+<table
+class="eqnarray-star"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10">E</span><sub ><span
+class="emr-7">1</span></sub>(<span
+class="emmi-10">z</span>)</td><td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"><span
+class="cmex-10"><img
+src="cmex10-5a.gif"alt=" integral "class="cmex-10--5a"align="middle"></span>
+ <sub> <span
+class="emmi-10">z</span></sub><sup><span
+class="cmsy-10"><img
+src="cmsy10-31.gif"alt=" oo "class="10--31"></span></sup><span
+class="emmi-10">t</span><sup ><span
+class="cmsy-7">-</span><span
+class="emr-7">1</span></sup><span
+class="emmi-10">e</span><sup ><span
+class="cmsy-7">-</span><span
+class="emmi-7">t</span></sup><span
+class="emmi-10">dt</span>   (the exponential integral)</td></tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span><sub ><span
+class="emmi-7">v</span></sub></td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"><span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"></span><img
+src="latexexa20x.gif"alt="[ ]
+ e--e - g'- b2
+ q"class="left" align="middle"></td> </tr></table>
+</div>
+<!--224--><p class="indent"> The Vavilov parameters are simply related to the Landau parameter by
+<span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span><sub ><span
+class="emmi-7">L</span></sub> = <span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span><sub ><span
+class="emmi-7">v</span></sub><span
+class="emmi-10">/<img
+src="emmi10-14.gif"alt="k"class="10--14"> </span><span
+class="cmsy-10">-</span> ln <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"></span>. It can be shown that as <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"> </span><span
+class="cmsy-10"><img
+src="cmsy10-21.gif"alt="--&gt;"class="10--21"> </span>0, the distribution of the variable <span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span><sub ><span
+class="emmi-7">L</span></sub>
+approaches that of Landau. For <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"> </span><span
+class="cmsy-10"><span
+class="underline">&lt;</span> </span>0<span
+class="emmi-10">.</span>01 the two distributions are already practically
+identical. Contrary to what many textbooks report, the Vavilov distribution <span
+class="emti-10">does not</span>
+approximate the Landau distribution for small <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"></span>, but rather the distribution of <span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span><sub ><span
+class="emmi-7">L</span></sub>
+defined above tends to the distribution of the true <span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"> </span>from the Landau density
+function. Thus the routine <span
+class="emtt-10">GVAVIV </span>samples the variable <span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span><sub ><span
+class="emmi-7">L</span></sub> rather than <span
+class="emmi-10"><img
+src="emmi10-15.gif"alt="c"class="10--15"></span><sub ><span
+class="emmi-7">v</span></sub>. For
+<span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"> </span><span
+class="cmsy-10"><span
+class="underline">&gt;</span> </span>10 the Vavilov distribution tends to a Gaussian distribution (see next
+section).
+ <h2 class="sectionHead">4 <a
+ name="1-50004"></a><a
+ name="QQ1-1-6"></a>Gaussian Theory</h2>
+<!--239--><p class="noindent">Various conflicting forms have been proposed for Gaussian straggling functions, but
+most of these appear to have little theoretical or experimental basis. However, it has
+been shown[<a
+ href="#Xbib-SELT">3</a>] that for <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"> </span><span
+class="cmsy-10"><span
+class="underline">&gt;</span> </span>10 the Vavilov distribution can be replaced by a Gaussian
+of the form : <div align="center" class="eqnarray"><a
+ name="1-5001r1"></a>
+<table
+class="eqnarray-star"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10">f</span>(<span
+class="emmi-10"><img
+src="emmi10-f.gif"alt="e"class="10--f">, <img
+src="emmi10-e.gif"alt="d"class="10--e">s</span>) <span
+class="cmsy-10"><img
+src="cmsy10-19.gif"alt=" ~~ "class="10--19"></span> 1 __________
+<span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle"></span><img
+src="latexexa21x.gif"alt=" V~ ------------
+ 2pk (1- b2/2)"class="sqrtsign" > exp <img
+src="latexexa22x.gif"alt="[(e- e)2 k ]
+ --------2-----2---
+ 2 q (1- b /2)"class="left" align="middle"></td><td
+align="center"nowrap
+class="eqnarray2"></td><td
+align="left"nowrap
+class="eqnarray3"></td></tr></table>
+</div>thus implying <div align="center" class="eqnarray"><a
+ name="1-5002r1"></a>
+<table
+class="eqnarray-star"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1">mean</td><td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"><img
+src="latexexa23x.gif"alt="e"class="bar" ></td> </tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-1b.gif"alt="s"class="10--1b"></span><sup ><span
+class="emr-7">2</span></sup></td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"><span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle"></span><sup ><span
+class="emr-7">2</span></sup>
+ <span
+class="emmi-10"><img
+src="emmi10-14.gif"alt="k"class="10--14"></span> (1 <span
+class="cmsy-10">- </span><span
+class="emmi-10"><img
+src="emmi10-c.gif"alt="b"class="emmi-10--c"align="middle"></span><sup ><span
+class="emr-7">2</span></sup><span
+class="emmi-10">/</span>2) = <span
+class="emmi-10"><img
+src="emmi10-18.gif"alt="q"class="emmi-10--18"align="middle">E</span>
+<span
+class="emr-7">max</span>(1 <span
+class="cmsy-10">- </span><span
+class="emmi-10"><img
+src="emmi10-c.gif"alt="b"class="emmi-10--c"align="middle"></span><sup ><span
+class="emr-7">2</span></sup><span
+class="emmi-10">/</span>2)</td></tr></table>
+</div>
+ <h2 class="sectionHead">5 <a
+ name="1-60005"></a><a
+ name="QQ1-1-7"></a>Urb&aacute;n model</h2>
+<!--260--><p class="noindent">The method for computing restricted energy losses with <span
+class="emmi-10"><img
+src="emmi10-e.gif"alt="d"class="10--e"></span>-ray production
+above given threshold energy in <span
+class="emtt-10">GEANT </span>is a Monte Carlo method that can
+be used for thin layers. It is fast and it can be used for any thickness of
+a medium. Approaching the limit of the validity of Landau's theory, the
+loss distribution approaches smoothly the Landau form as shown in Figure
+<a
+ href="#1-60012">2</a>.
+<a
+ name="1-60012"></a>
+ <hr class="float"><div align="center" class="float"
+><table class="float"><tr class="float"><td class="float"
+>
+<img
+src="latexexa24x.gif"alt="PIC">
+<br><div align="center"class="caption"><table class="caption"
+><tr valign="baseline" class="caption"><td class="id">Figure 2</td><td
+class="content">Energy loss distribution for a 3 GeV electron in Argon as given by
+standard <span
+class="emtt-10">GEANT</span>. The width of the layers is given in centimeters.</td></tr></table></div>
+ </td></tr></table></div><hr class="endfloat">
+<!--275--><p class="indent"> It is assumed that the atoms have only two energy levels with binding energy <span
+class="emmi-10">E</span><sub ><span
+class="emr-7">1</span></sub>
+and <span
+class="emmi-10">E</span><sub ><span
+class="emr-7">2</span></sub>. The particle--atom interaction will then be an excitation with energy loss <span
+class="emmi-10">E</span><sub ><span
+class="emr-7">1</span></sub>
+or <span
+class="emmi-10">E</span><sub ><span
+class="emr-7">2</span></sub>, or an ionisation with an energy loss distributed according to a function
+<span
+class="emmi-10">g</span>(<span
+class="emmi-10">E</span>) <span
+class="cmsy-10">~ </span>1<span
+class="emmi-10">/E</span><sup ><span
+class="emr-7">2</span></sup>: <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa25x.gif"alt=" (Emax +-I)I-1
+g(E) = Emax E2"class="mathdisplay"><a
+ name="1-6002r1"></a></center></td><td width="5%">(1)</td></tr></table>
+<!--283--><p class="indent"> The macroscopic cross-section for excitations (<span
+class="emmi-10">i </span>= 1<span
+class="emmi-10">, </span>2) is <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa26x.gif"alt=" f ln(2mb2g2/E )- b2
+i = C-i-------2-2-i----2 (1- r)
+ Ei ln(2mb g/I) - b"class="mathdisplay"><a
+ name="1-6003r2"></a></center></td><td width="5%">(2)</td></tr></table>
+and the macroscopic cross-section for ionisation is <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa27x.gif"alt="3 = C-------Emax---------r
+ I(Emax + I)ln(EmaIx+I)"class="mathdisplay"><a
+ name="1-6004r3"></a></center></td><td width="5%">(3)</td></tr></table>
+<span
+class="emmi-10">E</span><span
+class="emr-7">max</span> is the <span
+class="emtt-10">GEANT </span>cut for <span
+class="emmi-10"><img
+src="emmi10-e.gif"alt="d"class="10--e"></span>-production, or the maximum energy transfer minus mean
+ionisation energy, if it is smaller than this cut-off value. The following notation is
+used:
+ <div align="center"><table class="tabular"
+cellspacing="0pt" cellpadding="0"
+frame="void" ><colgroup><col
+id="TBL-3-1"><col
+id="TBL-3-2"></colgroup><tr
+valign="baseline" id="TBL-3-1-"><td align="left"nowrap id="TBL-3-1-1"
+><div class="td11"><span
+class="emmi-10">r, C</span></div></td><td align="left"nowrap id="TBL-3-1-2"
+><div class="td11">parameters of the model</div></td>
+</tr><tr
+valign="baseline" id="TBL-3-2-"><td align="left"nowrap id="TBL-3-2-1"
+><div class="td11"><span
+class="emmi-10">E</span><sub ><span
+class="emmi-7">i</span></sub> </div></td><td align="left"nowrap id="TBL-3-2-2"
+><div class="td11">atomic energy levels </div></td>
+</tr><tr
+valign="baseline" id="TBL-3-3-"><td align="left"nowrap id="TBL-3-3-1"
+><div class="td11"><span
+class="emmi-10">I </span></div></td><td align="left"nowrap id="TBL-3-3-2"
+><div class="td11">mean ionisation energy </div></td>
+</tr><tr
+valign="baseline" id="TBL-3-4-"><td align="left"nowrap id="TBL-3-4-1"
+><div class="td11"><span
+class="emmi-10">f</span><sub ><span
+class="emmi-7">i</span></sub> </div></td><td align="left"nowrap id="TBL-3-4-2"
+><div class="td11">oscillator strengths </div></td> </tr></table>
+</div>
+<!--306--><p class="indent"> The model has the parameters <span
+class="emmi-10">f</span><sub ><span
+class="emmi-7">i</span></sub> , <span
+class="emmi-10">E</span><sub ><span
+class="emmi-7">i</span></sub> , <span
+class="emmi-10">C </span>and <span
+class="emmi-10">r</span><span
+class="emmi-10"> </span>(0 <span
+class="cmsy-10"><span
+class="underline">&lt;</span> </span><span
+class="emmi-10">r </span><span
+class="cmsy-10"><span
+class="underline">&lt;</span> </span>1). The oscillator
+strengths <span
+class="emmi-10">f</span><sub ><span
+class="emmi-7">i</span></sub> and the atomic level energies <span
+class="emmi-10">E</span><sub ><span
+class="emmi-7">i</span></sub> should satisfy the constraints
+<div align="center" class="eqnarray"><a
+ name="1-6005r4"></a>
+<table
+class="eqnarray"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10">f</span><sub ><span
+class="emr-7">1</span></sub> + <span
+class="emmi-10">f</span><sub ><span
+class="emr-7">2</span></sub></td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3">1</td><td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4">(4)<a
+ name="1-6005r5"></a></td></tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10">f</span><sub ><span
+class="emr-7">1</span></sub> ln <span
+class="emmi-10">E</span><sub ><span
+class="emr-7">1</span></sub> + <span
+class="emmi-10">f</span><sub ><span
+class="emr-7">2</span></sub> ln <span
+class="emmi-10">E</span><sub ><span
+class="emr-7">2</span></sub></td><td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3">ln <span
+class="emmi-10">I</span></td><td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4">(5)<a
+ name="1-6005r6"></a></td></tr></table>
+</div>The parameter <span
+class="emmi-10">C </span>can be defined with the help of the mean energy loss <span
+class="emmi-10">dE/dx </span>in the
+following way: The numbers of collisions (<span
+class="emmi-10">n</span><sub ><span
+class="emmi-7">i</span></sub> , i = 1,2 for the excitation and 3 for the
+ionisation) follow the Poisson distribution with a mean number <span
+class="cmsy-10">&lt;</span><span
+class="emmi-10">n</span><sub ><span
+class="emmi-7">i</span></sub><span
+class="cmsy-10">&gt;</span>. In a step <span
+class="emmi-10">x</span>
+the mean number of collisions is <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa28x.gif"alt="&lt;n&gt; = x
+ i i"class="mathdisplay"><a
+ name="1-6006r6"></a></center></td><td width="5%">(6)</td></tr></table>
+The mean energy loss <span
+class="emmi-10">dE/dx </span>in a step is the sum of the excitation and ionisation
+contributions <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa29x.gif"alt=" [ ]
+dE integral Emax+I
+dx- x = 1E1 + 2E2 + 3 E g(E) dE x
+ I"class="mathdisplay"><a
+ name="1-6007r7"></a></center></td><td width="5%">(7)</td></tr></table>
+From this, using the equations (<a
+ href="#1-6003r2">2</a>), (<a
+ href="#1-6004r3">3</a>), (<a
+ href="#1-6005r4">4</a>) and (<a
+ href="#1-6005r5">5</a>), one can define the parameter <span
+class="emmi-10">C</span>
+<table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa30x.gif"alt="C = dE-
+ dx"class="mathdisplay"><a
+ name="1-6008r8"></a></center></td><td width="5%">(8)</td></tr></table>
+<!--335--><p class="indent"> The following values have been chosen in <span
+class="emtt-10">GEANT </span>for the other parameters:
+ <center>
+<img
+src="latexexa31x.gif"alt=" {
+ 0 ifZ &lt; 2
+f2 = 2/Z ifZ &gt; 2 ==&gt; f1 = 1- f2
+ ( )f11
+E2 = 10Z2eV ==&gt; E1 = EIf2
+r = 0.4 2"class="mathdisplay"></center> With
+these values the atomic level <span
+class="emmi-10">E</span><sub ><span
+class="emr-7">2</span></sub> corresponds approximately the K-shell energy of the
+atoms and <span
+class="emmi-10">Zf</span><sub ><span
+class="emr-7">2</span></sub> the number of K-shell electrons. <span
+class="emmi-10">r </span>is the only variable which can be
+tuned freely. It determines the relative contribution of ionisation and excitation to
+the energy loss.
+<!--354--><p class="indent"> The energy loss is computed with the assumption that the step length (or the
+relative energy loss) is small, and---in consequence---the cross-section can be
+considered constant along the path length. The energy loss due to the excitation is
+<table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa32x.gif"alt="Ee = n1E1 +n2E2"class="mathdisplay"><a
+ name="1-6009r9"></a></center></td><td width="5%">(9)</td></tr></table>
+where <span
+class="emmi-10">n</span><sub ><span
+class="emr-7">1</span></sub> and <span
+class="emmi-10">n</span><sub ><span
+class="emr-7">2</span></sub> are sampled from Poisson distribution as discussed above. The loss
+due to the ionisation can be generated from the distribution <span
+class="emmi-10">g</span>(<span
+class="emmi-10">E</span>) by the inverse
+transformation method: <div align="center" class="eqnarray"><a
+ name="1-6010r10"></a>
+<table
+class="eqnarray"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10">u </span>= <span
+class="emmi-10">F</span>(<span
+class="emmi-10">E</span>)</td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"><span
+class="cmex-10"><img
+src="cmex10-5a.gif"alt=" integral "class="cmex-10--5a"align="middle"></span>
+ <sub> <span
+class="emmi-10">I</span></sub><sup><span
+class="emmi-10">E</span></sup><span
+class="emmi-10">g</span>(<span
+class="emmi-10">x</span>)<span
+class="emmi-10">dx</span></td> <td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4"></td></tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10">E </span>= <span
+class="emmi-10">F</span><sup ><span
+class="cmsy-7">-</span><span
+class="emr-7">1</span></sup>(<span
+class="emmi-10">u</span>)</td><td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"> <span
+class="emmi-10">I</span>_____
+1 <span
+class="cmsy-10">- </span><span
+class="emmi-10">u</span> <span
+class="emmi-7">E</span><span
+class="emr-5">max</span>__
+<span
+class="emmi-7">E</span><span
+class="emr-5">max</span><span
+class="emr-7">+</span><span
+class="emmi-7">I</span> </td><td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4">(10)<a
+ name="1-6010r11"></a></td></tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"></td> <td
+align="center"nowrap
+class="eqnarray2"></td> <td
+align="left"nowrap
+class="eqnarray3"></td> <td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4">(11)<a
+ name="1-6010r12"></a></td></tr></table>
+</div>where <span
+class="emmi-10">u </span>is a uniform random number between <span
+class="emmi-10">F</span>(<span
+class="emmi-10">I</span>) = 0 and <span
+class="emmi-10">F</span>(<span
+class="emmi-10">E</span><span
+class="emr-7">max</span> + <span
+class="emmi-10">I</span>) = 1. The
+contribution from the ionisations will be <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa33x.gif"alt=" n sum 3 -----I------
+Ei = 1 -uj -Emax--
+ j=1 Emax+I"class="mathdisplay"><a
+ name="1-6011r12"></a></center></td><td width="5%">(12)</td></tr></table>
+where <span
+class="emmi-10">n</span><sub ><span
+class="emr-7">3</span></sub> is the number of ionisation (sampled from Poisson distribution). The
+energy loss in a step will then be <span
+class="emmi-10">E </span>= <span
+class="emmi-10">E</span><sub ><span
+class="emmi-7">e</span></sub> + <span
+class="emmi-10">E</span><sub ><span
+class="emmi-7">i</span></sub>.
+ <h3 class="subsectionHead">5.1 <a
+ name="1-70005.1"></a><a
+ name="QQ1-1-9"></a>Fast simulation for <span
+class="emmi-10">n</span><sub ><span
+class="emr-7">3</span></sub> <span
+class="cmsy-10"><span
+class="underline">&gt;</span> </span>16</h3>
+<!--380--><p class="noindent">If the number of ionisation <span
+class="emmi-10">n</span><sub ><span
+class="emr-7">3</span></sub> is bigger than 16, a faster sampling method can be
+used. The possible energy loss interval is divided in two parts: one in which the
+number of collisions is large and the sampling can be done from a Gaussian
+distribution and the other in which the energy loss is sampled for each collision. Let
+us call the former interval [<span
+class="emmi-10">I, <img
+src="emmi10-b.gif"alt="a"class="10--b">I</span>] the interval A, and the latter [<span
+class="emmi-10"><img
+src="emmi10-b.gif"alt="a"class="10--b">I, E</span><span
+class="emr-7">max</span>] the interval
+B. <span
+class="emmi-10"><img
+src="emmi10-b.gif"alt="a"class="10--b"> </span>lies between 1 and <span
+class="emmi-10">E</span><span
+class="emr-7">max</span><span
+class="emmi-10">/I</span>. A collision with a loss in the interval A happens
+with the probability <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa34x.gif"alt=" integral aI
+P(a) = g(E)dE = (Emax-+-I)(a---1)
+ I Emaxa"class="mathdisplay"><a
+ name="1-7001r13"></a></center></td><td width="5%">(13)</td></tr></table>
+The mean energy loss and the standard deviation for this type of collision are
+<table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa35x.gif"alt=" --1-- integral aI Ia-lna-
+&lt; E(a)&gt; = P (a) I E g(E) dE = a- 1"class="mathdisplay"><a
+ name="1-7002r14"></a></center></td><td width="5%">(14)</td></tr></table>
+and <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa36x.gif"alt=" integral aI ( 2 )
+s2(a) =--1-- E2 g(E) dE = I2a 1 - -aln-a2
+ P (a) I (a- 1)"class="mathdisplay"><a
+ name="1-7003r15"></a></center></td><td width="5%">(15)</td></tr></table>
+If the collision number is high , we assume that the number of the type A collisions
+can be calculated from a Gaussian distribution with the following mean value and
+standard deviation: <div align="center" class="eqnarray"><a
+ name="1-7004r16"></a>
+<table
+class="eqnarray"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="cmsy-10">&lt;</span><span
+class="emmi-10">n</span><sub ><span
+class="emmi-7">A</span></sub><span
+class="cmsy-10">&gt;</span></td><td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"><span
+class="emmi-10">n</span><sub ><span
+class="emr-7">3</span></sub><span
+class="emmi-10">P</span>(<span
+class="emmi-10"><img
+src="emmi10-b.gif"alt="a"class="10--b"></span>)</td> <td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4">(16)<a
+ name="1-7004r17"></a></td></tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-1b.gif"alt="s"class="10--1b"></span><sub><span
+class="emmi-10">A</span></sub><sup>2</sup></td> <td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"><span
+class="emmi-10">n</span><sub ><span
+class="emr-7">3</span></sub><span
+class="emmi-10">P</span>(<span
+class="emmi-10"><img
+src="emmi10-b.gif"alt="a"class="10--b"></span>)(1 <span
+class="cmsy-10">- </span><span
+class="emmi-10">P</span>(<span
+class="emmi-10"><img
+src="emmi10-b.gif"alt="a"class="10--b"></span>))</td><td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4">(17)<a
+ name="1-7004r18"></a></td></tr></table>
+</div>It is further assumed that the energy loss in these collisions has a Gaussian
+distribution with <div align="center" class="eqnarray"><a
+ name="1-7005r18"></a>
+<table
+class="eqnarray"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="cmsy-10">&lt;</span><span
+class="emmi-10">E</span><sub ><span
+class="emmi-7">A</span></sub><span
+class="cmsy-10">&gt;</span></td><td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"><span
+class="emmi-10">n</span><sub ><span
+class="emmi-7">A</span></sub><span
+class="cmsy-10">&lt;</span><span
+class="emmi-10">E</span>(<span
+class="emmi-10"><img
+src="emmi10-b.gif"alt="a"class="10--b"></span>)<span
+class="cmsy-10">&gt;</span></td><td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4">(18)<a
+ name="1-7005r19"></a></td></tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="emmi-10"><img
+src="emmi10-1b.gif"alt="s"class="10--1b"></span><sub><span
+class="emmi-10">E, A</span></sub><sup>2</sup></td><td
+align="center"nowrap
+class="eqnarray2">=</td><td
+align="left"nowrap
+class="eqnarray3"><span
+class="emmi-10">n</span><sub ><span
+class="emmi-7">A</span></sub><span
+class="emmi-10"><img
+src="emmi10-1b.gif"alt="s"class="10--1b"></span><sup ><span
+class="emr-7">2</span></sup>(<span
+class="emmi-10"><img
+src="emmi10-b.gif"alt="a"class="10--b"></span>)</td><td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4">(19)<a
+ name="1-7005r20"></a></td></tr></table>
+</div>The energy loss of these collision can then be sampled from the Gaussian
+distribution.
+<!--427--><p class="indent"> The collisions where the energy loss is in the interval B are sampled directly from
+<table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa37x.gif"alt=" n3- sum nA aI
+EB = 1--u-Emax+I-aI
+ i=1 i Emax+I"class="mathdisplay"><a
+ name="1-7006r20"></a></center></td><td width="5%">(20)</td></tr></table>
+The total energy loss is the sum of these two types of collisions: <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa38x.gif"alt="E = EA + EB"class="mathdisplay"><a
+ name="1-7007r21"></a></center></td><td width="5%">(21)</td></tr></table>
+<!--438--><p class="indent"> The approximation of equations ((<a
+ href="#1-7004r16">16</a>), (<a
+ href="#1-7004r17">17</a>), (<a
+ href="#1-7005r18">18</a>) and (<a
+ href="#1-7005r19">19</a>) can be used under the
+following conditions: <div align="center" class="eqnarray"><a
+ name="1-7008r22"></a>
+<table
+class="eqnarray"><tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="cmsy-10">&lt;</span><span
+class="emmi-10">n</span><sub ><span
+class="emmi-7">A</span></sub><span
+class="cmsy-10">&gt; - </span><span
+class="emmi-10">c <img
+src="emmi10-1b.gif"alt="s"class="10--1b"></span><sub ><span
+class="emmi-7">A</span></sub></td> <td
+align="center"nowrap
+class="eqnarray2"><span
+class="cmsy-10"><span
+class="underline">&gt;</span></span></td><td
+align="left"nowrap
+class="eqnarray3">0</td><td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4">(22)<a
+ name="1-7008r23"></a></td></tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="cmsy-10">&lt;</span><span
+class="emmi-10">n</span><sub ><span
+class="emmi-7">A</span></sub><span
+class="cmsy-10">&gt; </span>+ <span
+class="emmi-10">c <img
+src="emmi10-1b.gif"alt="s"class="10--1b"></span><sub ><span
+class="emmi-7">A</span></sub></td> <td
+align="center"nowrap
+class="eqnarray2"><span
+class="cmsy-10"><span
+class="underline">&lt;</span></span></td><td
+align="left"nowrap
+class="eqnarray3"><span
+class="emmi-10">n</span><sub ><span
+class="emr-7">3</span></sub></td><td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4">(23)<a
+ name="1-7008r24"></a></td></tr>
+<tr valign="middle" class="eqnarray"><td
+align="right"nowrap
+class="eqnarray1"><span
+class="cmsy-10">&lt;</span><span
+class="emmi-10">E</span><sub ><span
+class="emmi-7">A</span></sub><span
+class="cmsy-10">&gt; - </span><span
+class="emmi-10">c <img
+src="emmi10-1b.gif"alt="s"class="10--1b"></span><sub ><span
+class="emmi-7">E,A</span></sub></td><td
+align="center"nowrap
+class="eqnarray2"><span
+class="cmsy-10"><span
+class="underline">&gt;</span></span></td><td
+align="left"nowrap
+class="eqnarray3">0</td><td
+width="10" class="eqnarray4"></td><td
+align="right"nowrap
+class="eqnarray4">(24)<a
+ name="1-7008r25"></a></td></tr></table>
+</div>where <span
+class="emmi-10">c </span><span
+class="cmsy-10"><span
+class="underline">&gt;</span> </span>4. From the equations (<a
+ href="#1-7001r13">13</a>), (<a
+ href="#1-7004r16">16</a>) and (<a
+ href="#1-7005r18">18</a>) and from the conditions (<a
+ href="#1-7008r22">22</a>)
+and (<a
+ href="#1-7008r23">23</a>) the following limits can be derived: <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa39x.gif"alt=" (n3 + c2)(Emax + I) (n3 + c2)(Emax +I)
+amin =---------------2- &lt; a &lt; amax = -2---------------
+ n3(Emax + I)+ c I c(Emax + I)+ n3I"class="mathdisplay"><a
+ name="1-7009r25"></a></center></td><td width="5%">(25)</td></tr></table>
+This conditions gives a lower limit to number of the ionisations <span
+class="emmi-10">n</span><sub ><span
+class="emr-7">3</span></sub> for which the fast
+sampling can be done: <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa40x.gif"alt="n3 &gt; c2"class="mathdisplay"><a
+ name="1-7010r26"></a></center></td><td width="5%">(26)</td></tr></table>
+As in the conditions (<a
+ href="#1-7008r22">22</a>), (<a
+ href="#1-7008r23">23</a>) and (<a
+ href="#1-7008r24">24</a>) the value of <span
+class="emmi-10">c </span>is as minimum 4, one gets
+<span
+class="emmi-10">n</span><sub ><span
+class="emr-7">3</span></sub> <span
+class="cmsy-10"><span
+class="underline">&gt;</span> </span>16. In order to speed the simulation, the maximum value is used for
+<span
+class="emmi-10"><img
+src="emmi10-b.gif"alt="a"class="10--b"></span>.
+<!--469--><p class="indent"> The number of collisions with energy loss in the interval B (the number of
+interactions which has to be simulated directly) increases slowly with the total
+number of collisions <span
+class="emmi-10">n</span><sub ><span
+class="emr-7">3</span></sub>. The maximum number of these collisions can be estimated
+as <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa41x.gif"alt="nB,max = n3 -nA,min ~~ n3(&lt;nA&gt; - sA)"class="mathdisplay"><a
+ name="1-7011r27"></a></center></td><td width="5%">(27)</td></tr></table>
+From the previous expressions for <span
+class="cmsy-10">&lt;</span><span
+class="emmi-10">n</span><sub ><span
+class="emmi-7">A</span></sub><span
+class="cmsy-10">&gt; </span>and <span
+class="emmi-10"><img
+src="emmi10-1b.gif"alt="s"class="10--1b"></span><sub ><span
+class="emmi-7">A</span></sub> one can derive the condition
+<table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa42x.gif"alt=" -2n3c2-
+nB &lt; nB,max = n3 + c2"class="mathdisplay"><a
+ name="1-7012r28"></a></center></td><td width="5%">(28)</td></tr></table>
+The following values are obtained with <span
+class="emmi-10">c </span>= 4:
+ <div align="center"><table class="tabular"
+cellspacing="0pt" cellpadding="0"
+frame="void" ><colgroup><col
+id="TBL-6-1"><col
+id="TBL-6-2"><col
+id="TBL-6-3"><col
+id="TBL-6-4"><col
+id="TBL-6-5"></colgroup><tr
+valign="baseline" id="TBL-6-1-"><td align="left"nowrap id="TBL-6-1-1"
+><div class="td11"><span
+class="emmi-10">n</span><sub ><span
+class="emr-7">3</span></sub> </div></td><td align="left"nowrap id="TBL-6-1-2"
+><div class="td11"><span
+class="emmi-10">n</span><sub ><span
+class="emmi-7">B,max</span></sub></div></td><td align="center"nowrap id="TBL-6-1-3"
+><div class="td11"></div></td><td align="right"nowrap id="TBL-6-1-4"
+><div class="td11"> <span
+class="emmi-10">n</span><sub ><span
+class="emr-7">3</span></sub></div></td><td align="right"nowrap id="TBL-6-1-5"
+><div class="td11"><span
+class="emmi-10">n</span><sub ><span
+class="emmi-7">B,max</span></sub></div></td>
+</tr><tr
+class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
+valign="baseline" id="TBL-6-2-"><td align="left"nowrap id="TBL-6-2-1"
+><div class="td11">16 </div></td><td align="left"nowrap id="TBL-6-2-2"
+><div class="td11">16 </div></td><td align="center"nowrap id="TBL-6-2-3"
+><div class="td11"></div></td><td align="right"nowrap id="TBL-6-2-4"
+><div class="td11"> 200</div></td><td align="right"nowrap id="TBL-6-2-5"
+><div class="td11"> 29.63</div></td>
+</tr><tr
+valign="baseline" id="TBL-6-3-"><td align="left"nowrap id="TBL-6-3-1"
+><div class="td11">20 </div></td><td align="left"nowrap id="TBL-6-3-2"
+><div class="td11">17.78 </div></td><td align="center"nowrap id="TBL-6-3-3"
+><div class="td11"></div></td><td align="right"nowrap id="TBL-6-3-4"
+><div class="td11"> 500</div></td><td align="right"nowrap id="TBL-6-3-5"
+><div class="td11"> 31.01</div></td>
+</tr><tr
+valign="baseline" id="TBL-6-4-"><td align="left"nowrap id="TBL-6-4-1"
+><div class="td11">50 </div></td><td align="left"nowrap id="TBL-6-4-2"
+><div class="td11">24.24 </div></td><td align="center"nowrap id="TBL-6-4-3"
+><div class="td11"></div></td><td align="right"nowrap id="TBL-6-4-4"
+><div class="td11">1000</div></td><td align="right"nowrap id="TBL-6-4-5"
+><div class="td11"> 31.50</div></td>
+</tr><tr
+valign="baseline" id="TBL-6-5-"><td align="left"nowrap id="TBL-6-5-1"
+><div class="td11">100</div></td><td align="left"nowrap id="TBL-6-5-2"
+><div class="td11">27.59 </div></td><td align="center"nowrap id="TBL-6-5-3"
+><div class="td11"></div></td><td align="right"nowrap id="TBL-6-5-4"
+><div class="td11"> <span
+class="cmsy-10"><img
+src="cmsy10-31.gif"alt=" oo "class="10--31"></span></div></td><td align="right"nowrap id="TBL-6-5-5"
+><div class="td11"> 32.00</div></td> </tr></table>
+</div>
+ <h3 class="subsectionHead">5.2 <a
+ name="1-80005.2"></a><a
+ name="QQ1-1-10"></a>Special sampling for lower part of the spectrum</h3>
+<!--494--><p class="noindent">If the step length is very small (<span
+class="cmsy-10"><span
+class="underline">&lt;</span> </span>5 mm in gases, <span
+class="cmsy-10"><span
+class="underline">&lt;</span> </span>2-3 <span
+class="emmi-10"><img
+src="emmi10-16.gif"alt="m"class="emmi-10--16"align="middle"></span>m in solids) the model gives
+0 energy loss for some events. To avoid this, the probability of 0 energy loss is
+computed <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa43x.gif"alt=" -(&lt;n &gt;+&lt;n &gt;+&lt;n &gt;)
+P( E = 0) = e 1 2 3"class="mathdisplay"><a
+ name="1-8001r29"></a></center></td><td width="5%">(29)</td></tr></table>
+If the probability is bigger than 0.01 a special sampling is done, taking into
+account the fact that in these cases the projectile interacts only with the outer
+electrons of the atom. An energy level <span
+class="emmi-10">E</span><sub ><span
+class="emr-7">0</span></sub> = 10 eV is chosen to correspond to
+the outer electrons. The mean number of collisions can be calculated from
+<table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa44x.gif"alt=" 1 dE
+&lt;n&gt; = ----- x
+ E0 dx"class="mathdisplay"><a
+ name="1-8002r30"></a></center></td><td width="5%">(30)</td></tr></table>
+The number of collisions <span
+class="emmi-10">n </span>is sampled from Poisson distribution. In the case of the
+thin layers, all the collisions are considered as ionisations and the energy loss is
+computed as <table width="100%"
+class="equation"><tr><td>
+ <center>
+<img
+src="latexexa45x.gif"alt=" n
+ sum -----E0------
+E = 1 - EEmax+E-ui
+ i=1 max 0"class="mathdisplay"><a
+ name="1-8003r31"></a></center></td><td width="5%">(31)</td></tr></table>
+ <h2 class="likesectionHead"><a
+ name="1-9000"></a><a
+ name="QQ1-1-11"></a>References</h2>
+ <div class="thebibliography"><p class="bibitem">
+ [1]   <a
+ name="Xbib-LAND"></a>L.Landau. On the Energy Loss of Fast Particles by Ionisation. Originally
+ published in <span
+class="emti-10">J. Phys.</span>, 8:201, 1944. Reprinted in D.ter Haar, Editor,
+ <span
+class="emti-10">L.D.Landau, Collected papers </span>, page 417. Pergamon Press, Oxford, 1965.
+ </p><p class="bibitem">
+ [2]   <a
+ name="Xbib-SCH1"></a>B.Schorr. Programs for the Landau and the Vavilov distributions and
+ the corresponding random numbers. <span
+class="emti-10">Comp. Phys. Comm.</span>, 7:216, 1974.
+ </p><p class="bibitem">
+ [3]   <a
+ name="Xbib-SELT"></a>S.M.Seltzer and M.J.Berger. Energy loss straggling of protons and
+ mesons. In <span
+class="emti-10">Studies in Penetration of Charged Particles in Matter </span>, Nuclear
+ Science Series 39, Nat. Academy of Sciences, Washington DC, 1964.
+ </p><p class="bibitem">
+ [4]   <a
+ name="Xbib-TALM"></a>R.Talman. On the statistics of particle identification using ionization.
+ <span
+class="emti-10">Nucl. Inst. Meth.</span>, 159:189, 1979.
+ </p><p class="bibitem">
+ [5]   <a
+ name="Xbib-VAVI"></a>P.V.Vavilov. Ionisation losses of high energy heavy particles. <span
+class="emti-10">Soviet</span>
+ <span
+class="emti-10">Physics JETP </span>, 5:749, 1957.</p></div>
+
+</body>
+</html>
+
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.idv b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.idv
new file mode 100644
index 00000000000..b2eeb02a051
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.idv
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.lg b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.lg
new file mode 100644
index 00000000000..4740e4922d9
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.lg
@@ -0,0 +1,121 @@
+File: latexexa.html
+File: latexexa.css
+File: tex4ht.tmp
+Font_Class(1,"1"): <img src=""alt=""class="%s-%d--%x">
+Font_Class(3,"3"): <img src=""alt=""class="%s-%s-%d--%x"align="middle">
+File: tex4ht.tmp
+Font_Class(6,"6"): <span class="underline"></span>
+File: tex4ht.tmp
+Css: p.noindent { text-indent: 0em }
+Css: p.indent{ text-indent: 1.5em }
+Css: .sub, .sup {font-size:110%}
+Font_Css("4"): .small-caps{font-variant: small-caps; }
+Css: .Canvas { position:relative; }
+Css: img.mathdisplay{ margin-top: 1em; margin-bottom: 1em; }
+Css: li p.indent, li p.indent{ text-indent: 0em }
+Css: p.bibitem { text-indent: -2em; margin-left: 2em; }
+Css: .quote {margin-bottom:0.25em; margin-top:0.25em; margin-left:1em; }
+Css: DIV.td00{ margin-left:0; margin-right:0; }
+Css: DIV.td01{ margin-left:0; margin-right:5; }
+Css: DIV.td10{ margin-left:5; margin-right:0; }
+Css: DIV.td11{ margin-left:5; margin-right:5; }
+Css: .hline hr, .cline hr{ height : 1px; }
+Css: .verbatim {margin-bottom:0.5em; margin-top:0.5em; }
+Css: span.footnotetext{ font-size:75%; font-style:italic; }
+Css: span.TEX {letter-spacing: -0.125em; }
+Css: span.TEX span.E{ position:relative;top:0.5ex;left:-0.0417em;}
+Css: a span.TEX span.E {text-decoration: none; }
+Css: span.LATEX span.A{ position:relative; top:-0.5ex; left:-0.4em; font-size:85%;}
+Css: span.LATEX span.TEX{ position:relative; left: -0.4em; }
+Css: .marginpar {width:20%; float:right; text-align:left; margin-left:1em; margin-top:0.5em; font-size:85%; text-decoration:underline;}
+Css: .equation TD{text-align:center; }
+Css: .obeylines-h,.obeylines-v {white-space: nowrap; }
+Css: span.pmatrix img{vertical-align:middle;}
+Css: .underline{ text-decoration:underline; }
+Css: .overline{ text-decoration:overline; }
+Css: td.caption{white-space: nowrap; }
+Css: h2.titleHead{text-align:center;}
+Css: div.maketitle{ margin-bottom: 2em; }
+Css: h1.partHead{text-align: center}
+Css: .paragraphHead, .likeparagraphHead { margin-top:2em; font-weight: bold;}
+Css: .subparagraphHead, .likesubparagraphHead { font-weight: bold;}
+--- needs --- latexexa.idv[1] ==> /tmp/latexexa0x.gif ---
+--- needs --- latexexa.idv[2] ==> /tmp/latexexa1x.gif ---
+--- needs --- latexexa.idv[3] ==> /tmp/latexexa2x.gif ---
+--- needs --- latexexa.idv[4] ==> /tmp/latexexa3x.gif ---
+--- needs --- latexexa.idv[5] ==> /tmp/latexexa4x.gif ---
+--- needs --- latexexa.idv[6] ==> /tmp/latexexa5x.gif ---
+--- needs --- latexexa.idv[7] ==> /tmp/latexexa6x.gif ---
+--- needs --- latexexa.idv[8] ==> /tmp/latexexa7x.gif ---
+--- needs --- latexexa.idv[9] ==> /tmp/latexexa8x.gif ---
+--- needs --- latexexa.idv[10] ==> /tmp/latexexa9x.gif ---
+--- needs --- latexexa.idv[11] ==> /tmp/latexexa10x.gif ---
+--- needs --- latexexa.idv[12] ==> /tmp/latexexa11x.gif ---
+--- needs --- latexexa.idv[13] ==> /tmp/latexexa12x.gif ---
+--- needs --- latexexa.idv[14] ==> /tmp/latexexa13x.gif ---
+--- needs --- latexexa.idv[15] ==> /tmp/latexexa14x.gif ---
+--- needs --- latexexa.idv[16] ==> /tmp/latexexa15x.gif ---
+--- needs --- latexexa.idv[17] ==> /tmp/latexexa16x.gif ---
+--- needs --- latexexa.idv[18] ==> /tmp/latexexa17x.gif ---
+--- needs --- latexexa.idv[19] ==> /tmp/latexexa18x.gif ---
+--- needs --- latexexa.idv[20] ==> /tmp/latexexa19x.gif ---
+--- needs --- latexexa.idv[21] ==> /tmp/latexexa20x.gif ---
+--- needs --- latexexa.idv[22] ==> /tmp/latexexa21x.gif ---
+--- needs --- latexexa.idv[23] ==> /tmp/latexexa22x.gif ---
+--- needs --- latexexa.idv[24] ==> /tmp/latexexa23x.gif ---
+--- needs --- latexexa.idv[25] ==> /tmp/latexexa24x.gif ---
+--- needs --- latexexa.idv[26] ==> /tmp/latexexa25x.gif ---
+--- needs --- latexexa.idv[27] ==> /tmp/latexexa26x.gif ---
+--- needs --- latexexa.idv[28] ==> /tmp/latexexa27x.gif ---
+--- needs --- latexexa.idv[29] ==> /tmp/latexexa28x.gif ---
+--- needs --- latexexa.idv[30] ==> /tmp/latexexa29x.gif ---
+--- needs --- latexexa.idv[31] ==> /tmp/latexexa30x.gif ---
+--- needs --- latexexa.idv[32] ==> /tmp/latexexa31x.gif ---
+--- needs --- latexexa.idv[33] ==> /tmp/latexexa32x.gif ---
+--- needs --- latexexa.idv[34] ==> /tmp/latexexa33x.gif ---
+--- needs --- latexexa.idv[35] ==> /tmp/latexexa34x.gif ---
+--- needs --- latexexa.idv[36] ==> /tmp/latexexa35x.gif ---
+--- needs --- latexexa.idv[37] ==> /tmp/latexexa36x.gif ---
+--- needs --- latexexa.idv[38] ==> /tmp/latexexa37x.gif ---
+--- needs --- latexexa.idv[39] ==> /tmp/latexexa38x.gif ---
+--- needs --- latexexa.idv[40] ==> /tmp/latexexa39x.gif ---
+--- needs --- latexexa.idv[41] ==> /tmp/latexexa40x.gif ---
+--- needs --- latexexa.idv[42] ==> /tmp/latexexa41x.gif ---
+--- needs --- latexexa.idv[43] ==> /tmp/latexexa42x.gif ---
+--- needs --- latexexa.idv[44] ==> /tmp/latexexa43x.gif ---
+--- needs --- latexexa.idv[45] ==> /tmp/latexexa44x.gif ---
+--- needs --- latexexa.idv[46] ==> /tmp/latexexa45x.gif ---
+--- characters ---
+Font("cmex","10","100")
+--- needs --- latexexa.idv[47] ==> /tmp/cmex10-5a.gif ---
+Font("cmsy","7","100")
+Font("cmsy","10","100")
+--- needs --- latexexa.idv[48] ==> /tmp/cmsy10-31.gif ---
+--- needs --- latexexa.idv[49] ==> /tmp/cmsy10-21.gif ---
+--- needs --- latexexa.idv[50] ==> /tmp/cmsy10-19.gif ---
+Font("emr","10","100")
+Font("emr","17","100")
+Font("emr","12","100")
+Font("emtt","10","100")
+Font("emr","7","100")
+Font("emr","5","100")
+Font("emmi","10","100")
+--- needs --- latexexa.idv[51] ==> /tmp/emmi10-20.gif ---
+--- needs --- latexexa.idv[52] ==> /tmp/emmi10-1e.gif ---
+--- needs --- latexexa.idv[53] ==> /tmp/emmi10-1b.gif ---
+--- needs --- latexexa.idv[54] ==> /tmp/emmi10-1a.gif ---
+--- needs --- latexexa.idv[55] ==> /tmp/emmi10-19.gif ---
+--- needs --- latexexa.idv[56] ==> /tmp/emmi10-18.gif ---
+--- needs --- latexexa.idv[57] ==> /tmp/emmi10-16.gif ---
+--- needs --- latexexa.idv[58] ==> /tmp/emmi10-15.gif ---
+--- needs --- latexexa.idv[59] ==> /tmp/emmi10-14.gif ---
+--- needs --- latexexa.idv[60] ==> /tmp/emmi10-f.gif ---
+--- needs --- latexexa.idv[61] ==> /tmp/emmi10-e.gif ---
+--- needs --- latexexa.idv[62] ==> /tmp/emmi10-d.gif ---
+--- needs --- latexexa.idv[63] ==> /tmp/emmi10-c.gif ---
+--- needs --- latexexa.idv[64] ==> /tmp/emmi10-b.gif ---
+Font("emmi","7","100")
+--- needs --- latexexa.idv[65] ==> /tmp/emmi7-15.gif ---
+--- needs --- latexexa.idv[66] ==> /tmp/emmi7-14.gif ---
+Font("emmi","5","100")
+Font("emti","10","100")
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.log b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.log
new file mode 100644
index 00000000000..ee1982e0c86
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.log
@@ -0,0 +1,285 @@
+This is TeX, Version 3.14159 (Web2C 7.3) (format=latex 1999.3.30) 31 MAR 1999 09:15
+**latexexa
+(latexexa.tex
+LaTeX2e <1998/12/01>
+Babel <v3.6k> and hyphenation patterns for english, french, german, ngerman, du
+mylang, nohyphenation, loaded.
+(/texlive/texmf/tex/latex/base/article.cls
+Document Class: article 1999/01/07 v1.4a Standard LaTeX document class
+(/texlive/texmf/tex/latex/base/size10.clo
+File: size10.clo 1999/01/07 v1.4a Standard LaTeX file (size option)
+)
+\c@part=\count79
+\c@section=\count80
+\c@subsection=\count81
+\c@subsubsection=\count82
+\c@paragraph=\count83
+\c@subparagraph=\count84
+\c@figure=\count85
+\c@table=\count86
+\abovecaptionskip=\skip41
+\belowcaptionskip=\skip42
+\bibindent=\dimen102
+)
+(/texlive/texmf/tex/latex/graphics/graphicx.sty
+Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)
+
+(/texlive/texmf/tex/latex/graphics/keyval.sty
+Package: keyval 1999/03/16 v1.13 key=value parser (DPC)
+\KV@toks@=\toks14
+)
+(/texlive/texmf/tex/latex/graphics/graphics.sty
+Package: graphics 1999/02/16 v1.0l Standard LaTeX Graphics (DPC,SPQR)
+
+(/texlive/texmf/tex/latex/graphics/trig.sty
+Package: trig 1999/03/16 v1.09 sin cos tan (DPC)
+)
+(/texlive/texmf/tex/latex/texlive/graphics.cfg)
+Package graphics Info: Driver file: dvips.def on input line 80.
+
+(/texlive/texmf/tex/latex/graphics/dvips.def
+File: dvips.def 1999/02/16 v3.0i Driver-dependant file (DPC,SPQR)
+))
+\Gin@req@height=\dimen103
+\Gin@req@width=\dimen104
+)
+(/texlive/texmf/tex/latex/ltxmisc/url.sty
+Package: url 1999/03/02 ver 1.4 Verb mode for urls, email addresses, and file
+ names
+)
+(/texlive/texmf/tex/latex/base/fontenc.sty
+Package: fontenc 1999/02/24 v1.9t Standard LaTeX package
+
+(/texlive/texmf/tex/latex/base/t1enc.def
+File: t1enc.def 1999/02/24 v1.9t Standard LaTeX file
+LaTeX Font Info: Redeclaring font encoding T1 on input line 25.
+)) (/T/texmf.local/tex/latex/em/em.sty
+Package: em 1997/06/30 v0.02 Y&Y EM font definitions (BKPH & DTC)
+
+(/texlive/texmf/tex/latex/base/fontenc.sty
+Package: fontenc 1999/02/24 v1.9t Standard LaTeX package
+
+(/texlive/texmf/tex/latex/base/t1enc.def
+File: t1enc.def 1999/02/24 v1.9t Standard LaTeX file
+LaTeX Font Info: Redeclaring font encoding T1 on input line 25.
+)
+(/texlive/texmf/tex/latex/base/t1enc.def
+File: t1enc.def 1999/02/24 v1.9t Standard LaTeX file
+LaTeX Font Info: Redeclaring font encoding T1 on input line 25.
+))
+LaTeX Font Info: Redeclaring symbol font `operators' on input line 467.
+
+
+LaTeX Font Warning: Encoding `OT1' has changed to `T1' for symbol font
+(Font) `operators' in the math version `normal' on input line 467.
+
+
+LaTeX Font Info: Overwriting symbol font `operators' in version `normal'
+(Font) OT1/cmr/m/n --> T1/cmr/m/n on input line 467.
+
+LaTeX Font Warning: Encoding `OT1' has changed to `T1' for symbol font
+(Font) `operators' in the math version `bold' on input line 467.
+
+LaTeX Font Info: Overwriting symbol font `operators' in version `bold'
+(Font) OT1/cmr/bx/n --> T1/cmr/m/n on input line 467.
+LaTeX Font Info: Overwriting symbol font `operators' in version `bold'
+(Font) T1/cmr/m/n --> T1/cmr/bx/n on input line 468.
+LaTeX Font Info: Redeclaring math alphabet \mathbf on input line 470.
+LaTeX Font Info: Overwriting math alphabet `\mathbf' in version `normal'
+(Font) OT1/cmr/bx/n --> T1/cmr/bx/n on input line 470.
+LaTeX Font Info: Overwriting math alphabet `\mathbf' in version `bold'
+(Font) OT1/cmr/bx/n --> T1/cmr/bx/n on input line 470.
+LaTeX Font Info: Redeclaring math alphabet \mathrm on input line 471.
+LaTeX Font Info: Redeclaring math alphabet \mathsf on input line 472.
+LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `normal'
+(Font) OT1/cmss/m/n --> T1/cmss/m/n on input line 472.
+LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `bold'
+(Font) OT1/cmss/bx/n --> T1/cmss/m/n on input line 472.
+LaTeX Font Info: Redeclaring math alphabet \mathit on input line 473.
+LaTeX Font Info: Overwriting math alphabet `\mathit' in version `normal'
+(Font) OT1/cmr/m/it --> T1/cmr/m/it on input line 473.
+LaTeX Font Info: Overwriting math alphabet `\mathit' in version `bold'
+(Font) OT1/cmr/bx/it --> T1/cmr/m/it on input line 473.
+LaTeX Font Info: Redeclaring math alphabet \mathtt on input line 474.
+LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `normal'
+(Font) OT1/cmtt/m/n --> T1/cmtt/m/n on input line 474.
+LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `bold'
+(Font) OT1/cmtt/m/n --> T1/cmtt/m/n on input line 474.
+LaTeX Font Info: Overwriting math alphabet `\mathbf' in version `bold'
+(Font) T1/cmr/bx/n --> T1/cmr/bx/n on input line 476.
+LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `bold'
+(Font) T1/cmss/m/n --> T1/cmss/bx/n on input line 477.
+LaTeX Font Info: Overwriting math alphabet `\mathrm' in version `bold'
+(Font) T1/cmr/m/n --> T1/cmr/bx/n on input line 478.
+LaTeX Font Info: Overwriting math alphabet `\mathit' in version `bold'
+(Font) T1/cmr/m/it --> T1/cmr/bx/it on input line 479.
+LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `bold'
+(Font) T1/cmtt/m/n --> T1/cmtt/bx/n on input line 480.
+LaTeX Font Info: Redeclaring math symbol \Gamma on input line 485.
+LaTeX Font Info: Redeclaring math symbol \Delta on input line 486.
+LaTeX Font Info: Redeclaring math symbol \Theta on input line 487.
+LaTeX Font Info: Redeclaring math symbol \Lambda on input line 488.
+LaTeX Font Info: Redeclaring math symbol \Xi on input line 489.
+LaTeX Font Info: Redeclaring math symbol \Pi on input line 490.
+LaTeX Font Info: Redeclaring math symbol \Sigma on input line 491.
+LaTeX Font Info: Redeclaring math symbol \Upsilon on input line 492.
+LaTeX Font Info: Redeclaring math symbol \Phi on input line 493.
+LaTeX Font Info: Redeclaring math symbol \Psi on input line 494.
+LaTeX Font Info: Redeclaring math symbol \Omega on input line 495.
+LaTeX Font Info: Redeclaring math accent \acute on input line 504.
+LaTeX Font Info: Redeclaring math accent \grave on input line 505.
+LaTeX Font Info: Redeclaring math accent \ddot on input line 506.
+LaTeX Font Info: Redeclaring math accent \tilde on input line 507.
+LaTeX Font Info: Redeclaring math accent \bar on input line 508.
+LaTeX Font Info: Redeclaring math accent \breve on input line 509.
+LaTeX Font Info: Redeclaring math accent \check on input line 510.
+LaTeX Font Info: Redeclaring math accent \hat on input line 511.
+LaTeX Font Info: Redeclaring math accent \dot on input line 512.
+) (/texlive/texmf/tex/latex/tex4ht/tex4ht.sty
+Package: tex4ht
+)
+(/texlive/texmf/tex/latex/tex4ht/tex4ht.sty
+--- needs --- tex4ht latexexa ---
+\tmp:cnt=\count87
+\openout15 = `tex4ht.tmp'.
+
+(tex4ht.tmp)
+\tmp:dim=\skip43
+ ((Preamble.4ht )) (latexexa.xref)
+\:refout=\write3
+\openout3 = `latexexa.xref'.
+
+\:tokwrite=\toks15
+\:tokpage=\toks16
+\openout15 = `latexexa.otc'.
+
+\:tocout=\write4
+\openout4 = `latexexa.toc'.
+
+
+--- file latexexa.css ---
+(/texlive/texmf/tex/latex/tex4ht/tex4ht.4ht
+(/texlive/texmf/tex/latex/tex4ht/latex.4ht
+LaTeX Info: Redefining \` on input line 1294.
+LaTeX Info: Redefining \' on input line 1297.
+LaTeX Info: Redefining \^ on input line 1300.
+LaTeX Info: Redefining \~ on input line 1302.
+LaTeX Info: Redefining \" on input line 1305.
+LaTeX Info: Redefining \c on input line 1307.
+LaTeX Info: Redefining \t on input line 1309.
+LaTeX Info: Redefining \H on input line 1310.
+LaTeX Info: Redefining \. on input line 1311.
+LaTeX Info: Redefining \u on input line 1312.
+LaTeX Info: Redefining \vec on input line 1313.
+LaTeX Info: Redefining \v on input line 1314.
+LaTeX Info: Redefining \= on input line 1315.
+LaTeX Info: Redefining \widetilde on input line 1317.
+LaTeX Info: Redefining \widehat on input line 1319.
+)
+(/texlive/texmf/tex/latex/tex4ht/fontmath.4ht)
+(/texlive/texmf/tex/latex/tex4ht/article.4ht)
+(/texlive/texmf/tex/latex/tex4ht/url.4ht)
+(/texlive/texmf/tex/latex/tex4ht/graphics.4ht))) (latexexa.aux)
+\openout1 = `latexexa.aux'.
+
+LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 11.
+LaTeX Font Info: ... okay on input line 11.
+LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 11.
+LaTeX Font Info: ... okay on input line 11.
+LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 11.
+LaTeX Font Info: ... okay on input line 11.
+LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 11.
+LaTeX Font Info: ... okay on input line 11.
+LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 11.
+LaTeX Font Info: ... okay on input line 11.
+LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 11.
+LaTeX Font Info: ... okay on input line 11.
+ [1
+
+]
+l. 27 Writing latexexa.idv[1] (latexexa0x.gif)
+l. 33 Writing latexexa.idv[2] (latexexa1x.gif)
+[2] [3] [4] [5
+
+]
+l. 100 Writing latexexa.idv[3] (latexexa2x.gif)
+File: phys332-1.eps Graphic file (type eps)
+<phys332-1.eps> [6
+
+]
+l. 129 Writing latexexa.idv[4] (latexexa3x.gif)
+l. 130 Writing latexexa.idv[5] (latexexa4x.gif)
+l. 134 Writing latexexa.idv[6] (latexexa5x.gif)
+[7
+
+]
+l. 168 Writing latexexa.idv[7] (latexexa6x.gif)
+l. 173 Writing latexexa.idv[8] (latexexa7x.gif)
+l. 177 Writing latexexa.idv[9] (latexexa8x.gif)
+l. 179 Writing latexexa.idv[10] (latexexa9x.gif)
+l. 183 Writing latexexa.idv[11] (latexexa10x.gif)
+[8]
+l. 202 Writing latexexa.idv[12] (latexexa11x.gif)
+l. 203 Writing latexexa.idv[13] (latexexa12x.gif)
+l. 207 Writing latexexa.idv[14] (latexexa13x.gif)
+l. 208 Writing latexexa.idv[15] (latexexa14x.gif)
+l. 210 Writing latexexa.idv[16] (latexexa15x.gif)
+l. 211 Writing latexexa.idv[17] (latexexa16x.gif)
+l. 212 Writing latexexa.idv[18] (latexexa17x.gif)
+l. 213 Writing latexexa.idv[19] (latexexa18x.gif)
+l. 214 Writing latexexa.idv[20] (latexexa19x.gif)
+l. 220 Writing latexexa.idv[21] (latexexa20x.gif)
+[9]
+l. 246 Writing latexexa.idv[22] (latexexa21x.gif)
+l. 247 Writing latexexa.idv[23] (latexexa22x.gif)
+l. 252 Writing latexexa.idv[24] (latexexa23x.gif)
+[10] [11
+
+]
+l. 268 Writing latexexa.idv[25] (latexexa24x.gif)
+File: phys332-2.eps Graphic file (type eps)
+<phys332-2.eps> [12
+
+]
+l. 279 Writing latexexa.idv[26] (latexexa25x.gif)
+l. 284 Writing latexexa.idv[27] (latexexa26x.gif)
+l. 290 Writing latexexa.idv[28] (latexexa27x.gif)
+[13
+
+]
+l. 318 Writing latexexa.idv[29] (latexexa28x.gif)
+l. 323 Writing latexexa.idv[30] (latexexa29x.gif)
+[14]
+l. 331 Writing latexexa.idv[31] (latexexa30x.gif)
+l. 337 Writing latexexa.idv[32] (latexexa31x.gif)
+l. 358 Writing latexexa.idv[33] (latexexa32x.gif)
+[15]
+l. 370 Writing latexexa.idv[34] (latexexa33x.gif)
+[16]
+l. 389 Writing latexexa.idv[35] (latexexa34x.gif)
+l. 396 Writing latexexa.idv[36] (latexexa35x.gif)
+l. 402 Writing latexexa.idv[37] (latexexa36x.gif)
+[17]
+l. 429 Writing latexexa.idv[38] (latexexa37x.gif)
+l. 434 Writing latexexa.idv[39] (latexexa38x.gif)
+[18]
+l. 453 Writing latexexa.idv[40] (latexexa39x.gif)
+l. 461 Writing latexexa.idv[41] (latexexa40x.gif)
+l. 473 Writing latexexa.idv[42] (latexexa41x.gif)
+[19]
+l. 479 Writing latexexa.idv[43] (latexexa42x.gif)
+l. 497 Writing latexexa.idv[44] (latexexa43x.gif)
+[20]
+l. 506 Writing latexexa.idv[45] (latexexa44x.gif)
+l. 512 Writing latexexa.idv[46] (latexexa45x.gif)
+[21] [22] (latexexa.aux) )
+Here is how much of TeX's memory you used:
+ 3178 strings out of 10905
+ 31191 string characters out of 72703
+ 101183 words of memory out of 263001
+ 6117 multiletter control sequences out of 10000+0
+ 20729 words of font info for 41 fonts, out of 200000 for 1000
+ 14 hyphenation exceptions out of 1000
+ 28i,14n,24p,338b,560s stack positions out of 300i,100n,500p,30000b,4000s
+
+Output written on latexexa.dvi (22 pages, 73912 bytes).
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.otc b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.otc
new file mode 100644
index 00000000000..43614e1f94f
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.otc
@@ -0,0 +1,13 @@
+\expandafter\ifx\csname doTocEntry\endcsname\relax \expandafter\endinput\fi
+\doTocEntry\tocsection{1}{\csname a:TocEntry\endcsname{1}{QQ1-1-1}{QQ2-1-1}{Introduction}}{2}\relax
+\doTocEntry\toclof{1}{\Link{1-10061}{}\ignorespaces The variable $\xi /I_0$ can be used to measure the validity range of the Landau theory. It depends on the type and energy of the particle, $Z$, $A$ and the ionisation potential of the material and the layer thickness. \EndLink}{figure}
+\doTocEntry\tocsection{2}{\csname a:TocEntry\endcsname{1}{QQ1-1-3}{QQ2-1-3}{Landau theory}}{7}\relax
+\doTocEntry\tocsubsection{2.1}{\csname a:TocEntry\endcsname{1}{QQ1-1-4}{QQ2-1-4}{Restrictions}}{7}\relax
+\doTocEntry\tocsection{3}{\csname a:TocEntry\endcsname{1}{QQ1-1-5}{QQ2-1-5}{Vavilov theory}}{9}\relax
+\doTocEntry\tocsection{4}{\csname a:TocEntry\endcsname{1}{QQ1-1-6}{QQ2-1-6}{Gaussian Theory}}{10}\relax
+\doTocEntry\tocsection{5}{\csname a:TocEntry\endcsname{1}{QQ1-1-7}{QQ2-1-7}{Urb\protect\' an model}}{10}\relax
+\doTocEntry\toclof{2}{\Link{1-60012}{}\ignorespaces Energy loss distribution for a 3 GeV electron in Argon as given by standard \protect\texttt {GEANT}. The width of the layers is given in centimeters.\EndLink}{figure}
+\doTocEntry\tocsubsection{5.1}{\csname a:TocEntry\endcsname{1}{QQ1-1-9}{QQ2-1-9}{Fast simulation for $n_3 \geq 16$}}{16}\relax
+\doTocEntry\tocsubsection{5.2}{\csname a:TocEntry\endcsname{1}{QQ1-1-10}{QQ2-1-10}{Special sampling for lower part of the spectrum}}{20}\relax
+\doTocEntry\toclikesection{}{\csname a:TocEntry\endcsname{1}{QQ1-1-11}{QQ2-1-11}{References}}{21}\relax
+\par
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.tex b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.tex
new file mode 100644
index 00000000000..faa7158a0ca
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.tex
@@ -0,0 +1,549 @@
+\documentclass{article}
+\usepackage{graphicx}
+\usepackage{url}
+\title{Simulation of Energy Loss Straggling}
+\author{Maria Physicist}
+\newcommand{\Emax}{\ensuremath{E_{\mathrm{max}}}}
+\newcommand{\GEANT}{\texttt{GEANT}}
+\usepackage[T1]{fontenc}
+\usepackage{em}
+\usepackage{tex4ht}
+\begin{document}
+\maketitle
+
+\section{Introduction}
+
+Due to the statistical nature of ionisation energy loss, large
+fluctuations can occur in the amount of energy deposited by a particle
+traversing an absorber element. Continuous processes such as multiple
+scattering and energy loss play a relevant role in the longitudinal
+and lateral development of electromagnetic and hadronic
+showers, and in the case of sampling calorimeters the
+measured resolution can be significantly affected by such fluctuations
+in their active layers. The description of ionisation fluctuations is
+characterised by the significance parameter $\kappa$, which is
+proportional to the ratio of mean energy loss to the maximum allowed
+energy transfer in a single collision with an atomic electron
+\[
+\kappa =\frac{\xi}{\Emax}
+\]
+\Emax{}
+is the maximum transferable energy in a single collision with
+an atomic electron.
+\[
+\Emax =\frac{2 m_e \beta^2\gamma^2 }
+{1 + 2\gamma m_e/m_x + \left ( m_e/m_x\right)^2},
+\]
+where $\gamma = E/m_x$, $E$ is energy and
+$m_x$ the mass of the incident particle,
+$\beta^2 = 1 - 1/\gamma^2$ and $m_e$ is the electron mass.
+$\xi$ comes from the Rutherford scattering cross section
+and is defined as:
+\begin{eqnarray*} \xi = \frac{2\pi z^2 e^4 N_{Av} Z \rho \delta x}
+ {m_e \beta^2 c^2 A} = 153.4 \frac{z^2} {\beta^2} \frac{Z}{A}
+ \rho \delta x \quad\mathrm{keV},
+\end{eqnarray*}
+where
+
+\begin{tabular}{ll}
+$z$ & charge of the incident particle \\
+$N_{Av}$ & Avogadro's number \\
+$Z$ & atomic number of the material \\
+$A$ & atomic weight of the material \\
+$\rho$ & density \\
+$ \delta x$ & thickness of the material \\
+\end{tabular}
+
+$\kappa$ measures the contribution of the collisions with energy
+transfer close to \Emax. For a given absorber, $\kappa$ tends
+towards large values if $\delta x$ is large and/or if $\beta$ is
+small. Likewise, $\kappa$ tends towards zero if $\delta x $ is small
+and/or if $\beta$ approaches 1.
+
+The value of $\kappa$ distinguishes two regimes which occur in the
+description of ionisation fluctuations :
+
+\begin{enumerate}
+\item A large number of collisions involving the loss of all or most
+ of the incident particle energy during the traversal of an absorber.
+
+ As the total energy transfer is composed of a multitude of small
+ energy losses, we can apply the central limit theorem and describe
+ the fluctuations by a Gaussian distribution. This case is
+ applicable to non-relativistic particles and is described by the
+ inequality $\kappa > 10 $ (i.e. when the mean energy loss in the
+ absorber is greater than the maximum energy transfer in a single
+ collision).
+
+\item Particles traversing thin counters and incident electrons under
+ any conditions.
+
+ The relevant inequalities and distributions are $ 0.01 < \kappa < 10
+ $, Vavilov distribution, and $\kappa < 0.01 $, Landau distribution.
+\end{enumerate}
+
+An additional regime is defined by the contribution of the collisions
+with low energy transfer which can be estimated with the relation
+$\xi/I_0$, where $I_0$ is the mean ionisation potential of the atom.
+Landau theory assumes that the number of these collisions is high, and
+consequently, it has a restriction $\xi/I_0 \gg 1$. In \GEANT{}
+(see URL \url{http://wwwinfo.cern.ch/asdoc/geant/geantall.html}), the
+limit of Landau theory has been set at $\xi/I_0 = 50$. Below this
+limit special models taking into account the atomic structure of the
+material are used. This is important in thin layers and gaseous
+materials. Figure \ref{fg:phys332-1} shows the behaviour of $\xi/I_0$
+as a function of the layer thickness for an electron of 100 keV and 1
+GeV of kinetic energy in Argon, Silicon and Uranium.
+
+\begin{figure}
+ \centering
+ \includegraphics[width=.6\linewidth]{phys332-1}
+ \caption{The variable $\xi/I_0$ can be used to measure the
+ validity range of the Landau theory. It depends
+ on the type and energy of the particle, $Z$, $A$
+ and the ionisation potential of the material and
+ the layer thickness.
+ }
+ \label{fg:phys332-1}
+\end{figure}
+
+In the following sections, the different theories and models for the
+energy loss fluctuation are described. First, the Landau theory and
+its limitations are discussed, and then, the Vavilov and Gaussian
+straggling functions and the methods in the thin layers and gaseous
+materials are presented.
+
+\section{Landau theory}
+\label{sec:phys332-1}
+
+For a particle of mass $m_x$ traversing a thickness of material
+$\delta x $, the Landau probability distribution may be written in
+terms of the universal Landau function $\phi(\lambda)$
+as\cite{bib-LAND}:
+\begin{eqnarray*}
+f( \epsilon , \delta x ) & = &\frac{1}{\xi} \phi ( \lambda )
+\end{eqnarray*}
+where
+\begin{eqnarray*}
+\phi(\lambda )& = & \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty}
+\exp \left ( u \ln u + \lambda u \right ) du \hspace{2cm} c \geq 0 \\
+\lambda & = & \frac{\epsilon -\bar{\epsilon} }{\xi}
+ - \gamma' - \beta^2 - \ln \frac{\xi}{\Emax} \\
+\gamma' & = & 0.422784\dots = 1 - \gamma \\
+\gamma & = & 0.577215\dots \mbox{(Euler's constant)} \\
+\bar{\epsilon} & = & \mbox{average energy loss} \\
+\epsilon & = & \mbox{actual energy loss}
+\end{eqnarray*}
+
+\subsection{Restrictions}
+
+The Landau formalism makes two restrictive assumptions :
+\begin{enumerate}
+\item The typical energy loss is small compared to the maximum energy
+ loss in a single collision. This restriction is removed in the
+ Vavilov theory (see section \ref{vavref}).
+\item The typical energy loss in the absorber should be large compared
+ to the binding energy of the most tightly bound electron. For
+ gaseous detectors, typical energy losses are a few keV which is
+ comparable to the binding energies of the inner electrons. In such
+ cases a more sophisticated approach which accounts for atomic energy
+ levels\cite{bib-TALM} is necessary to accurately simulate data
+ distributions. In \GEANT, a parameterised model by L. Urb\'{a}n is
+ used (see section \ref{urban}).
+\end{enumerate}
+
+In addition, the average value of the Landau distribution is infinite.
+Summing the Landau fluctuation obtained to the average energy from the
+$dE/dx$ tables, we obtain a value which is larger than the one coming
+from the table. The probability to sample a large value is small, so
+it takes a large number of steps (extractions) for the average
+fluctuation to be significantly larger than zero. This introduces a
+dependence of the energy loss on the step size which can affect
+calculations.
+
+A solution to this has been to introduce a limit on the value of the
+variable sampled by the Landau distribution in order to keep the
+average fluctuation to 0. The value obtained from the \texttt{GLANDO}
+routine is:
+\[
+\delta dE/dx = \epsilon - \bar{\epsilon} = \xi ( \lambda - \gamma'
++\beta^2 +\ln \frac{\xi}{\Emax})
+\]
+In order for this to have average 0, we must impose that:
+\[
+\bar{\lambda} = -\gamma' - \beta^2 -\ln \frac{\xi}{\Emax}
+\]
+
+This is realised introducing a $\lambda_{\mathrm{max}}(\bar{\lambda})$
+such that if only values of $\lambda \leq \lambda_{\mathrm{max}}$ are
+accepted, the average value of the distribution is $\bar{\lambda}$.
+
+A parametric fit to the universal Landau distribution has been
+performed, with following result:
+\[
+\lambda_{\mathrm{max}} = 0.60715 +
+ 1.1934\bar{\lambda}+(0.67794+0.052382\bar{\lambda})
+ \exp(0.94753+0.74442\bar{\lambda})
+\]
+only values smaller than $\lambda_{\mathrm{max}}$ are accepted, otherwise the
+distribution is resampled.
+
+
+
+\newpage
+\section{Vavilov theory}
+\label{vavref}
+
+Vavilov\cite{bib-VAVI} derived a more accurate straggling distribution
+by introducing the kinematic limit on the maximum transferable energy
+in a single collision, rather than using $ \Emax = \infty $.
+Now we can write\cite{bib-SCH1}:
+\begin{eqnarray*}
+f \left ( \epsilon, \delta s \right ) & = & \frac{1}{\xi} \phi_{v}
+\left ( \lambda_{v}, \kappa, \beta^{2} \right )
+\end{eqnarray*}
+where
+\begin{eqnarray*}
+\phi_{v} \left ( \lambda_{v}, \kappa, \beta^{2} \right ) & = &
+\frac{1}{2 \pi i} \int^{c+i\infty}_{c-i\infty}\phi \left( s \right )
+e^{\lambda s} ds \hspace{2cm} c \geq 0 \\
+\phi \left ( s \right ) & = &
+\exp \left [ \kappa ( 1 + \beta^{2}\gamma ) \right ]
+~ \exp \left [ \psi \left ( s \right ) \right ], \\
+\psi \left ( s \right ) & = & s \ln \kappa + ( s + \beta^{2} \kappa )
+\left [ \ln (s/\kappa) + E_{1} (s/\kappa) \right ] - \kappa e^{-s/\kappa},
+\end{eqnarray*}
+and
+\begin{eqnarray*}
+E_{1}(z) & = & \int^{\infty}_{z} t^{-1} e^{-t} dt
+\mbox{\hspace{1cm} (the exponential integral)} \\
+\lambda_v & = & \kappa \left [ \frac{\epsilon - \bar{\epsilon}}{\xi}
+- \gamma' - \beta^2 \right]
+\end{eqnarray*}
+
+The Vavilov parameters are simply related to the Landau parameter by
+$\lambda_L = \lambda_v/\kappa - \ln\kappa $. It can be shown that as
+$\kappa \rightarrow 0$, the distribution of the variable $\lambda_L$
+approaches that of Landau. For $\kappa \leq 0.01$ the two
+distributions are already practically identical. Contrary to what many
+textbooks report, the Vavilov distribution \emph{does not} approximate
+the Landau distribution for small $\kappa$, but rather the
+distribution of $\lambda_L$ defined above tends to the distribution of
+the true $\lambda$ from the Landau density function. Thus the routine
+\texttt{GVAVIV} samples the variable $\lambda_L$ rather than
+$\lambda_v$. For $\kappa \geq 10$ the Vavilov distribution tends to a
+Gaussian distribution (see next section).
+
+\section{Gaussian Theory}
+
+Various conflicting forms have been proposed for Gaussian straggling
+functions, but most of these appear to have little theoretical or
+experimental basis. However, it has been shown\cite{bib-SELT} that
+for $\kappa \geq 10 $ the Vavilov distribution can be replaced by a
+Gaussian of the form :
+\begin{eqnarray*}
+f( \epsilon , \delta s) \approx \frac{1}
+{\xi \sqrt{\frac{2 \pi}{\kappa} \left( 1 - \beta^2/2 \right)}}
+ \exp \left [ \frac{( \epsilon - \bar{\epsilon} )^2}{2} \frac{\kappa}
+ {\xi^2 (1- \beta^2/2)}\right ]
+\end{eqnarray*}
+thus implying
+\begin{eqnarray*}
+\mathrm{mean} & = & \bar{\epsilon} \\
+\sigma^2 & = & \frac{\xi^2}{\kappa} (1-\beta^2/2) = \xi
+ \Emax (1-\beta^2/2)
+\end{eqnarray*}
+
+\section{Urb\'an model}
+\label{urban}
+
+The method for computing restricted energy losses with $\delta$-ray
+production above given threshold energy in \GEANT{} is a Monte
+Carlo method that can be used for thin layers. It is fast and it can
+be used for any thickness of a medium. Approaching the limit of the
+validity of Landau's theory, the loss distribution approaches smoothly
+the Landau form as shown in Figure \ref{fg:phys332-2}.
+\begin{figure}
+ \centering
+ \includegraphics[width=.6\linewidth]{phys332-2}
+ \caption{Energy loss distribution for a 3 GeV electron in
+ Argon as given by standard \GEANT. The width of the layers is
+ given in centimeters.}
+ \label{fg:phys332-2}
+\end{figure}
+
+It is assumed that the atoms have only two energy levels with binding
+energy $E_1$ and $E_2$. The particle--atom interaction will then be
+an excitation with energy loss $E_1$ or $E_2$, or an ionisation with
+an energy loss distributed according to a function $g(E) \sim 1/E^2$:
+\begin{equation}
+g(E) = \frac{(\Emax + I)I}{\Emax} \frac{1}{E^2}
+\end{equation}
+
+The macroscopic cross-section for excitations ($i=1,2$) is
+\begin{equation}
+\label{eq:sigex}
+\Sigma_i = C \frac{f_i}{E_i} \frac{\ln (2 m \beta^2 \gamma^2/E_i) - \beta^2}
+ {\ln (2 m \beta^2 \gamma^2/ I) - \beta^2}(1-r)
+\end{equation}
+and the macroscopic cross-section for ionisation is
+\begin{equation}
+\label{eq:sigion}
+\Sigma_3 = C \frac{\Emax}{I(\Emax+I) \ln(\frac{\Emax+I}{I})}
+ ~ r
+\end{equation}
+\Emax{} is the \GEANT{} cut for $\delta$-production, or the maximum
+energy transfer minus mean ionisation energy, if it is smaller than
+this cut-off value. The following notation is used:
+
+\begin{tabular}{ll}
+$r, C$ & parameters of the model \\
+$E_i$ & atomic energy levels \\
+$I$ & mean ionisation energy \\
+${f_i}$ & oscillator strengths
+\end{tabular}
+
+The model has the parameters $f_i$, $E_i$, $C$ and $r ~(0\leq r\leq
+1)$. The oscillator strengths $f_i$ and the atomic level energies
+$E_i$ should satisfy the constraints
+\begin{eqnarray}
+f_1 + f_2 & = & 1 \label{eq:fisum}\\
+f_1 \ln E_1 + f_2 \ln E_2 & = & \ln I \label{eq:flnsum}
+\end{eqnarray}
+The parameter $C$ can be defined with the help of the mean energy loss
+$dE/dx$ in the following way: The numbers of collisions ($n_i$, i =
+1,2 for the excitation and 3 for the ionisation) follow the Poisson
+distribution with a mean number $ \langle n_i \rangle $. In a step
+$\Delta x$ the mean number of collisions is
+\begin{equation}
+\langle n_i \rangle = \Sigma_i \Delta x
+\end{equation}
+The mean energy loss $dE/dx$ in a step is the sum of the excitation
+and ionisation contributions
+\begin{equation}
+\frac{dE}{dx} \Delta x = \left[ \Sigma_1 E_1 + \Sigma_2 E_2 +
+ \Sigma_3 \int_{I}^{\Emax+I} E~g(E)~dE \right]
+ \Delta x
+\end{equation}
+From this, using the equations (\ref{eq:sigex}), (\ref{eq:sigion}),
+(\ref{eq:fisum}) and (\ref{eq:flnsum}), one can define the parameter
+$C$
+\begin{equation}
+C = \frac{dE}{dx}
+\end{equation}
+
+The following values have been chosen in \GEANT{} for the other
+parameters:
+\[
+\begin{array}{lcl}
+f_2 = \left\{ \begin{array}{ll}
+ 0 & \mathrm{if}\, Z \leq 2 \\
+ 2/Z & \mathrm{if}\, Z > 2 \\
+ \end{array} \right. & \Rightarrow & f_1 = 1 - f_2 \\
+E_2 = 10 Z^2 \mathrm{eV} & \Rightarrow & E_1 = \left(\frac{I}{E_{2}^{f_2}}
+ \right)^{\frac{1}{f_1}} \\
+r = 0.4 & & \\
+\end{array}
+\]
+With these values the atomic level $E_2$ corresponds approximately
+the K-shell energy of the atoms and $Zf_2$ the number of K-shell
+electrons. $r$ is the only variable which can be tuned freely. It
+determines the relative contribution of ionisation and
+excitation to the energy loss.
+
+The energy loss is computed with the assumption that the step length
+(or the relative energy loss) is small, and---in consequence---the
+cross-section can be considered constant along the path length. The
+energy loss due to the excitation is
+\begin{equation}
+\Delta E_e = n_1 E_1 + n_2 E_2
+\end{equation}
+where $n_1$ and $n_2$ are sampled from Poisson distribution as
+discussed above. The loss due to the ionisation can be generated from
+the distribution $g(E)$ by the inverse transformation method:
+\begin{eqnarray}
+u = F(E) & = & \int_{I}^E g(x) dx \nonumber \\
+E = F^{-1}(u) & = & \frac{I}{1 - u \frac {\Emax}{\Emax+I}} \\
+\end{eqnarray}
+where $u$ is a uniform random number between $F(I)=0$ and
+$F(\Emax+I)=1$. The contribution from the ionisations will be
+\begin{equation}
+\Delta E_i = \sum_{j=1}^{n_3} \frac{I}
+ {1 - u_j \frac {\Emax}{\Emax + I}}
+\end{equation}
+where $n_3$ is the number of ionisation (sampled from Poisson
+distribution). The energy loss in a step will then be $\Delta E =
+\Delta E_e + \Delta E_i$.
+
+\subsection{Fast simulation for $n_3 \geq 16$}
+
+If the number of ionisation $n_3$ is bigger than 16, a faster sampling
+method can be used. The possible energy loss interval is divided in
+two parts: one in which the number of collisions is large and the
+sampling can be done from a Gaussian distribution and the other in
+which the energy loss is sampled for each collision. Let us call the
+former interval $[I, \alpha I]$ the interval A, and the latter
+$[\alpha I,\Emax]$ the interval B. $\alpha$ lies between 1 and
+$\Emax/I$. A collision with a loss in the interval A happens with
+the probability
+\begin{equation}
+\label{eq:phys332-5}
+P(\alpha) = \int_I^{\alpha I} g(\!E\!) \, dE =
+ \frac {( \Emax + I) (\alpha - 1)}{\Emax \alpha}
+\end{equation}
+The mean energy loss and the standard deviation for this type
+of collision are
+\begin{equation}
+\langle \Delta E(\alpha) \rangle = \frac{1}{P(\alpha)}
+ \int_I^{\alpha I} E \, g(\!E\!) \, dE =
+ \frac{I \alpha \ln \alpha}{\alpha - 1}
+\end{equation}
+and
+\begin{equation}
+\sigma^2(\alpha) = \frac{1}{P(\alpha)}
+ \int_I^{\alpha I} E^2 \, g(\!E\!) \, dE =
+ I^2 \alpha \left( 1 - \frac{\alpha \ln \! ^2 \alpha}{(\alpha - 1)^2} \right)
+\end{equation}
+If the collision number is high , we assume that the number of the
+type A collisions can be calculated from a Gaussian distribution
+with the following mean value and standard deviation:
+\begin{eqnarray}
+\label{eq:phys332-1}
+\langle n_A \rangle & = & n_3 P(\alpha) \\
+\label{eq:phys332-2}
+\sigma_A^2 & = & n_3 P(\alpha) ( 1 - P(\alpha))
+\end{eqnarray}
+It is further assumed that the energy loss in these collisions
+has a Gaussian distribution with
+\begin{eqnarray}
+\label{eq:phys332-3}
+\langle \Delta E_A \rangle & = & n_A \langle \Delta E(\alpha) \rangle \\
+\label{eq:phys332-4}
+\sigma_{E,A}^2 & = & n_A \sigma^2(\alpha)
+\end{eqnarray}
+The energy loss of these collision can then be sampled from the
+Gaussian distribution.
+
+The collisions where the energy loss is in the interval B are sampled
+directly from
+\begin{equation}
+\Delta E_B = \sum_{i=1}^{n_3 - n_A} \frac{\alpha I}
+ {1 - u_i \frac{\Emax + I - \alpha I}{\Emax + I}}
+\end{equation}
+The total energy loss is the sum of these two types of collisions:
+\begin{equation}
+\Delta E = \Delta E_A + \Delta E_B
+\end{equation}
+
+The approximation of equations ((\ref{eq:phys332-1}),
+(\ref{eq:phys332-2}), (\ref{eq:phys332-3}) and (\ref{eq:phys332-4})
+can be used under the following conditions:
+\begin{eqnarray}
+\label{eq:phys332-6}
+\langle n_A \rangle - c \, \sigma_A & \geq & 0 \\
+\label{eq:phys332-7}
+\langle n_A \rangle + c \, \sigma_A & \leq & n_3 \\
+\label{eq:phys332-8}
+\langle \Delta E_A \rangle - c \, \sigma_{E,A} & \geq & 0
+\end{eqnarray}
+where $c \geq 4$. From the equations (\ref{eq:phys332-5}),
+(\ref{eq:phys332-1}) and (\ref{eq:phys332-3}) and from the conditions
+(\ref{eq:phys332-6}) and (\ref{eq:phys332-7}) the following limits can
+be derived:
+\begin{equation}
+\alpha_{\mathrm{min}} = \frac{(n_3 + c^2)(\Emax+I)}
+ {n_3 (\Emax + I) + c^2 I} \; \leq \alpha \; \leq
+\alpha_{\mathrm{max}} = \frac{(n_3 + c^2)(\Emax+I)}
+ {c^2 (\Emax + I) + n_3 I}
+\end{equation}
+This conditions gives a lower limit to number of the ionisations $n_3$
+for which the fast sampling can be done:
+\begin{equation}
+n_3 \; \geq \; c^2
+\end{equation}
+As in the conditions (\ref{eq:phys332-6}), (\ref{eq:phys332-7}) and
+(\ref{eq:phys332-8}) the value of $c$ is as minimum 4, one gets $n_3
+\; \geq 16$. In order to speed the simulation, the maximum value is
+used for $\alpha$.
+
+The number of collisions with energy loss in the interval B (the
+number of interactions which has to be simulated directly) increases
+slowly with the total number of collisions $n_3$. The maximum number
+of these collisions can be estimated as
+\begin{equation}
+n_{B,max} = n_3 - n_{A,min} \approx n_3 (\langle n_A \rangle
+ - \sigma_A)
+\end{equation}
+From the previous expressions for $\langle n_A \rangle$ and $\sigma_A$
+one can derive the condition
+\begin{equation}
+n_B \; \leq \; n_{B,max} = \frac{2 n_3 c^2}{n_3+c^2}
+\end{equation}
+The following values are obtained with $c=4$:
+
+\begin{tabular}{llcrr}
+$n_3$ & $n_{B,max}$ & & $n_3$ & $n_{B,max}$\\ \hline
+16 & 16 & & 200 & 29.63\\
+20 & 17.78 & & 500 & 31.01 \\
+50 & 24.24 & & 1000 & 31.50 \\
+100 & 27.59 & & $\infty$ & 32.00
+\end{tabular}
+
+\subsection{Special sampling for lower part of the spectrum}
+
+If the step length is very small ($\leq 5$ mm in gases, $\leq$ 2-3
+$\mu$m in solids) the model gives 0 energy loss for some events. To
+avoid this, the probability of 0 energy loss is computed
+\begin{equation}
+P( \Delta E=0) = e^{-( \langle n_1 \rangle + \langle n_2 \rangle
+ + \langle n_3 \rangle )}
+\end{equation}
+If the probability is bigger than 0.01 a special sampling is done,
+taking into account the fact that in these cases the projectile
+interacts only with the outer electrons of the atom. An energy level
+$E_0 = 10$ eV is chosen to correspond to the outer electrons. The mean
+number of collisions can be calculated from
+\begin{equation}
+\langle n \rangle = \frac{1}{E_0} \frac{dE}{dx} \Delta x
+\end{equation}
+The number of collisions $n$ is sampled from Poisson distribution.
+In the case of the thin layers, all the collisions are considered as
+ionisations and the energy loss is computed as
+\begin{equation}
+\Delta E = \sum_{i=1}^n \frac{E_0}
+ {1 - \frac {\Emax}{\Emax + E_0} u_i}
+\end{equation}
+
+\begin{thebibliography}{10}
+\bibitem{bib-LAND}
+L.Landau.
+\newblock On the Energy Loss of Fast Particles by Ionisation.
+\newblock Originally published in \emph{J. Phys.}, 8:201, 1944.
+\newblock Reprinted in D.ter Haar, Editor, \emph{L.D.Landau, Collected
+ papers}, page 417. Pergamon Press, Oxford, 1965.
+
+\bibitem{bib-SCH1}
+B.Schorr.
+\newblock Programs for the Landau and the Vavilov distributions and the
+ corresponding random numbers.
+\newblock \emph{Comp. Phys. Comm.}, 7:216, 1974.
+
+\bibitem{bib-SELT}
+S.M.Seltzer and M.J.Berger.
+\newblock Energy loss straggling of protons and mesons.
+\newblock In \emph{Studies in Penetration of Charged Particles in
+ Matter}, Nuclear Science Series~39, Nat. Academy of Sciences,
+ Washington DC, 1964.
+
+\bibitem{bib-TALM}
+R.Talman.
+\newblock On the statistics of particle identification using ionization.
+\newblock \emph{Nucl. Inst. Meth.}, 159:189, 1979.
+
+\bibitem{bib-VAVI}
+P.V.Vavilov.
+\newblock Ionisation losses of high energy heavy particles.
+\newblock \emph{Soviet Physics JETP}, 5:749, 1957.
+\end{thebibliography}
+
+\end{document}
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.toc b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.toc
new file mode 100644
index 00000000000..15064d9096e
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.toc
@@ -0,0 +1,12 @@
+\expandafter\ifx\csname doTocEntry\endcsname\relax \expandafter\endinput\fi
+\doTocEntry\tocsection{1}{\csname a:TocEntry\endcsname{1}{QQ1-1-1}{QQ2-1-1}{Introduction}}{2}\relax
+\doTocEntry\toclof{1}{\Link{1-10061}{}\ignorespaces The variable $\xi /I_0$ can be used to measure the validity range of the Landau theory. It depends on the type and energy of the particle, $Z$, $A$ and the ionisation potential of the material and the layer thickness. \EndLink}{figure}
+\doTocEntry\tocsection{2}{\csname a:TocEntry\endcsname{1}{QQ1-1-3}{QQ2-1-3}{Landau theory}}{7}\relax
+\doTocEntry\tocsubsection{2.1}{\csname a:TocEntry\endcsname{1}{QQ1-1-4}{QQ2-1-4}{Restrictions}}{7}\relax
+\doTocEntry\tocsection{3}{\csname a:TocEntry\endcsname{1}{QQ1-1-5}{QQ2-1-5}{Vavilov theory}}{9}\relax
+\doTocEntry\tocsection{4}{\csname a:TocEntry\endcsname{1}{QQ1-1-6}{QQ2-1-6}{Gaussian Theory}}{10}\relax
+\doTocEntry\tocsection{5}{\csname a:TocEntry\endcsname{1}{QQ1-1-7}{QQ2-1-7}{Urb\protect\' an model}}{10}\relax
+\doTocEntry\toclof{2}{\Link{1-60012}{}\ignorespaces Energy loss distribution for a 3 GeV electron in Argon as given by standard \protect\texttt {GEANT}. The width of the layers is given in centimeters.\EndLink}{figure}
+\doTocEntry\tocsubsection{5.1}{\csname a:TocEntry\endcsname{1}{QQ1-1-9}{QQ2-1-9}{Fast simulation for $n_3 \geq 16$}}{16}\relax
+\doTocEntry\tocsubsection{5.2}{\csname a:TocEntry\endcsname{1}{QQ1-1-10}{QQ2-1-10}{Special sampling for lower part of the spectrum}}{20}\relax
+\doTocEntry\toclikesection{}{\csname a:TocEntry\endcsname{1}{QQ1-1-11}{QQ2-1-11}{References}}{21}\relax
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.xref b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.xref
new file mode 100644
index 00000000000..4c7a40b1849
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/latexexa.xref
@@ -0,0 +1,81 @@
+\:CrossWord{)F1F-}{latexexa.html}{1}%
+\:CrossWord{)title)}{Simulation of Energy Loss Straggling}{1}%
+\:CrossWord{)M1x0}{;}{2}%
+\:CrossWord{)Q1-10001}{1}{2}%
+\:CrossWord{)QQQ1-1-1}{1}{2}%
+\:CrossWord{)Q1-1001r1}{1}{3}%
+\:CrossWord{)M2x1}{;}{3}%
+\:CrossWord{)Q1-1003x1}{1}{3}%
+\:CrossWord{)Q1-1005x2}{1}{3}%
+\:CrossWord{)Q1-10061}{1}{5}%
+\:CrossWord{1cAp0}{1-10061}{6}%
+\:CrossWord{)Q1-20002}{1}{7}%
+\:CrossWord{)QQQ1-1-3}{1}{7}%
+\:CrossWord{)Q1-2001r1}{1}{7}%
+\:CrossWord{)Q1-2002r1}{1}{7}%
+\:CrossWord{)Q1-30002.1}{1}{7}%
+\:CrossWord{)QQQ1-1-4}{1}{7}%
+\:CrossWord{)Q1-3002x1}{1}{7}%
+\:CrossWord{)Q1-3004x2}{1}{8}%
+\:CrossWord{)Q1-40003}{1}{9}%
+\:CrossWord{)QQQ1-1-5}{1}{9}%
+\:CrossWord{)Q1-4001r1}{1}{9}%
+\:CrossWord{)Q1-4002r1}{1}{9}%
+\:CrossWord{)Q1-4003r1}{1}{9}%
+\:CrossWord{)Q1-50004}{1}{10}%
+\:CrossWord{)QQQ1-1-6}{1}{10}%
+\:CrossWord{)Q1-5001r1}{1}{10}%
+\:CrossWord{)Q1-5002r1}{1}{10}%
+\:CrossWord{)Q1-60005}{1}{10}%
+\:CrossWord{)QQQ1-1-7}{1}{10}%
+\:CrossWord{)Q1-60012}{1}{11}%
+\:CrossWord{2cAp0}{1-60012}{12}%
+\:CrossWord{)Q1-6002r1}{1}{13}%
+\:CrossWord{)Q1-6003r2}{1}{13}%
+\:CrossWord{)Q1-6004r3}{1}{13}%
+\:CrossWord{)M3x7}{;}{14}%
+\:CrossWord{)Q1-6005r4}{1}{14}%
+\:CrossWord{)Q1-6005r5}{1}{14}%
+\:CrossWord{)Q1-6005r6}{1}{14}%
+\:CrossWord{)Q1-6006r6}{1}{14}%
+\:CrossWord{)Q1-6007r7}{1}{15}%
+\:CrossWord{)Q1-6008r8}{1}{15}%
+\:CrossWord{)Q1-6009r9}{1}{16}%
+\:CrossWord{)Q1-6010r10}{1}{16}%
+\:CrossWord{)Q1-6010r11}{1}{16}%
+\:CrossWord{)Q1-6010r12}{1}{16}%
+\:CrossWord{)Q1-6011r12}{1}{16}%
+\:CrossWord{)Q1-70005.1}{1}{16}%
+\:CrossWord{)QQQ1-1-9}{1}{16}%
+\:CrossWord{)Q1-7001r13}{1}{17}%
+\:CrossWord{)Q1-7002r14}{1}{17}%
+\:CrossWord{)Q1-7003r15}{1}{17}%
+\:CrossWord{)Q1-7004r16}{1}{17}%
+\:CrossWord{)Q1-7004r17}{1}{17}%
+\:CrossWord{)Q1-7004r18}{1}{17}%
+\:CrossWord{)Q1-7005r18}{1}{18}%
+\:CrossWord{)Q1-7005r19}{1}{18}%
+\:CrossWord{)Q1-7005r20}{1}{18}%
+\:CrossWord{)Q1-7006r20}{1}{18}%
+\:CrossWord{)Q1-7007r21}{1}{18}%
+\:CrossWord{)Q1-7008r22}{1}{18}%
+\:CrossWord{)Q1-7008r23}{1}{18}%
+\:CrossWord{)Q1-7008r24}{1}{18}%
+\:CrossWord{)Q1-7008r25}{1}{19}%
+\:CrossWord{)Q1-7009r25}{1}{19}%
+\:CrossWord{)Q1-7010r26}{1}{19}%
+\:CrossWord{)Q1-7011r27}{1}{20}%
+\:CrossWord{)Q1-7012r28}{1}{20}%
+\:CrossWord{)M4x9}{;}{20}%
+\:CrossWord{)Q1-80005.2}{1}{20}%
+\:CrossWord{)QQQ1-1-10}{1}{20}%
+\:CrossWord{)Q1-8001r29}{1}{20}%
+\:CrossWord{)Q1-8002r30}{1}{21}%
+\:CrossWord{)Q1-8003r31}{1}{21}%
+\:CrossWord{)Q1-9000}{1}{21}%
+\:CrossWord{)QQQ1-1-11}{1}{21}%
+\:CrossWord{)QXbib-LAND}{1}{21}%
+\:CrossWord{)QXbib-SCH1}{1}{21}%
+\:CrossWord{)QXbib-SELT}{1}{21}%
+\:CrossWord{)QXbib-TALM}{1}{21}%
+\:CrossWord{)QXbib-VAVI}{1}{22}%
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/phys332-1.eps b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/phys332-1.eps
new file mode 100644
index 00000000000..8299292087f
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/phys332-1.eps
@@ -0,0 +1,419 @@
+%!PS-Adobe-2.0 EPSF-2.0
+%%BoundingBox: 0 0 567 567
+%%Title: regime.eps
+%%Creator: HIGZ Version 1.20/02
+%%CreationDate: 93/11/12 09.41
+%%EndComments
+80 dict begin
+/s {stroke} def /l {lineto} def /m {moveto} def /t { translate} def
+/sw {stringwidth} def /r {rotate} def /rl {roll} def
+/d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def
+/c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def
+/cl {closepath} def /sf {scalefont setfont} def
+/box {m dup 0 exch d exch 0 d 0 exch neg d cl} def
+/bl {box s} def /bf {box f} def
+/mp {newpath /y exch def /x exch def} def
+/side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def
+/mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def
+/mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def
+/mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def
+/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26 {mt s} def
+/m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def
+ /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def
+ /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d
+ 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def
+ /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
+ 4 {side} repeat cl fill gr} def
+ /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
+ 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d
+ x w2 sub y w2 add m w w neg d x w2 sub y w2
+ sub m w w d s} def
+/m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def
+/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def
+/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
+/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
+/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
+{dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch
+newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont
+/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
+/Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def
+/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
+201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
+212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
+217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
+221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
+228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
+237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
+244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
+/Times-Roman /Times-Roman accvec ReEncode
+/Times-Italic /Times-Italic accvec ReEncode
+/Times-Bold /Times-Bold accvec ReEncode
+/Times-BoldItalic /Times-BoldItalic accvec ReEncode
+/Helvetica /Helvetica accvec ReEncode
+/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
+/Helvetica-Bold /Helvetica-Bold accvec ReEncode
+/Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode
+/Courier /Courier accvec ReEncode
+/Courier-Oblique /Courier-Oblique accvec ReEncode
+/Courier-Bold /Courier-Bold accvec ReEncode
+/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
+/oshow {gsave [] 0 sd true charpath stroke gr} def
+/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
+ text sw pop xs add /xs exch def} def
+/stwb { /fs exch def /fn exch def /nbas exch def /textf exch def
+textf length /tlen exch def nbas tlen gt {/nbas tlen def} if
+fn findfont fs sf textf dup length nbas sub nbas getinterval sw
+pop neg xs add /xs exch def} def
+/accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal
+69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral
+74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright
+79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
+83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
+88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
+50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
+55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus
+ 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second
+ 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin
+ 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset
+ 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement
+ 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth
+ 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown
+ 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
+/Symbol /Special accspe ReEncode
+gsave .25 .25 scale
+%%EndProlog
+ gsave 0 0 t 0 setgray [] 0 sd 1 lw 4 lw 1814 1814 227 227 bl 231 346 m 240 354
+ l 249 362 l 259 370 l 268 378 l 277 386 l 286 394 l 295 401 l 304 409 l 313 417
+ l 322 425 l 331 433 l 340 441 l 349 449 l 358 457 l 367 465 l 376 473 l 386 481
+ l 395 489 l 404 496 l 413 504 l 422 512 l 431 520 l 440 528 l 449 536 l 458 544
+ l 467 552 l 476 560 l 485 568 l 494 576 l 503 584 l 513 592 l 522 599 l 531 607
+ l 540 615 l 549 623 l 558 631 l 567 639 l 576 647 l 585 655 l 594 663 l 603 671
+ l 612 679 l 621 687 l 631 694 l 640 702 l 649 710 l 658 718 l 667 726 l 676 734
+ l s 676 734 m 685 742 l 694 750 l 703 758 l 712 766 l 721 774 l 730 782 l 739
+ 789 l 748 797 l 758 805 l 767 813 l 776 821 l 785 829 l 794 837 l 803 845 l 812
+ 853 l 821 861 l 830 869 l 839 877 l 848 885 l 857 892 l 866 900 l 875 908 l 885
+ 916 l 894 924 l 903 932 l 912 940 l 921 948 l 930 956 l 939 964 l 948 972 l 957
+ 980 l 966 987 l 975 995 l 984 1003 l 993 1011 l 1002 1019 l 1012 1027 l 1021
+ 1035 l 1030 1043 l 1039 1051 l 1048 1059 l 1057 1067 l 1066 1075 l 1075 1083 l
+ 1084 1090 l 1093 1098 l 1102 1106 l 1111 1114 l 1120 1122 l s 1120 1122 m 1129
+ 1130 l 1139 1138 l 1148 1146 l 1157 1154 l 1166 1162 l 1175 1170 l 1184 1178 l
+ 1193 1185 l 1202 1193 l 1211 1201 l 1220 1209 l 1229 1217 l 1238 1225 l 1247
+ 1233 l 1256 1241 l 1266 1249 l 1275 1257 l 1284 1265 l 1293 1273 l 1302 1281 l
+ 1311 1288 l 1320 1296 l 1329 1304 l 1338 1312 l 1347 1320 l 1356 1328 l 1365
+ 1336 l 1374 1344 l 1383 1352 l 1393 1360 l 1402 1368 l 1411 1376 l 1420 1383 l
+ 1429 1391 l 1438 1399 l 1447 1407 l 1456 1415 l 1465 1423 l 1474 1431 l 1483
+ 1439 l 1492 1447 l 1501 1455 l 1510 1463 l 1520 1471 l 1529 1479 l 1538 1486 l
+ 1547 1494 l 1556 1502 l 1565 1510 l s 1565 1510 m 1574 1518 l 1583 1526 l 1592
+ 1534 l 1601 1542 l 1610 1550 l 1619 1558 l 1628 1566 l 1637 1574 l 1647 1581 l
+ 1656 1589 l 1665 1597 l 1674 1605 l 1683 1613 l 1692 1621 l 1701 1629 l 1710
+ 1637 l 1719 1645 l 1728 1653 l 1737 1661 l 1746 1669 l 1755 1676 l 1765 1684 l
+ 1774 1692 l 1783 1700 l 1792 1708 l 1801 1716 l 1810 1724 l 1819 1732 l 1828
+ 1740 l 1837 1748 l 1846 1756 l 1855 1764 l 1864 1772 l 1873 1779 l 1882 1787 l
+ 1892 1795 l 1901 1803 l 1910 1811 l 1919 1819 l 1928 1827 l 1937 1835 l 1946
+ 1843 l 1955 1851 l 1964 1859 l 1973 1867 l 1982 1874 l 1991 1882 l 2000 1890 l
+ 2009 1898 l s 2009 1898 m 2019 1906 l 2028 1914 l 2037 1922 l s 1 lw 227 227 m
+ 227 2041 l s 4 lw 244 247 m 227 247 l s 244 274 m 227 274 l s 244 297 m 227 297
+ l s 244 317 m 227 317 l s 261 335 m 227 335 l s
+ /xs 0 def
+(10)
+ /Helvetica-Bold 43 stwn
+ gsave 181 319
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(10)
+ show
+ gr
+ /xs 0 def
+(-2)
+ /Helvetica-Bold 35 stwn
+ gsave 213 358
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 35 sf 0 0 m
+(-2)
+ show
+ gr
+ 244 454 m 227 454 l s 244 524 m 227 524 l s 244 573 m 227 573 l s 244 612 m 227
+ 612 l s 244 643 m 227 643 l s 244 670 m 227 670 l s 244 693 m 227 693 l s 244
+ 713 m 227 713 l s 261 731 m 227 731 l s
+ /xs 0 def
+(10)
+ /Helvetica-Bold 43 stwn
+ gsave 181 715
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(10)
+ show
+ gr
+ /xs 0 def
+(-1)
+ /Helvetica-Bold 35 stwn
+ gsave 213 754
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 35 sf 0 0 m
+(-1)
+ show
+ gr
+ 244 850 m 227 850 l s 244 920 m 227 920 l s 244 969 m 227 969 l s 244 1008 m
+ 227 1008 l s 244 1039 m 227 1039 l s 244 1066 m 227 1066 l s 244 1089 m 227
+ 1089 l s 244 1109 m 227 1109 l s 261 1127 m 227 1127 l s
+ /xs 0 def
+(1)
+ /Helvetica-Bold 43 stwn
+ gsave 181 1111
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(1)
+ show
+ gr
+ 244 1246 m 227 1246 l s 244 1316 m 227 1316 l s 244 1365 m 227 1365 l s 244
+ 1404 m 227 1404 l s 244 1435 m 227 1435 l s 244 1462 m 227 1462 l s 244 1485 m
+ 227 1485 l s 244 1505 m 227 1505 l s 261 1523 m 227 1523 l s
+ /xs 0 def
+(10)
+ /Helvetica-Bold 43 stwn
+ gsave 181 1507
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(10)
+ show
+ gr
+ 244 1642 m 227 1642 l s 244 1712 m 227 1712 l s 244 1761 m 227 1761 l s 244
+ 1800 m 227 1800 l s 244 1831 m 227 1831 l s 244 1858 m 227 1858 l s 244 1881 m
+ 227 1881 l s 244 1901 m 227 1901 l s 261 1919 m 227 1919 l s
+ /xs 0 def
+(10)
+ /Helvetica-Bold 43 stwn
+ gsave 181 1903
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(10)
+ show
+ gr
+ /xs 0 def
+(2)
+ /Helvetica-Bold 35 stwn
+ gsave 213 1926
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 35 sf 0 0 m
+(2)
+ show
+ gr
+ 244 2038 m 227 2038 l s 1 lw 227 227 m 2041 227 l s 4 lw 227 261 m 227 227 l s
+ 680 261 m 680 227 l s 1134 261 m 1134 227 l s 1588 261 m 1588 227 l s 2041 261
+ m 2041 227 l s
+ /xs 0 def
+(0.01)
+ /Helvetica-Bold 43 stwn
+ gsave 227 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.01)
+ show
+ gr
+ /xs 0 def
+(0.1)
+ /Helvetica-Bold 43 stwn
+ gsave 680 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.1)
+ show
+ gr
+ /xs 0 def
+(1)
+ /Helvetica-Bold 43 stwn
+ gsave 1134 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(1)
+ show
+ gr
+ /xs 0 def
+(10)
+ /Helvetica-Bold 43 stwn
+ gsave 1588 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(10)
+ show
+ gr
+ /xs 0 def
+(100)
+ /Helvetica-Bold 43 stwn
+ gsave 2041 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(100)
+ show
+ gr
+ 231 243 m 240 251 l 249 258 l 259 266 l 268 274 l 277 282 l 286 290 l 295 298 l
+ 304 306 l 313 314 l 322 322 l 331 330 l 340 338 l 349 346 l 358 354 l 367 361 l
+ 376 369 l 386 377 l 395 385 l 404 393 l 413 401 l 422 409 l 431 417 l 440 425 l
+ 449 433 l 458 441 l 467 449 l 476 456 l 485 464 l 494 472 l 503 480 l 513 488 l
+ 522 496 l 531 504 l 540 512 l 549 520 l 558 528 l 567 536 l 576 544 l 585 551 l
+ 594 559 l 603 567 l 612 575 l 621 583 l 631 591 l 640 599 l 649 607 l 658 615 l
+ 667 623 l 676 631 l s 676 631 m 685 639 l 694 647 l 703 654 l 712 662 l 721 670
+ l 730 678 l 739 686 l 748 694 l 758 702 l 767 710 l 776 718 l 785 726 l 794 734
+ l 803 742 l 812 749 l 821 757 l 830 765 l 839 773 l 848 781 l 857 789 l 866 797
+ l 875 805 l 885 813 l 894 821 l 903 829 l 912 837 l 921 845 l 930 852 l 939 860
+ l 948 868 l 957 876 l 966 884 l 975 892 l 984 900 l 993 908 l 1002 916 l 1012
+ 924 l 1021 932 l 1030 940 l 1039 947 l 1048 955 l 1057 963 l 1066 971 l 1075
+ 979 l 1084 987 l 1093 995 l 1102 1003 l 1111 1011 l 1120 1019 l s 1120 1019 m
+ 1129 1027 l 1139 1035 l 1148 1043 l 1157 1050 l 1166 1058 l 1175 1066 l 1184
+ 1074 l 1193 1082 l 1202 1090 l 1211 1098 l 1220 1106 l 1229 1114 l 1238 1122 l
+ 1247 1130 l 1256 1138 l 1266 1145 l 1275 1153 l 1284 1161 l 1293 1169 l 1302
+ 1177 l 1311 1185 l 1320 1193 l 1329 1201 l 1338 1209 l 1347 1217 l 1356 1225 l
+ 1365 1233 l 1374 1241 l 1383 1248 l 1393 1256 l 1402 1264 l 1411 1272 l 1420
+ 1280 l 1429 1288 l 1438 1296 l 1447 1304 l 1456 1312 l 1465 1320 l 1474 1328 l
+ 1483 1336 l 1492 1343 l 1501 1351 l 1510 1359 l 1520 1367 l 1529 1375 l 1538
+ 1383 l 1547 1391 l 1556 1399 l 1565 1407 l s 1565 1407 m 1574 1415 l 1583 1423
+ l 1592 1431 l 1601 1438 l 1610 1446 l 1619 1454 l 1628 1462 l 1637 1470 l 1647
+ 1478 l 1656 1486 l 1665 1494 l 1674 1502 l 1683 1510 l 1692 1518 l 1701 1526 l
+ 1710 1534 l 1719 1541 l 1728 1549 l 1737 1557 l 1746 1565 l 1755 1573 l 1765
+ 1581 l 1774 1589 l 1783 1597 l 1792 1605 l 1801 1613 l 1810 1621 l 1819 1629 l
+ 1828 1636 l 1837 1644 l 1846 1652 l 1855 1660 l 1864 1668 l 1873 1676 l 1882
+ 1684 l 1892 1692 l 1901 1700 l 1910 1708 l 1919 1716 l 1928 1724 l 1937 1732 l
+ 1946 1739 l 1955 1747 l 1964 1755 l 1973 1763 l 1982 1771 l 1991 1779 l 2000
+ 1787 l 2009 1795 l s 2009 1795 m 2019 1803 l 2028 1811 l 2037 1819 l s
+ [12 12] 0 sd 231 1636 m 240 1644 l 249 1652 l 259 1660 l 268 1668 l 277 1676 l
+ 286 1684 l 295 1692 l 304 1700 l 313 1708 l 322 1716 l 331 1724 l 340 1732 l
+ 349 1739 l 358 1747 l 367 1755 l 376 1763 l 386 1771 l 395 1779 l 404 1787 l
+ 413 1795 l 422 1803 l 431 1811 l 440 1819 l 449 1827 l 458 1834 l 467 1842 l
+ 476 1850 l 485 1858 l 494 1866 l 503 1874 l 513 1882 l 522 1890 l 531 1898 l
+ 540 1906 l 549 1914 l 558 1922 l 567 1930 l 576 1937 l 585 1945 l 594 1953 l
+ 603 1961 l 612 1969 l 621 1977 l 631 1985 l 640 1993 l 649 2001 l 658 2009 l
+ 667 2017 l 676 2025 l s 676 2025 m 685 2032 l 694 2040 l 695 2041 l s 231 1533
+ m 240 1541 l 249 1549 l 259 1557 l 268 1565 l 277 1573 l 286 1581 l 295 1589 l
+ 304 1596 l 313 1604 l 322 1612 l 331 1620 l 340 1628 l 349 1636 l 358 1644 l
+ 367 1652 l 376 1660 l 386 1668 l 395 1676 l 404 1684 l 413 1692 l 422 1699 l
+ 431 1707 l 440 1715 l 449 1723 l 458 1731 l 467 1739 l 476 1747 l 485 1755 l
+ 494 1763 l 503 1771 l 513 1779 l 522 1787 l 531 1794 l 540 1802 l 549 1810 l
+ 558 1818 l 567 1826 l 576 1834 l 585 1842 l 594 1850 l 603 1858 l 612 1866 l
+ 621 1874 l 631 1882 l 640 1890 l 649 1897 l 658 1905 l 667 1913 l 676 1921 l s
+ 676 1921 m 685 1929 l 694 1937 l 703 1945 l 712 1953 l 721 1961 l 730 1969 l
+ 739 1977 l 748 1985 l 758 1992 l 767 2000 l 776 2008 l 785 2016 l 794 2024 l
+ 803 2032 l 812 2040 l 813 2041 l s [4 8] 0 sd 231 1662 m 240 1670 l 249 1678 l
+ 259 1686 l 268 1693 l 277 1701 l 286 1709 l 295 1717 l 304 1725 l 313 1733 l
+ 322 1741 l 331 1749 l 340 1757 l 349 1765 l 358 1773 l 367 1781 l 376 1789 l
+ 386 1796 l 395 1804 l 404 1812 l 413 1820 l 422 1828 l 431 1836 l 440 1844 l
+ 449 1852 l 458 1860 l 467 1868 l 476 1876 l 485 1884 l 494 1891 l 503 1899 l
+ 513 1907 l 522 1915 l 531 1923 l 540 1931 l 549 1939 l 558 1947 l 567 1955 l
+ 576 1963 l 585 1971 l 594 1979 l 603 1987 l 612 1994 l 621 2002 l 631 2010 l
+ 640 2018 l 649 2026 l 658 2034 l 666 2041 l s 231 1558 m 240 1566 l 249 1574 l
+ 259 1582 l 268 1590 l 277 1598 l 286 1606 l 295 1614 l 304 1622 l 313 1630 l
+ 322 1638 l 331 1646 l 340 1653 l 349 1661 l 358 1669 l 367 1677 l 376 1685 l
+ 386 1693 l 395 1701 l 404 1709 l 413 1717 l 422 1725 l 431 1733 l 440 1741 l
+ 449 1749 l 458 1756 l 467 1764 l 476 1772 l 485 1780 l 494 1788 l 503 1796 l
+ 513 1804 l 522 1812 l 531 1820 l 540 1828 l 549 1836 l 558 1844 l 567 1851 l
+ 576 1859 l 585 1867 l 594 1875 l 603 1883 l 612 1891 l 621 1899 l 631 1907 l
+ 640 1915 l 649 1923 l 658 1931 l 667 1939 l 676 1947 l s 676 1947 m 685 1954 l
+ 694 1962 l 703 1970 l 712 1978 l 721 1986 l 730 1994 l 739 2002 l 748 2010 l
+ 758 2018 l 767 2026 l 776 2034 l 784 2041 l s [12 15 4 15] 0 sd 263 1800 m 2041
+ 1800 l s
+ gsave 1134 1738
+ t 0 r 0 0 m
+ /Symbol findfont 78 sf 0 0 m
+(x)
+ show
+ currentpoint pop 0 t
+ /Helvetica-Bold findfont 78 sf 0 0 m
+(/I)
+ show
+ currentpoint pop 0 t
+ /Helvetica-Bold findfont 55 sf 0 -26 m
+(0)
+ show
+ currentpoint pop 0 t
+ /Helvetica-Bold findfont 78 sf 0 0 m
+( \074 50)
+ show
+ gr
+ [] 0 sd 1134 612 m 1530 612 l s [12 12] 0 sd 1134 533 m 1530 533 l s [4 8] 0 sd
+ 1134 454 m 1530 454 l s
+ gsave 1589 584
+ t 0 r 0 0 m
+ /Helvetica-Bold findfont 78 sf 0 0 m
+(Argon)
+ show
+ gr
+ gsave 1589 505
+ t 0 r 0 0 m
+ /Helvetica-Bold findfont 78 sf 0 0 m
+(Silicon)
+ show
+ gr
+ gsave 1589 426
+ t 0 r 0 0 m
+ /Helvetica-Bold findfont 78 sf 0 0 m
+(Uranium)
+ show
+ gr
+ [] 0 sd 871 -316 1055 691 bl
+ gsave 1213 1011
+ t 0 r 0 0 m
+ /Helvetica-Bold findfont 78 sf 0 0 m
+(1 GeV)
+ show
+ gr
+ gsave 778 1099
+ t 0 r 0 0 m
+ /Helvetica-Bold findfont 78 sf 0 0 m
+(100 keV)
+ show
+ gr
+ gsave 679 1852
+ t 0 r 0 0 m
+ /Helvetica-Bold findfont 78 sf 0 0 m
+(1 GeV)
+ show
+ gr
+ gsave 223 1907
+ t 0 r 0 0 m
+ /Helvetica-Bold findfont 78 sf 0 0 m
+(100 keV)
+ show
+ gr
+ /xs 0 def
+(Step,\040)
+ /Helvetica-Bold 43 stwn
+(\133)
+ /Special 43 stwn
+(cm)
+ /Helvetica-Bold 43 stwn
+(\135)
+ /Special 43 stwn
+ gsave 2041 104
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(Step,\040)
+ show
+ currentpoint pop 0 t
+ /Special findfont 43 sf 0 0 m
+(\133)
+ show
+ currentpoint pop 0 t
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(cm)
+ show
+ currentpoint pop 0 t
+ /Special findfont 43 sf 0 0 m
+(\135)
+ show
+ gr
+ gsave 57 2009
+ t 0 r 0 0 m
+ /Symbol findfont 43 sf 0 0 m
+(x)
+ show
+ currentpoint pop 0 t
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(/I)
+ show
+ currentpoint pop 0 t
+ /Helvetica-Bold findfont 30 sf 0 -14 m
+(0)
+ show
+ gr
+gr gr showpage
+end
+%%EOF
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/phys332-2.eps b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/phys332-2.eps
new file mode 100644
index 00000000000..e255ddadf55
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/phys332-2.eps
@@ -0,0 +1,556 @@
+%!PS-Adobe-2.0 EPSF-2.0
+%%BoundingBox: 0 0 567 567
+%%Title: curves.eps
+%%Creator: HIGZ Version 1.19/01
+%%CreationDate: 93/07/16 12.02
+%%EndComments
+80 dict begin
+/s {stroke} def /l {lineto} def /m {moveto} def /t { translate} def
+/sw {stringwidth} def /r {rotate} def /rl {roll} def
+/d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def
+/c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def
+/cl {closepath} def /sf {scalefont setfont} def
+/box {m dup 0 exch d exch 0 d 0 exch neg d cl} def
+/bl {box s} def /bf {box f} def
+/mp {newpath /y exch def /x exch def} def
+/side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def
+/mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def
+/mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def
+/mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def
+/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26 {mt s} def
+/m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def
+ /m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def
+ /m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d
+ 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d 0 w3 neg d w3 neg 0 d cl s } def
+ /m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
+ 4 {side} repeat cl fill gr} def
+ /m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
+ 5 {side} repeat s gr} def /m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d
+ x w2 sub y w2 add m w w neg d x w2 sub y w2
+ sub m w w d s} def
+/m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def
+/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def
+/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
+/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
+/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
+{dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch
+newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont
+/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
+/Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def
+/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
+201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
+212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
+217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
+221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
+228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
+237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
+244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
+/Times-Roman /Times-Roman accvec ReEncode
+/Times-Italic /Times-Italic accvec ReEncode
+/Times-Bold /Times-Bold accvec ReEncode
+/Times-BoldItalic /Times-BoldItalic accvec ReEncode
+/Helvetica /Helvetica accvec ReEncode
+/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
+/Helvetica-Bold /Helvetica-Bold accvec ReEncode
+/Helvetica-BoldOblique /Helvetica-BoldOblique accvec ReEncode
+/Courier /Courier accvec ReEncode
+/Courier-Oblique /Courier-Oblique accvec ReEncode
+/Courier-Bold /Courier-Bold accvec ReEncode
+/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
+/oshow {gsave [] 0 sd true charpath stroke gr} def
+/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
+ text sw pop xs add /xs exch def} def
+/stwb { /fs exch def /fn exch def /nbas exch def /textf exch def
+textf length /tlen exch def nbas tlen gt {/nbas tlen def} if
+fn findfont fs sf textf dup length nbas sub nbas getinterval sw
+pop neg xs add /xs exch def} def
+/accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal
+69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral
+74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright
+79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
+83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
+88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
+50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
+55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus
+ 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second
+ 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin
+ 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset
+ 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement
+ 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth
+ 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown
+ 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
+/Symbol /Special accspe ReEncode
+gsave .25 .25 scale
+%%EndProlog
+ gsave 0 0 t 0 setgray [] 0 sd 1 lw 4 lw 2268 2268 0 0 bl
+ gsave 771 1813
+ t 0 r 0 0 m
+ /Helvetica-Bold findfont 47 sf 0 0 m
+(Landau)
+ show
+ gr
+ /xs 0 def
+(40)
+ /Helvetica-Bold 54 stwn
+ gsave 862 1533
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 54 sf 0 0 m
+(40)
+ show
+ gr
+ /xs 0 def
+(20)
+ /Helvetica-Bold 54 stwn
+ gsave 789 1347
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 54 sf 0 0 m
+(20)
+ show
+ gr
+ /xs 0 def
+(10)
+ /Helvetica-Bold 54 stwn
+ gsave 771 1011
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 54 sf 0 0 m
+(10)
+ show
+ gr
+ /xs 0 def
+(5)
+ /Helvetica-Bold 54 stwn
+ gsave 699 824
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 54 sf 0 0 m
+(5)
+ show
+ gr
+ /xs 0 def
+(1)
+ /Helvetica-Bold 54 stwn
+ gsave 517 740
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 54 sf 0 0 m
+(1)
+ show
+ gr
+ /xs 0 def
+(0.5)
+ /Helvetica-Bold 54 stwn
+ gsave 336 525
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 54 sf 0 0 m
+(0.5)
+ show
+ gr
+ /xs 0 def
+(dE/dx\040)
+ /Helvetica-Bold 43 stwn
+(M)
+ /Special 43 stwn
+(GeV/cm)
+ /Helvetica-Bold 43 stwn
+(N)
+ /Special 43 stwn
+( `)
+ /Helvetica-Bold 43 stwn
+ gsave 2041 104
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(dE/dx\040)
+ show
+ currentpoint pop 0 t
+ /Special findfont 43 sf 0 0 m
+(M)
+ show
+ currentpoint pop 0 t
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(GeV/cm)
+ show
+ currentpoint pop 0 t
+ /Special findfont 43 sf 0 0 m
+(N)
+ show
+ currentpoint pop 0 t
+ /Helvetica-Bold findfont 43 sf 0 0 m
+( `)
+ show
+ gr
+ /xs 0 def
+(Counts)
+ /Helvetica-Bold 43 stwn
+ gsave 68 2041
+ t 90 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(Counts)
+ show
+ gr
+ 1814 1814 227 227 bl 227 227 m 227 227 l 249 227 l 272 227 l 295 227 l 318 227
+ l 340 227 l 363 227 l 386 227 l 408 227 l 431 227 l 454 227 l 476 227 l 499 227
+ l 522 227 l 544 227 l 567 227 l 590 227 l 612 227 l 635 227 l 658 227 l 658 231
+ l 680 231 l 680 397 l 703 397 l 703 1300 l 726 1300 l 726 1860 l 748 1860 l 748
+ 1697 l 771 1697 l 771 1393 l 794 1393 l 794 992 l 816 992 l 816 831 l 839 831 l
+ 839 636 l 862 636 l 862 516 l 885 516 l 885 481 l 907 481 l 907 443 l 930 443 l
+ 930 380 l 953 380 l 953 343 l 975 343 l 975 324 l 998 324 l 998 283 l 1021 283
+ l 1021 301 l 1043 301 l 1043 288 l 1066 288 l 1066 294 l 1089 294 l 1089 272 l
+ 1111 272 l 1111 262 l 1134 262 l 1134 272 l 1157 272 l 1157 251 l 1179 251 l
+ 1179 253 l 1202 253 l 1202 255 l 1225 255 l 1225 257 l 1247 257 l 1247 245 l
+ 1270 245 l 1270 244 l 1293 244 l 1293 247 l 1315 247 l 1315 249 l 1338 249 l
+ 1338 240 l 1361 240 l 1361 231 l 1383 231 l 1383 244 l 1406 244 l 1406 234 l
+ 1429 234 l 1429 231 l 1452 231 l 1452 238 l 1474 238 l 1497 238 l 1497 234 l
+ 1520 234 l 1520 236 l 1542 236 l 1542 231 l 1565 231 l 1565 234 l 1588 234 l
+ 1588 232 l 1610 232 l 1610 231 l 1633 231 l 1633 229 l 1656 229 l 1656 234 l
+ 1678 234 l 1701 234 l 1701 232 l 1724 232 l 1724 229 l 1746 229 l 1769 229 l
+ 1769 234 l 1792 234 l 1792 227 l 1814 227 l 1814 232 l 1837 232 l 1837 234 l
+ 1860 234 l 1860 229 l 1882 229 l 1882 231 l 1905 231 l 1905 227 l 1928 227 l
+ 1928 229 l 1950 229 l 1950 227 l 1973 227 l 1973 229 l 1996 229 l 1996 231 l
+ 2019 231 l 2041 231 l 2041 227 l s 1 lw 227 227 m 227 2041 l s 4 lw 261 227 m
+ 227 227 l s 244 264 m 227 264 l s 244 301 m 227 301 l s 244 339 m 227 339 l s
+ 244 376 m 227 376 l s 261 413 m 227 413 l s 244 451 m 227 451 l s 244 488 m 227
+ 488 l s 244 525 m 227 525 l s 244 563 m 227 563 l s 261 600 m 227 600 l s 244
+ 637 m 227 637 l s 244 675 m 227 675 l s 244 712 m 227 712 l s 244 749 m 227 749
+ l s 261 787 m 227 787 l s 244 824 m 227 824 l s 244 861 m 227 861 l s 244 899 m
+ 227 899 l s 244 936 m 227 936 l s 261 973 m 227 973 l s 244 1011 m 227 1011 l s
+ 244 1048 m 227 1048 l s 244 1085 m 227 1085 l s 244 1123 m 227 1123 l s 261
+ 1160 m 227 1160 l s 244 1197 m 227 1197 l s 244 1235 m 227 1235 l s 244 1272 m
+ 227 1272 l s 244 1309 m 227 1309 l s 261 1347 m 227 1347 l s 244 1384 m 227
+ 1384 l s 244 1421 m 227 1421 l s 244 1459 m 227 1459 l s 244 1496 m 227 1496 l
+ s 261 1533 m 227 1533 l s 244 1570 m 227 1570 l s 244 1608 m 227 1608 l s 244
+ 1645 m 227 1645 l s 244 1682 m 227 1682 l s 261 1720 m 227 1720 l s 244 1757 m
+ 227 1757 l s 244 1794 m 227 1794 l s 244 1832 m 227 1832 l s 244 1869 m 227
+ 1869 l s 261 1906 m 227 1906 l s 261 1906 m 227 1906 l s 244 1944 m 227 1944 l
+ s 244 1981 m 227 1981 l s 244 2018 m 227 2018 l s
+ /xs 0 def
+(0)
+ /Helvetica-Bold 43 stwn
+ gsave 181 211
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0)
+ show
+ gr
+ /xs 0 def
+(100)
+ /Helvetica-Bold 43 stwn
+ gsave 181 398
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(100)
+ show
+ gr
+ /xs 0 def
+(200)
+ /Helvetica-Bold 43 stwn
+ gsave 181 584
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(200)
+ show
+ gr
+ /xs 0 def
+(300)
+ /Helvetica-Bold 43 stwn
+ gsave 181 771
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(300)
+ show
+ gr
+ /xs 0 def
+(400)
+ /Helvetica-Bold 43 stwn
+ gsave 181 957
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(400)
+ show
+ gr
+ /xs 0 def
+(500)
+ /Helvetica-Bold 43 stwn
+ gsave 181 1144
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(500)
+ show
+ gr
+ /xs 0 def
+(600)
+ /Helvetica-Bold 43 stwn
+ gsave 181 1331
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(600)
+ show
+ gr
+ /xs 0 def
+(700)
+ /Helvetica-Bold 43 stwn
+ gsave 181 1517
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(700)
+ show
+ gr
+ /xs 0 def
+(800)
+ /Helvetica-Bold 43 stwn
+ gsave 181 1704
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(800)
+ show
+ gr
+ /xs 0 def
+(900)
+ /Helvetica-Bold 43 stwn
+ gsave 181 1891
+ t 0 r xs neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(900)
+ show
+ gr
+ 1 lw 227 227 m 2041 227 l s 4 lw 227 261 m 227 227 l s 263 244 m 263 227 l s
+ 299 244 m 299 227 l s 336 244 m 336 227 l s 372 244 m 372 227 l s 408 261 m 408
+ 227 l s 445 244 m 445 227 l s 481 244 m 481 227 l s 517 244 m 517 227 l s 553
+ 244 m 553 227 l s 590 261 m 590 227 l s 626 244 m 626 227 l s 662 244 m 662 227
+ l s 699 244 m 699 227 l s 735 244 m 735 227 l s 771 261 m 771 227 l s 807 244 m
+ 807 227 l s 844 244 m 844 227 l s 880 244 m 880 227 l s 916 244 m 916 227 l s
+ 953 261 m 953 227 l s 989 244 m 989 227 l s 1025 244 m 1025 227 l s 1061 244 m
+ 1061 227 l s 1098 244 m 1098 227 l s 1134 261 m 1134 227 l s 1170 244 m 1170
+ 227 l s 1207 244 m 1207 227 l s 1243 244 m 1243 227 l s 1279 244 m 1279 227 l s
+ 1315 261 m 1315 227 l s 1352 244 m 1352 227 l s 1388 244 m 1388 227 l s 1424
+ 244 m 1424 227 l s 1461 244 m 1461 227 l s 1497 261 m 1497 227 l s 1533 244 m
+ 1533 227 l s 1569 244 m 1569 227 l s 1606 244 m 1606 227 l s 1642 244 m 1642
+ 227 l s 1678 261 m 1678 227 l s 1715 244 m 1715 227 l s 1751 244 m 1751 227 l s
+ 1787 244 m 1787 227 l s 1823 244 m 1823 227 l s 1860 261 m 1860 227 l s 1896
+ 244 m 1896 227 l s 1932 244 m 1932 227 l s 1969 244 m 1969 227 l s 2005 244 m
+ 2005 227 l s 2041 261 m 2041 227 l s
+ /xs 0 def
+(0)
+ /Helvetica-Bold 43 stwn
+ gsave 227 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0)
+ show
+ gr
+ /xs 0 def
+(0.01)
+ /Helvetica-Bold 43 stwn
+ gsave 408 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.01)
+ show
+ gr
+ /xs 0 def
+(0.02)
+ /Helvetica-Bold 43 stwn
+ gsave 590 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.02)
+ show
+ gr
+ /xs 0 def
+(0.03)
+ /Helvetica-Bold 43 stwn
+ gsave 771 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.03)
+ show
+ gr
+ /xs 0 def
+(0.04)
+ /Helvetica-Bold 43 stwn
+ gsave 953 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.04)
+ show
+ gr
+ /xs 0 def
+(0.05)
+ /Helvetica-Bold 43 stwn
+ gsave 1134 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.05)
+ show
+ gr
+ /xs 0 def
+(0.06)
+ /Helvetica-Bold 43 stwn
+ gsave 1315 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.06)
+ show
+ gr
+ /xs 0 def
+(0.07)
+ /Helvetica-Bold 43 stwn
+ gsave 1497 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.07)
+ show
+ gr
+ /xs 0 def
+(0.08)
+ /Helvetica-Bold 43 stwn
+ gsave 1678 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.08)
+ show
+ gr
+ /xs 0 def
+(0.09)
+ /Helvetica-Bold 43 stwn
+ gsave 1860 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.09)
+ show
+ gr
+ /xs 0 def
+(0.1)
+ /Helvetica-Bold 43 stwn
+ gsave 2041 172
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(0.1)
+ show
+ gr
+ /xs 0 def
+(x 10)
+ /Helvetica-Bold 43 stwn
+ gsave 2041 109
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 43 sf 0 0 m
+(x 10)
+ show
+ gr
+ /xs 0 def
+(-4)
+ /Helvetica-Bold 35 stwn
+ gsave 2105 141
+ t 0 r xs 2 div neg 0 t 0 0 m
+ /Helvetica-Bold findfont 35 sf 0 0 m
+(-4)
+ show
+ gr
+ [12 12] 0 sd 227 227 m 227 227 l 249 227 l 272 227 l 295 227 l 318 227 l 340
+ 227 l 363 227 l 386 227 l 408 227 l 431 227 l 454 227 l 476 227 l 499 227 l 522
+ 227 l 544 227 l 544 229 l 567 229 l 567 232 l 590 232 l 590 270 l 612 270 l 612
+ 352 l 635 352 l 635 546 l 658 546 l 658 901 l 680 901 l 680 1199 l 703 1199 l
+ 703 1490 l 726 1490 l 726 1628 l 748 1628 l 748 1533 l 771 1533 l 771 1404 l
+ 794 1404 l 794 1048 l 816 1048 l 816 738 l 839 738 l 839 572 l 862 572 l 862
+ 417 l 885 417 l 885 331 l 907 331 l 907 272 l 930 272 l 930 244 l 953 244 l 953
+ 231 l 975 231 l 998 231 l 998 227 l 1021 227 l 1043 227 l 1066 227 l 1089 227 l
+ 1111 227 l 1134 227 l 1157 227 l 1179 227 l 1202 227 l 1225 227 l 1247 227 l
+ 1270 227 l 1293 227 l 1315 227 l 1338 227 l 1361 227 l 1361 227 l 1383 227 l
+ 1406 227 l 1429 227 l 1452 227 l 1474 227 l 1497 227 l 1520 227 l 1542 227 l
+ 1565 227 l 1588 227 l 1610 227 l 1633 227 l 1656 227 l 1678 227 l 1701 227 l
+ 1724 227 l 1746 227 l 1769 227 l 1792 227 l 1814 227 l 1837 227 l 1860 227 l
+ 1882 227 l 1905 227 l 1928 227 l 1928 227 l 1950 227 l 1973 227 l 1996 227 l
+ 2019 227 l 2041 227 l s [4 8] 0 sd 227 227 m 227 227 l 249 227 l 272 227 l 295
+ 227 l 318 227 l 340 227 l 363 227 l 386 227 l 408 227 l 431 227 l 454 227 l 476
+ 227 l 499 227 l 499 231 l 522 231 l 522 244 l 544 244 l 544 257 l 567 257 l 567
+ 315 l 590 315 l 590 447 l 612 447 l 612 613 l 635 613 l 635 833 l 658 833 l 658
+ 1029 l 680 1029 l 680 1190 l 703 1190 l 703 1212 l 726 1212 l 726 1285 l 748
+ 1285 l 748 1141 l 771 1141 l 771 1085 l 794 1085 l 794 884 l 816 884 l 816 775
+ l 839 775 l 839 619 l 862 619 l 862 492 l 885 492 l 885 413 l 907 413 l 907 369
+ l 930 369 l 930 294 l 953 294 l 953 290 l 975 290 l 975 260 l 998 260 l 998 244
+ l 1021 244 l 1021 238 l 1043 238 l 1043 234 l 1066 234 l 1066 229 l 1089 229 l
+ 1089 231 l 1111 231 l 1111 227 l 1134 227 l 1134 229 l 1157 229 l 1157 227 l
+ 1179 227 l 1202 227 l 1225 227 l 1247 227 l 1270 227 l 1293 227 l 1315 227 l
+ 1338 227 l 1361 227 l 1361 227 l 1383 227 l 1406 227 l 1429 227 l 1452 227 l
+ 1474 227 l 1497 227 l 1520 227 l 1542 227 l 1565 227 l 1588 227 l 1610 227 l
+ 1633 227 l 1656 227 l 1678 227 l 1701 227 l 1724 227 l 1746 227 l 1769 227 l
+ 1792 227 l 1814 227 l 1837 227 l 1860 227 l 1882 227 l 1905 227 l 1928 227 l
+ 1928 227 l 1950 227 l 1973 227 l 1996 227 l 2019 227 l 2041 227 l s
+ [12 15 4 15] 0 sd 227 227 m 227 227 l 249 227 l 272 227 l 295 227 l 318 227 l
+ 340 227 l 363 227 l 386 227 l 408 227 l 431 227 l 431 229 l 454 229 l 454 234 l
+ 476 234 l 476 242 l 499 242 l 499 277 l 522 277 l 522 335 l 544 335 l 544 412 l
+ 567 412 l 567 580 l 590 580 l 590 749 l 612 749 l 612 889 l 635 889 l 635 953 l
+ 658 953 l 658 984 l 680 984 l 680 1009 l 703 1009 l 703 942 l 726 942 l 726 962
+ l 748 962 l 748 869 l 771 869 l 771 820 l 794 820 l 794 725 l 816 725 l 816 677
+ l 839 677 l 839 580 l 862 580 l 862 492 l 885 492 l 885 458 l 907 458 l 907 404
+ l 930 404 l 930 341 l 953 341 l 953 328 l 975 328 l 975 315 l 998 315 l 998 277
+ l 1021 277 l 1021 270 l 1043 270 l 1043 255 l 1066 255 l 1066 262 l 1089 262 l
+ 1089 236 l 1111 236 l 1134 236 l 1134 238 l 1157 238 l 1157 231 l 1179 231 l
+ 1179 229 l 1202 229 l 1202 227 l 1225 227 l 1225 231 l 1247 231 l 1247 227 l
+ 1270 227 l 1293 227 l 1315 227 l 1338 227 l 1338 229 l 1361 229 l 1361 227 l
+ 1383 227 l 1406 227 l 1429 227 l 1452 227 l 1474 227 l 1497 227 l 1520 227 l
+ 1542 227 l 1565 227 l 1588 227 l 1610 227 l 1633 227 l 1656 227 l 1678 227 l
+ 1701 227 l 1724 227 l 1746 227 l 1769 227 l 1792 227 l 1814 227 l 1837 227 l
+ 1860 227 l 1882 227 l 1905 227 l 1928 227 l 1928 227 l 1950 227 l 1973 227 l
+ 1996 227 l 2019 227 l 2041 227 l s [] 0 sd 227 227 m 227 227 l 249 227 l 272
+ 227 l 295 227 l 318 227 l 340 227 l 363 227 l 386 227 l 408 227 l 408 232 l 431
+ 232 l 431 247 l 454 247 l 454 277 l 476 277 l 476 324 l 499 324 l 499 419 l 522
+ 419 l 522 544 l 544 544 l 544 600 l 567 600 l 567 738 l 590 738 l 590 742 l 612
+ 742 l 612 830 l 635 830 l 635 798 l 658 798 l 658 789 l 680 789 l 680 764 l 703
+ 764 l 703 772 l 726 772 l 726 766 l 748 766 l 748 691 l 771 691 l 771 596 l 794
+ 596 l 794 619 l 816 619 l 816 565 l 839 565 l 839 553 l 862 553 l 862 479 l 885
+ 479 l 885 430 l 907 430 l 907 423 l 930 423 l 930 456 l 953 456 l 953 393 l 975
+ 393 l 975 361 l 998 361 l 998 359 l 1021 359 l 1021 346 l 1043 346 l 1043 329 l
+ 1066 329 l 1066 307 l 1089 307 l 1089 285 l 1111 285 l 1111 294 l 1134 294 l
+ 1134 281 l 1157 281 l 1157 270 l 1179 270 l 1179 260 l 1202 260 l 1202 247 l
+ 1225 247 l 1247 247 l 1247 245 l 1270 245 l 1270 234 l 1293 234 l 1315 234 l
+ 1338 234 l 1361 234 l 1361 244 l 1383 244 l 1383 229 l 1406 229 l 1406 232 l
+ 1429 232 l 1429 229 l 1452 229 l 1452 231 l 1474 231 l 1474 227 l 1497 227 l
+ 1497 229 l 1520 229 l 1520 227 l 1542 227 l 1542 231 l 1565 231 l 1565 229 l
+ 1588 229 l 1610 229 l 1610 227 l 1633 227 l 1656 227 l 1678 227 l 1701 227 l
+ 1724 227 l 1746 227 l 1769 227 l 1792 227 l 1814 227 l 1837 227 l 1860 227 l
+ 1882 227 l 1905 227 l 1928 227 l 1928 227 l 1950 227 l 1973 227 l 1996 227 l
+ 2019 227 l 2041 227 l s [] 0 sd 227 227 m 227 231 l 249 231 l 249 234 l 272 234
+ l 272 249 l 295 249 l 295 266 l 318 266 l 318 270 l 340 270 l 340 300 l 363 300
+ l 363 384 l 386 384 l 386 460 l 408 460 l 408 499 l 431 499 l 431 570 l 454 570
+ l 454 667 l 476 667 l 476 691 l 499 691 l 499 706 l 522 706 l 522 699 l 544 699
+ l 544 706 l 567 706 l 567 660 l 590 660 l 590 671 l 612 671 l 612 585 l 635 585
+ l 635 563 l 658 563 l 658 559 l 680 559 l 680 555 l 703 555 l 703 490 l 726 490
+ l 726 434 l 748 434 l 748 454 l 771 454 l 771 423 l 794 423 l 794 395 l 816 395
+ l 816 393 l 839 393 l 839 389 l 862 389 l 862 331 l 885 331 l 885 348 l 907 348
+ l 907 328 l 930 328 l 930 331 l 953 331 l 953 315 l 975 315 l 975 326 l 998 326
+ l 998 303 l 1021 303 l 1021 309 l 1043 309 l 1043 287 l 1066 287 l 1066 303 l
+ 1089 303 l 1089 313 l 1111 313 l 1111 292 l 1134 292 l 1134 279 l 1157 279 l
+ 1157 272 l 1179 272 l 1179 292 l 1202 292 l 1202 305 l 1225 305 l 1225 257 l
+ 1247 257 l 1247 268 l 1270 268 l 1270 273 l 1293 273 l 1293 268 l 1315 268 l
+ 1315 270 l 1338 270 l 1338 255 l 1361 255 l 1361 259 l 1383 259 l 1383 255 l
+ 1406 255 l 1406 266 l 1429 266 l 1429 249 l 1452 249 l 1452 251 l 1474 251 l
+ 1474 268 l 1497 268 l 1497 244 l 1520 244 l 1520 238 l 1542 238 l 1542 244 l
+ 1565 244 l 1588 244 l 1588 247 l 1610 247 l 1633 247 l 1633 242 l 1656 242 l
+ 1656 238 l 1678 238 l 1678 240 l 1701 240 l 1701 245 l 1724 245 l 1724 244 l
+ 1746 244 l 1746 234 l 1769 234 l 1792 234 l 1814 234 l 1837 234 l 1837 238 l
+ 1860 238 l 1860 236 l 1882 236 l 1882 238 l 1905 238 l 1905 232 l 1928 232 l
+ 1928 232 l 1950 232 l 1950 236 l 1973 236 l 1973 234 l 1996 234 l 2019 234 l
+ 2019 236 l 2041 236 l 2041 227 l s [12 12] 0 sd 227 227 m 227 326 l 249 326 l
+ 249 268 l 272 268 l 272 354 l 295 354 l 295 404 l 318 404 l 318 406 l 340 406 l
+ 340 473 l 363 473 l 363 516 l 386 516 l 386 542 l 408 542 l 408 652 l 431 652 l
+ 431 654 l 454 654 l 454 593 l 476 593 l 476 667 l 499 667 l 499 568 l 522 568 l
+ 522 637 l 544 637 l 544 682 l 567 682 l 567 587 l 590 587 l 590 598 l 612 598 l
+ 612 496 l 635 496 l 635 522 l 658 522 l 658 527 l 680 527 l 680 466 l 703 466 l
+ 703 464 l 726 464 l 726 440 l 748 440 l 748 436 l 771 436 l 771 371 l 794 371 l
+ 794 400 l 816 400 l 816 384 l 839 384 l 839 341 l 862 341 l 862 335 l 885 335 l
+ 885 301 l 907 301 l 907 324 l 930 324 l 930 313 l 953 313 l 953 316 l 975 316 l
+ 975 296 l 998 296 l 998 285 l 1021 285 l 1021 288 l 1043 288 l 1043 279 l 1066
+ 279 l 1066 268 l 1089 268 l 1089 260 l 1111 260 l 1111 283 l 1134 283 l 1134
+ 255 l 1157 255 l 1157 266 l 1179 266 l 1179 255 l 1202 255 l 1202 259 l 1225
+ 259 l 1225 245 l 1247 245 l 1247 251 l 1270 251 l 1270 245 l 1293 245 l 1293
+ 257 l 1315 257 l 1315 251 l 1338 251 l 1338 245 l 1361 245 l 1361 242 l 1383
+ 242 l 1383 255 l 1406 255 l 1406 236 l 1429 236 l 1429 242 l 1452 242 l 1452
+ 249 l 1474 249 l 1474 257 l 1497 257 l 1497 238 l 1520 238 l 1542 238 l 1542
+ 240 l 1565 240 l 1588 240 l 1588 242 l 1610 242 l 1610 244 l 1633 244 l 1633
+ 253 l 1656 253 l 1656 247 l 1678 247 l 1678 245 l 1701 245 l 1701 253 l 1724
+ 253 l 1724 240 l 1746 240 l 1746 238 l 1769 238 l 1769 242 l 1792 242 l 1792
+ 240 l 1814 240 l 1814 249 l 1837 249 l 1837 236 l 1860 236 l 1860 240 l 1882
+ 240 l 1905 240 l 1905 242 l 1928 242 l 1928 240 l 1950 240 l 1950 231 l 1973
+ 231 l 1973 240 l 1996 240 l 1996 247 l 2019 247 l 2019 244 l 2041 244 l 2041
+ 227 l s
+gr gr showpage
+end
+%%EOF
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/tex4ht.env b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/tex4ht.env
new file mode 100644
index 00000000000..4787cd8341c
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/tex4ht.env
@@ -0,0 +1,70 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% tex4ht.env / .tex4ht %
+% %
+% Notes: %
+% 1. empty lines are harmful %
+% 2. place this file in your work %
+% directory and/or root directory %
+% and/or in directory `xxx' of your %
+% choice. In the latest case, compile %
+% tex4ht.c with `#define HTFDIR xxx' %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Replace the directories `candy/...' %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+tcandy/tex/texmf/fonts/tfm/!
+tcandy/tex/texmf/fonts/vf/!
+icandy/tex4ht.dir/
+icandy/tex4ht.dir/ht-fonts/iso88591/!
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% aliases for .htf fonts %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+acmbsy cmsy
+acmbx cmr
+acmitt cmtt
+acmsl cmr
+acmss cmti
+acmtcsc cmtt
+acmtex cmtt
+acmu cmti
+aptmb cmr
+aptmr7 cmr
+aptmri cmti
+% To activate the following aliases,
+% remove the leading space character
+ adcbx ectt
+ adccc ecsx
+ adcit ectt
+ adcr ectt
+ adcsi ecsx
+ adcsl ecsx
+ adcss ecsx
+ adctc ecsx
+ adcti ectt
+ aecbx ec
+ aecsl ec
+ aecsltt ec
+ aectt ec
+ apcrb7t pcrr7t
+ apcrro7t pcrr7t
+ aphvr7t ptmr7t
+ aptmb7t ptmr7t
+ aptmr8t ectt
+ aptmri8t ectt
+ aptmro7t ptmr7t
+ awncyi wncyr
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Default scripts, shifted rightward 1 pos
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+s--- needs --- %%1.idv[%%2] ==> /tmp/%%3 ---
+ b--- characters ---
+ g.gif
+Gdvips -Pem -f %%1 -pp %%2 > tmp.ps
+Gconvert -crop 0x0 -density 110x110 -transparency '#FFFFFF' tmp.ps %%3
+S*
+% t4ht -d%%2
+Mmv %%1 %%2%%3
+Ccp %%1 %%2%%3
+% t4ht -d%%2 -m%%1
+Achmod %%1 %%2%%3
+Hgold/tex4ht.dir/
+
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/tex4ht.tmp b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/tex4ht.tmp
new file mode 100644
index 00000000000..41b58e2cf47
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/tex4ht.tmp
@@ -0,0 +1,2 @@
+
+/* css.sty */ \ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch4/tmp.ps b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/tmp.ps
new file mode 100644
index 00000000000..21e63e4bf00
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch4/tmp.ps
@@ -0,0 +1,542 @@
+%!PS-Adobe-2.0
+%%Creator: dvips(k) 5.85 Copyright 1999 Radical Eye Software
+%%Title: latexexa.idv
+%%Pages: 1
+%%PageOrder: Ascend
+%%BoundingBox: 0 0 596 842
+%%DocumentFonts: EMR10 EMMI7
+%%DocumentPaperSizes: a4
+%%EndComments
+%DVIPSWebPage: (www.radicaleye.com)
+%DVIPSCommandLine: dvips -Pem -f latexexa.idv -pp 66
+%DVIPSParameters: dpi=600, compressed
+%DVIPSSource: TeX output 1999.03.31:0915
+%%BeginProcSet: texc.pro
+%!
+/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
+N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
+mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
+0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
+landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
+mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
+matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
+exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
+statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
+N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
+/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
+/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
+array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
+df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
+definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
+}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
+B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
+1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
+1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
+0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
+sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
+rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
+gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
+/chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
+/cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
+A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
+get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
+ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
+fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
+{2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
+chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
+1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
+forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
+/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
+}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
+bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
+mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
+SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
+userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
+1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
+index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
+/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
+/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
+(LaserWriter 16/600)]{A length product length le{A length product exch 0
+exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
+end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
+grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
+imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
+exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
+fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
+delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
+B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
+p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
+rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end
+
+%%EndProcSet
+%%BeginProcSet: tex256.enc
+% @psencodingfile{
+% author = "Y&Y, Inc.",
+% version = "1.1",
+% date = "1 April 1996",
+% filename = "tex256.enc",
+% email = "tech-help@YandY.com",
+% address = "45 Walden Street // Concord, MA 01742, USA",
+% codetable = "ISO/ASCII",
+% checksum = "xx",
+% docstring = "Encoding for fonts in Adobe Type 1 format for use with TeX."
+% }
+%
+% Character code assignments are those in Cork (T1) encoding
+%
+% SAMPLE USAGE (in `psfonts.map' file for DVIPS):
+%
+% lbr LucidaBright "T1Encoding ReEncodeFont" <tex256.enc <lbr.pfb
+%
+% This tells DVIPS that the font called `lbr' in TeX has PostScript
+% FontName `LucidaBright.' It asks DVIPS to expand the file `lbr.pfb'
+% into PFA form, to include the attached `tex256.enc' encoding vector,
+% and to actually reencode the font based on that encoding vector.
+%
+/T1Encoding [
+/grave % 0
+/acute % 1
+/circumflex % 2
+/tilde % 3
+/dieresis % 4
+/hungarumlaut % 5
+/ring % 6
+/caron % 7
+/breve % 8
+/macron % 9
+/dotaccent % 10
+/cedilla % 11
+/ogonek % 12
+/quotesinglbase % 13
+/guilsinglleft % 14
+/guilsinglright % 15
+
+/quotedblleft % 16
+/quotedblright % 17
+/quotedblbase % 18
+/guillemotleft % 19
+/guillemotright % 20
+/endash % 21
+/emdash % 22
+/cwm % 23 % /bom /zerowidthnobreakspace
+/perthousand % 24 % /perzero (useless)
+/dotlessi % 25
+/dotlessj % 26
+/ff % 27
+/fi % 28
+/fl % 29
+/ffi % 30
+/ffl % 31
+
+/visiblespace % 32 % /visiblespace (useless)
+/exclam % 33
+/quotedbl % 34
+/numbersign % 35
+/dollar % 36
+/percent % 37
+/ampersand % 38
+/quoteright % 39
+/parenleft % 40
+/parenright % 41
+/asterisk % 42
+/plus % 43
+/comma % 44
+/hyphen % 45
+/period % 46
+/slash % 47
+
+/zero % 48
+/one % 49
+/two % 50
+/three % 51
+/four % 52
+/five % 53
+/six % 54
+/seven % 55
+/eight % 56
+/nine % 57
+/colon % 58
+/semicolon % 59
+/less % 60
+/equal % 61
+/greater % 62
+/question % 63
+
+/at % 64
+/A % 65
+/B % 66
+/C % 67
+/D % 68
+/E % 69
+/F % 70
+/G % 71
+/H % 72
+/I % 73
+/J % 74
+/K % 75
+/L % 76
+/M % 77
+/N % 78
+/O % 79
+
+/P % 80
+/Q % 81
+/R % 82
+/S % 83
+/T % 84
+/U % 85
+/V % 86
+/W % 87
+/X % 88
+/Y % 89
+/Z % 90
+/bracketleft % 91
+/backslash % 92
+/bracketright % 93
+/asciicircum % 94
+/underscore % 95 % /underline
+/quoteleft % 96
+/a % 97
+/b % 98
+/c % 99
+/d % 100
+/e % 101
+/f % 102
+/g % 103
+/h % 104
+/i % 105
+/j % 106
+/k % 107
+/l % 108
+/m % 109
+/n % 110
+/o % 111
+
+/p % 112
+/q % 113
+/r % 114
+/s % 115
+/t % 116
+/u % 117
+/v % 118
+/w % 119
+/x % 120
+/y % 121
+/z % 122
+/braceleft % 123
+/bar % 124
+/braceright % 125
+/asciitilde % 126
+/sfthyphen % 127 % /hyphen /dash (hanging hyphen)
+
+/Abreve % 128
+/Aogonek % 129
+/Cacute % 130
+/Ccaron % 131
+/Dcaron % 132
+/Ecaron % 133
+/Eogonek % 134
+/Gbreve % 135
+/Lacute % 136
+/Lcaron % 137 % /Lquoteright
+/Lslash % 138
+/Nacute % 139
+/Ncaron % 140
+/Eng % 141 % /Ng
+/Ohungarumlaut % 142
+/Racute % 143
+
+/Rcaron % 144
+/Sacute % 145
+/Scaron % 146
+/Scedilla % 147 % /Scommaaccent
+/Tcaron % 148
+/Tcedilla % 149 % /Tcommaaccent
+/Uhungarumlaut % 150
+/Uring % 151
+/Ydieresis % 152
+/Zacute % 153
+/Zcaron % 154
+/Zdotaccent % 155
+/IJ % 156
+/Idotaccent % 157
+/dcroat % 158 % /dbar % /dmacron
+/section % 159
+
+/abreve % 160
+/aogonek % 161
+/cacute % 162
+/ccaron % 163
+/dcaron % 164 % /dquoteright
+/ecaron % 165
+/eogonek % 166
+/gbreve % 167
+/lacute % 168
+/lcaron % 169 % /lquoteright
+/lslash % 170
+/nacute % 171
+/ncaron % 172
+/eng % 173 % /ng
+/ohungarumlaut % 174
+/racute % 175
+
+/rcaron % 176
+/sacute % 177
+/scaron % 178
+/scedilla % 179 % /scommaaccent
+/tcaron % 180 % /tquoteright
+/tcedilla % 181 % /tcommaaccent
+/uhungarumlaut % 182
+/uring % 183
+/ydieresis % 184
+/zacute % 185
+/zcaron % 186
+/zdotaccent % 187
+/ij % 188
+/exclamdown % 189
+/questiondown % 190
+/sterling % 191
+
+/Agrave % 192
+/Aacute % 193
+/Acircumflex % 194
+/Atilde % 195
+/Adieresis % 196
+/Aring % 197
+/AE % 198
+/Ccedilla % 199
+/Egrave % 200
+/Eacute % 201
+/Ecircumflex % 202
+/Edieresis % 203
+/Igrave % 204
+/Iacute % 205
+/Icircumflex % 206
+/Idieresis % 207
+
+/Eth % 208
+/Ntilde % 209
+/Ograve % 210
+/Oacute % 211
+/Ocircumflex % 212
+/Otilde % 213
+/Odieresis % 214
+/OE % 215 % UGH multiple in Latin 1
+/Oslash % 216
+/Ugrave % 217
+/Uacute % 218
+/Ucircumflex % 219
+/Udieresis % 220
+/Yacute % 221
+/Thorn % 222
+/SS % 223 % Ugh germandbls in Latin 1
+
+/agrave % 224
+/aacute % 225
+/acircumflex % 226
+/atilde % 227
+/adieresis % 228
+/aring % 229
+/ae % 230
+/ccedilla % 231
+/egrave % 232
+/eacute % 233
+/ecircumflex % 234
+/edieresis % 235
+/igrave % 236
+/iacute % 237
+/icircumflex % 238
+/idieresis % 239
+
+/eth % 240
+/ntilde % 241
+/ograve % 242
+/oacute % 243
+/ocircumflex % 244
+/otilde % 245
+/odieresis % 246
+/oe % 247 % UGH divide in Latin 1
+/oslash % 248
+/ugrave % 249
+/uacute % 250
+/ucircumflex % 251
+/udieresis % 252
+/yacute % 253
+/thorn % 254
+/germandbls % 255 % UGH ydieresis in Latin 1
+] def
+
+%%EndProcSet
+%%BeginProcSet: texps.pro
+%!
+TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
+index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
+exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics
+exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub
+dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def}
+ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict
+end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{
+dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1
+roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def
+dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}
+if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}
+def end
+
+%%EndProcSet
+%%BeginProcSet: special.pro
+%!
+TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
+/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N
+/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N
+/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{
+/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho
+X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
+/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{
+/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known
+{userdict/md get type/dicttype eq{userdict begin md length 10 add md
+maxlength ge{/md md dup length 20 add dict copy def}if end md begin
+/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S
+atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{
+itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll
+transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
+curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf
+pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}
+if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1
+-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3
+get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip
+yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub
+neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{
+noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop
+90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get
+neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr
+1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr
+2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4
+-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S
+TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{
+Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale
+}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState
+save N userdict maxlength dict begin/magscale true def normalscale
+currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts
+/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x
+psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx
+psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub
+TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{
+psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2
+roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath
+moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict
+begin/SpecialSave save N gsave normalscale currentpoint TR
+@SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{
+CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto
+closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx
+sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR
+}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse
+CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury
+lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N
+/@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end}
+repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N
+/@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX
+currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY
+moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X
+/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0
+1 startangle endangle arc savematrix setmatrix}N end
+
+%%EndProcSet
+%%BeginFont: EMMI7
+%!PS-AdobeFont-1.1: EMMI7 001.103
+%%CreationDate: 1997 Mar 16 07:49:05
+%%RevisionDate: 1997 Jul 25 05:43:12
+
+% Copyright (C) 1996, 1997 Y&Y, Inc. All Rights Reserved.
+% Notice: This font is not in the public domain.
+% Notice: European Modern is a trademark of Y&Y, Inc.
+
+11 dict begin
+/FontInfo 9 dict dup begin
+/version (001.103) readonly def
+/Notice (Copyright (c) 1992--1997 Y&Y, Inc. All Right Reserved. http://www.YandY.com) readonly def
+/FullName (EMMI7) readonly def
+/FamilyName (European Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.036 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/FontName /EMMI7 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 20 /kappa put
+readonly def
+/FontBBox{0 -250 1171 750}readonly def
+/UniqueXX 5092826
+currentdict end
+currentfile eexec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+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont
+TeXDict begin 39158280 55380996 1000 600 600 (latexexa.idv)
+@start /Fa 235[39 20[{}1 58.1154 /EMMI7 rf end
+%%EndProlog
+%%BeginSetup
+%%Feature: *Resolution 600dpi
+TeXDict begin
+%%BeginPaperSize: a4
+a4
+%%EndPaperSize
+
+%%EndSetup
+%%Page: 66 1
+66 0 bop 1432 2628 a Fa(\024)p eop
+%%Trailer
+end
+userdict /end-hook known{end-hook}if
+%%EOF