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diff --git a/Master/texmf-doc/doc/english/latex-web-companion/apa/latexexa.xml b/Master/texmf-doc/doc/english/latex-web-companion/apa/latexexa.xml deleted file mode 100644 index 9d23dd47752..00000000000 --- a/Master/texmf-doc/doc/english/latex-web-companion/apa/latexexa.xml +++ /dev/null @@ -1,171 +0,0 @@ -<?xml version="1.0"?> -<!DOCTYPE document SYSTEM "latexexa.dtd" []> -<document> -<frontmatter> - <title>Simulation of Energy Loss Straggling</title> - <author>Maria Physicist</author> - <date>January 14, 1999</date> -</frontmatter> -<bodymatter> -<section id="intro"> <stitle>Introduction</stitle> -<par>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 <inlinemath> -<math><mi>κ</mi></math></inlinemath>, which is proportional to -the ratio of mean energy loss to the maximum allowed energy transfer -in a single collision with an atomic electron - -<displaymath><math><mrow> -<mi>κ</mi><mo>=</mo> <mfrac> <mrow> -<mi>ξ</mi></mrow><mrow><msub><mi>E</mi><mrow><mi>max </mi> </mrow> -</msub> </mrow> </mfrac> </mrow></math></displaymath> - -<inlinemath><math><msub><mi>E</mi><mrow><mi>max </mi> </mrow> </msub> -</math></inlinemath> is the maximum transferable energy in a single -collision with an atomic electron. - -.... - -</section> -<section id="vavref"><stitle>Vavilov theory</stitle> -<par>Vavilov<cite refid="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 -<inlinemath> <math><msub><mi>E</mi><mrow><mi>max </mi> </mrow> </msub> -<mo>=</mo><mi>∞</mi></math></inlinemath>. Now we can write<cite -refid="bib-SCH1"/>: <eqnarray><subeqn><math><mi>f</mi> <mfenced -open='(' -close=')'><mi>ε</mi><mo>,</mo><mi>δ</mi><mi>s</mi></mfenced> -<mo>=</mo> -<mfrac><mrow><mn>1</mn></mrow><mrow><mi>ξ</mi></mrow></mfrac> -<msub><mi>φ</mi><mrow><mi>v</mi></mrow> -</msub> <mfenced open='(' -close=')'><msub><mi>λ</mi><mrow><mi>v</mi></mrow> </msub> -<mo>,</mo><mi>κ</mi><mo>,</mo><msup><mi>β</mi><mrow><mn>2</mn> -</mrow> </msup> </mfenced> <mtext></mtext> </math></subeqn></eqnarray> -where -<eqnarray><subeqn><math><msub><mi>φ</mi><mrow><mi>v</mi></mrow> -</msub> <mfenced open='(' -close=')'><msub><mi>λ</mi><mrow><mi>v</mi></mrow> </msub> -<mo>,</mo><mi>κ</mi><mo>,</mo><msup><mi>β</mi><mrow><mn>2</mn> -</mrow> </msup> </mfenced> <mo>=</mo> -<mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi></mrow> -</mfrac><msubsup><mo>∫</mo> -<mrow><mi>c</mi><mo>+</mo><mi>i</mi><mi>∞</mi></mrow> -<mrow><mi>c</mi><mo>-</mo><mi>i</mi><mi>∞</mi> -</mrow></msubsup><mi>φ</mi><mfenced -open='(' -close=')'><mi>s</mi></mfenced><msup><mi>e</mi><mrow><mi>λ</mi><mi>s</mi> -</mrow> </msup> <mi>d</mi><mi>s</mi><mspace -width='2cm'/><mi>c</mi><mo>≥</mo><mn>0</mn> <mtext></mtext> -</math></subeqn><subeqn><math> </math></subeqn><subeqn -><math><mi>φ</mi><mfenced open='(' close=')'><mi>s</mi></mfenced> -<mo>=</mo> <mo>exp</mo><mfenced open='[' -close=']'><mi>κ</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo> -<msup><mi>β</mi><mrow><mn>2</mn> -</mrow> </msup> -<mi>γ</mi><mo>)</mo></mrow></mfenced><mo>exp</mo><mfenced -open='[' close=']'><mi>ψ</mi> <mfenced open='(' -close=')'><mi>s</mi></mfenced></mfenced><mo>,</mo> <mtext></mtext> -</math></subeqn><subeqn><math> </math></subeqn><subeqn -><math><mi>ψ</mi> <mfenced open='(' close=')'><mi>s</mi></mfenced> -<mo>=</mo> <mi>s</mi><mo>ln</mo> -<mi>κ</mi><mo>+</mo><mrow><mo>(</mo><mi>s</mi><mo>+</mo><msup> -<mi>β</mi><mrow><mn>2</mn> -</mrow> </msup> <mi>κ</mi><mo>)</mo></mrow><mfenced open='[' -close=']'><mo>ln</mo> -<mrow><mo>(</mo><mi>s</mi><mo>/</mo><mi>κ</mi><mo>)</mo></mrow> -<mo>+</mo><msub><mi>E</mi><mrow> -<mn>1</mn> </mrow> </msub> -<mrow><mo>(</mo><mi>s</mi><mo>/</mo><mi>κ</mi><mo>)</mo> -</mrow></mfenced><mo>-</mo><mi>κ</mi><msup><mi>e</mi><mrow> -<mo>-</mo><mi>s</mi><mo>/</mo><mi>κ</mi> -</mrow> </msup> <mo>,</mo> <mtext></mtext> </math></subeqn></eqnarray> -and <eqnarray><subeqn><math><msub><mi>E</mi><mrow><mn>1</mn> </mrow> -</msub> <mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow> -<mo>=</mo><msubsup> <mo>∫</mo> -<mrow><mi>∞</mi></mrow><mrow><mi>z</mi></mrow></msubsup> -<msup><mi>t</mi><mrow><mo>-</mo><mn>1</mn> -</mrow> </msup> <msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi> </mrow> -</msup> <mi>d</mi><mi>t</mi><mspace width='1cm'/><mtext>(the -exponential integral)</mtext> <mtext></mtext> </math></subeqn><subeqn -><math> </math></subeqn><subeqn -><math><msub><mi>λ</mi><mrow><mi>v</mi></mrow> </msub> -<mo>=</mo> <mi>κ</mi><mfenced open='[' -close=']'><mfrac><mrow><mi>ε</mi><mo>-</mo><munderover -accent='true'><mi>ε</mi><mrow></mrow><mo>⌅</mo></munderover> -</mrow> <mrow><mi>ξ</mi></mrow></mfrac> -<mo>-</mo><mi>γ</mi><mi>′</mi> -<mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn> </mrow> </msup> -</mfenced> <mtext></mtext> </math></subeqn></eqnarray> -</par> -<par>The Vavilov parameters are simply related to the Landau parameter -by <inlinemath><math><msub><mi>λ</mi><mrow><mi>L</mi> </mrow> -</msub> <mo>=</mo><msub><mi>λ</mi><mrow><mi>v</mi></mrow> -</msub> <mo>/</mo><mi>κ</mi><mo>-</mo><mo>ln</mo> -<mi>κ</mi></math></inlinemath>. It can be shown that as -<inlinemath> <math> -<mi>κ</mi><mo>→</mo><mn>0</mn></math></inlinemath>, the -distribution of the variable <inlinemath> <math> -<msub><mi>λ</mi><mrow><mi>L</mi> </mrow> </msub> -</math></inlinemath> approaches that of Landau. For <inlinemath> -<math> -<mi>κ</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>1</mn> -</math></inlinemath> -the two distributions are already practically identical. Contrary to -what many textbooks report, the Vavilov distribution <emph> does -not</emph> approximate the Landau distribution for small -<inlinemath><math><mi>κ</mi></math></inlinemath>, but rather the -distribution of <inlinemath> <math> -<msub><mi>λ</mi><mrow><mi>L</mi> </mrow> </msub> -</math></inlinemath> defined above tends to the distribution of the -true <inlinemath><math><mi>λ</mi></math></inlinemath> from the -Landau density function. Thus the routine <texttt> GVAVIV</texttt> -samples the variable <inlinemath> -<math><msub><mi>λ</mi><mrow><mi>L</mi> </mrow> </msub> -</math></inlinemath> rather than <inlinemath> <math> -<msub><mi>λ</mi><mrow><mi>v</mi></mrow> </msub> -</math></inlinemath>. For <inlinemath> <math> -<mi>κ</mi><mo>≥</mo><mn>1</mn><mn>0</mn></math></inlinemath> -the Vavilov distribution tends to a Gaussian distribution (see next -section). </par> -</section> -..... -</section> -<section class="star"><stitle>References</stitle> -<bibliography> -<bibitem id="bib-LAND"> -<par>L.Landau. On the Energy Loss of Fast Particles by -Ionisation. Originally published in <emph>J. Phys.</emph>, 8:201, -1944. Reprinted in D.ter Haar, Editor, <emph>L.D.Landau, Collected -papers</emph>, page 417. Pergamon Press, Oxford, 1965. </par> -</bibitem> -<bibitem id="bib-SCH1"> -<par>B.Schorr. Programs for the Landau and the Vavilov distributions -and the corresponding random numbers. <emph>Comp. Phys. Comm.</emph>, -7:216, 1974. </par> -</bibitem> -<bibitem id="bib-SELT"> -<par>S.M.Seltzer and M.J.Berger. Energy loss straggling of protons and -mesons. In <emph>Studies in Penetration of Charged Particles in -Matter</emph>, Nuclear Science Series 39, Nat. Academy of Sciences, -Washington DC, 1964. </par> -</bibitem> -<bibitem id="bib-TALM"> -<par>R.Talman. On the statistics of particle identification using -ionization. <emph>Nucl. Inst. Meth.</emph>, 159:189, 1979. </par> -</bibitem> -<bibitem id="bib-VAVI"> -<par>P.V.Vavilov. Ionisation losses of high energy heavy -particles. <emph>Soviet Physics JETP</emph>, 5:749, 1957.</par> -</bibitem> -</bibliography> -</section> -</bodymatter> -</document> |