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author | Karl Berry <karl@freefriends.org> | 2009-05-23 00:23:51 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2009-05-23 00:23:51 +0000 |
commit | a683c3d7e9fac38ec713f23fb6b9d2c7143aea82 (patch) | |
tree | 424ab223921f85fd3f167a4ccd0e2d37d05c2927 /Master/texmf-dist/doc/latex/latex-web-companion/apa/latexexa.xml | |
parent | 5beb5368a684995153c8566797ba054f21c666af (diff) |
move english latex doc out of texmf-doc
git-svn-id: svn://tug.org/texlive/trunk@13412 c570f23f-e606-0410-a88d-b1316a301751
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diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/apa/latexexa.xml b/Master/texmf-dist/doc/latex/latex-web-companion/apa/latexexa.xml new file mode 100644 index 00000000000..9d23dd47752 --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/apa/latexexa.xml @@ -0,0 +1,171 @@ +<?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> |