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diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/apa/latexexa.ltx b/Master/texmf-dist/doc/latex/latex-web-companion/apa/latexexa.ltx deleted file mode 100644 index 2e334aa4cc5..00000000000 --- a/Master/texmf-dist/doc/latex/latex-web-companion/apa/latexexa.ltx +++ /dev/null @@ -1,109 +0,0 @@ -\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}} -\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. - -....... - -\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). -.... - -\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} |