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Diffstat (limited to 'Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex')
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1 files changed, 13 insertions, 13 deletions
diff --git a/Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex b/Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex index c06b7e5d58a..d7fdeeec58e 100644 --- a/Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex +++ b/Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex @@ -23,30 +23,30 @@ energy transfer in a single collision with an atomic electron: \graffito{You might get unexpected results using math in chapter or section heads. Consider the \texttt{pdfspacing} option.} \begin{equation} -\kappa =\frac{\xi}{E_{\mathrm{max}}} %\mathbb{ZNR} +\kappa =\frac{\xi}{E_{\textrm{max}}} %\mathbb{ZNR} \end{equation} -$E_{\mathrm{max}}$ is the maximum transferable energy in a single +$E_{\textrm{max}}$ is the maximum transferable energy in a single collision with an atomic electron. \[ -E_{\mathrm{max}} =\frac{2 m_{\mathrm{e}} \beta^2\gamma^2 }{1 + -2\gamma m_{\mathrm{e}}/m_{\mathrm{x}} + \left ( m_{\mathrm{e}} -/m_{\mathrm{x}}\right)^2}\ , +E_{\textrm{max}} =\frac{2 m_{\textrm{e}} \beta^2\gamma^2 }{1 + +2\gamma m_{\textrm{e}}/m_{\textrm{x}} + \left ( m_{\textrm{e}} +/m_{\textrm{x}}\right)^2}\ , \] -where $\gamma = E/m_{\mathrm{x}}$, $E$ is energy and -$m_{\mathrm{x}}$ the mass of the incident particle, -$\beta^2 = 1 - 1/\gamma^2$ and $m_{\mathrm{e}}$ is the electron mass. +where $\gamma = E/m_{\textrm{x}}$, $E$ is energy and +$m_{\textrm{x}}$ the mass of the incident particle, +$\beta^2 = 1 - 1/\gamma^2$ and $m_{\textrm{e}}$ 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_{\mathrm{Av}} Z \rho -\delta x}{m_{\mathrm{e}} \beta^2 c^2 A} = 153.4 \frac{z^2}{\beta^2} +\begin{eqnarray*} \xi = \frac{2\pi z^2 e^4 N_{\textrm{Av}} Z \rho +\delta x}{m_{\textrm{e}} \beta^2 c^2 A} = 153.4 \frac{z^2}{\beta^2} \frac{Z}{A} - \rho \delta x \quad\mathrm{keV}, + \rho \delta x \quad\textrm{keV}, \end{eqnarray*} where \begin{tabular}{ll} $z$ & charge of the incident particle \\ -$N_{\mathrm{Av}}$ & Avogadro's number \\ +$N_{\textrm{Av}}$ & Avogadro's number \\ $Z$ & atomic number of the material \\ $A$ & atomic weight of the material \\ $\rho$ & density \\ @@ -54,7 +54,7 @@ $ \delta x$ & thickness of the material \\ \end{tabular} $\kappa$ measures the contribution of the collisions with energy -transfer close to $E_{\mathrm{max}}$. For a given absorber, $\kappa$ +transfer close to $E_{\textrm{max}}$. 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 |