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Update docs for EGSnrc 2025 release
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48 changes: 48 additions & 0 deletions doc/pirs3100/formula.repository
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\form#0:$\overline{g}$
\form#1:$\textrm{K}$
\form#2:$\textrm{K}_\mathrm{col}$
\form#3:$\overline{\mu}_\mathrm{tr}/\rho$
\form#4:$\overline{\mu}_\mathrm{en}/\rho$
\form#5:$\mu_\mathrm{en}$
\form#6:$\mu_\mathrm{en}/\rho$
\form#7:$\mu_\mathrm{tr}/\rho$
\form#8:$\sigma$
\form#9:$T_0$
\form#10:$\overline{E}_\mathrm{rad}$
\form#11:\begin{equation} Y = \frac{\overline{E}_\mathrm{rad}}{T_0}. \end{equation}
\form#12:$Y_\mathrm{brems}$
\form#13:$\overline{E}_\mathrm{tot}$
\form#14:$T(E)$
\form#15:$\overline{T}$
\form#16:\begin{equation}\label{def_mutr} \left(\frac{\mu_\mathrm{tr}}{\rho}\right) = \frac{\overline{E}_\mathrm{tr}}{E} \cdot \left(\frac{\mu}{\rho}\right), \end{equation}
\form#17:$\overline{E}_\mathrm{tr}$
\form#18:$\mu/\rho$
\form#19:\begin{equation}\label{def_muen} \left(\frac{\mu_\mathrm{en}}{\rho}\right) = \left(1-\overline{g}\right) \cdot \left(\frac{\mu_\mathrm{tr}}{\rho}\right) = \frac{\overline{E}_\mathrm{ab}}{E} \cdot \left(\frac{\mu}{\rho}\right), \end{equation}
\form#20:$\overline{E}_\mathrm{ab}$
\form#21:$\overline{\overline{E}}_\mathrm{rad}$
\form#22:\begin{equation}\label{eq_g_mono} \overline{g} = \frac{\overline{\overline{E}}_\mathrm{rad}}{\overline{E}_\mathrm{tr}}, \end{equation}
\form#23:\begin{equation}\label{EradP} \overline{\overline{E}}_\mathrm{rad} = \overline{E}_\mathrm{tr} - \overline{E}_\mathrm{ab}. \end{equation}
\form#24:\begin{equation}\label{eq:K} \frac{K}{\phi} = E \cdot \left(\mu_\mathrm{tr}/\rho\right), \end{equation}
\form#25:\begin{equation}\label{eq:Kcol} \frac{K_\mathrm{col}}{\phi} = E \cdot \left(\mu_\mathrm{en}/\rho\right). \end{equation}
\form#26:\begin{equation}\label{eq:def} \frac{K}{\phi} = \int \phi(E) \cdot E \cdot \left[\frac{\mu_\mathrm{tr}(E)}{\rho}\right] \cdot dE/\int \phi(E) \cdot dE. \end{equation}
\form#27:\begin{equation}\label{eq:Kpoly} \frac{K}{\phi} = \left<\mu_\mathrm{tr}/\rho\right>_{\psi} \cdot \left<E\right>_{\phi} = \left<E\cdot\mu_\mathrm{tr}/\rho\right>_{\phi}. \end{equation}
\form#28:$\mu_\mathrm{tr}$
\form#29:\begin{equation}\label{eq:Kpolycol}\label{eq_kerma_0} \frac{K_\mathrm{col}}{\phi} = \left<\mu_\mathrm{en}/\rho\right>_{\psi} \cdot \left<E\right>_{\phi} = \left<E\cdot\mu_\mathrm{en}/\rho\right>_{\phi}. \end{equation}
\form#30:\begin{equation}\label{eq_kerma_1} \frac{K_\mathrm{col}}{\phi} = \left(1-\overline{g}\right) \frac{K}{\phi} = \left(1-\overline{g}\right) \left<E\cdot\mu_\mathrm{tr}/\rho\right>_{\phi}, \end{equation}
\form#31:\begin{equation} \overline{g} = 1 - \frac{\left<E\cdot\mu_\mathrm{en}\right>_{\phi}}{\left<E\cdot\mu_\mathrm{tr}\right>_{\phi}}, \end{equation}
\form#32:\begin{equation}\label{eq:g} \overline{g} = 1 - \frac{\left<\overline{E}_\mathrm{en}\cdot\mu\right>_{\phi}}{\left<\overline{E}_\mathrm{tr}\cdot\mu\right>_{\phi}} = \frac{\left<\overline{\overline{E}}_\mathrm{rad}\cdot\mu\right>_{\phi}}{\left<\overline{E}_\mathrm{tr}\cdot\mu\right>_{\phi}} \end{equation}
\form#33:$\left<\mu_\mathrm{tr}/\rho\right>_{\psi}$
\form#34:\begin{equation} \left<\mu_\mathrm{tr}/\rho\right>_{\psi} = \frac{\left<E\cdot\mu_\mathrm{tr}/\rho\right>_{\phi}}{\left<E\right>_{\phi}} = \frac{\left<\overline{E}_\mathrm{tr}\cdot\mu\right>_{\phi}}{\left<E\right>_{\phi}}, \end{equation}
\form#35:$\left<\mu_\mathrm{en}/\rho\right>_{\psi}$
\form#36:\begin{equation}\label{eq_muen_0} \left<\mu_\mathrm{en}/\rho\right>_{\psi} = \frac{\left<E\cdot\mu_\mathrm{en}/\rho\right>_{\phi}}{\left<E\right>_{\phi}} = \frac{\left<\overline{E}_\mathrm{en}\cdot\mu\right>_{\phi}}{\left<E\right>_{\phi}}, \end{equation}
\form#37:\begin{equation}\label{eq_muen_1} \left<\mu_\mathrm{en}/\rho\right>_{\psi} = \left(1-\overline{g}\right) \left<\mu_\mathrm{tr}/\rho\right>_{\psi}, \end{equation}
\form#38:$\sigma/\sqrt{4/3}$
\form#39:$\sigma/2$
\form#40:$E$
\form#41:$q$
\form#42:$\Delta\mathrm{E}$
\form#43:$E_\mathrm{min}, ..., E_\mathrm{min} + i \cdot \Delta\mathrm{E}, ..., E_\mathrm{max}$
\form#44:$\Delta_\mathrm{log}$
\form#45:\begin{equation} \Delta_\mathrm{log} = log\left(\frac{E_\mathrm{max}}{E_\mathrm{min}}\right)/\left(N-1\right) \end{equation}
\form#46:\begin{equation} E_i = e^{log(E_\mathrm{min})+i \cdot \Delta_\mathrm{log}} \end{equation}
\form#47:\begin{equation} \sigma(\mu_\mathrm{tr}) = \frac{\sigma}{\sqrt{m}} \qquad \textrm{and} \qquad \sigma(1-\overline{g}) = \frac{\sigma}{\sqrt{m/(m-1)}} \end{equation}
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