Coarse group flux
\phi_{\ell G} = \sum_{g\in G}\,\phi_{\ell g}~~,
Absorption, $\bar{\nu}\sigma_f$, and edit cross sections
\sigma_{xG} = \sum_{g\in G} \sigma_{xg} \frac{\phi_{0g}}{\phi_{0G}}~~,
Transport cross section for leakage calculation
\sigma_{trG}^{PN} = \sum_{g\in G} \sigma_{trg}^{PN} \frac{\phi_{1g}}{\phi_{1G}}~~,
P$_{\ell}$-weighted total cross section
\sigma_{\ell tG}^{PN} = \sum_{g \in G} \sigma_{\ell tg}^{PN} \frac{\phi_{\ell g}}{\phi_{\ell G}}~~,
Scattering matrix cross sections
\sigma_{\ell G \leftarrow G^\prime}^{PN} = \sum_{g \in G} \,\sum_{g^\prime \in G^\prime}\, \sigma_{\ell g^\prime \leftarrow g}^{PN} \frac{\phi_{\ell g^\prime}}{\phi_{\ell G^\prime}}~~,
and
Steady-state and delay fission spectrum $\chi$
\chi_G = \displaystyle{\sum_{g \epsilon G}}\chi_g~~.
The coarse-group SN equations can be derived from the coarse-group PN equations; therefore, Eqs.~(\ref{eq27}) through (\ref{eq213}) apply with $g$ replaced by $G$. The flux components can be read in from some previous calculation or generated from the model weight function used to generate the MATXS library with
\phi_{\ell g} = \frac{C_g}{\displaystyle{\Pi^{\ell}_{k=0}} [\sigma_{0g} + \sigma_{ktg}]}~~.
In practice only $k{=}0$ and $k{=}1$ are available on the MATXS library, and $k{=}1$ is used for all higher orders.
Note that there are four different uses for input fluxes in TRANSX: (1) collapse, (2) fission $\chi$, (3) transport cross section and (4) elastic scattering corrections.
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