\sigma_g, \sigma_{\ell g \leftarrow g^{\prime}}, \bar{\nu}_g \sigma_{fg},
and
\chi_g,
The SN codes also traditionally use a particle-balance cross section (often loosely called ``absorption'') defined by
\sigma_{ag} = \sigma_g - \sum_{g^{\prime}} \sigma_{0g^{\prime}\leftarrow g}~~.
This quantity is also computed by TRANSX by adding all the absorption reactions [$(n,\gamma)$, fission, $(n,p)$, $(n,\alpha)$, {\it etc}.] and subtracting $(n,2n)$, twice $(n,3n)$, and so on. The two methods are formally equivalent, except that small numerical differences due to cross-section processing lead to unreasonable values for $\sigma_{ag}$, as computed from Eq.~(\ref{eq223}), when $\sigma_{ag}$ is small with respect to $\sigma_g$. In such cases, $\sigma_{ag}$ is replaced by the value from the direct calculation, and the $\sigma_g$ position of the transport table is adjusted accordingly. Note that $\sigma_{ag}$ can be negative if more particles are produced by $(n,xn)$ reactions than are absorbed. Negative values occur in coupled sets as well, as will be seen below.
When the flux calculation is complete, it is often necessary to compute some response such as heating, radiation damage, gas production, photon production, or dose to tissue. Therefore, SN codes allow for reading several response-function edit cross sections, $\sigma_{Eg}$.
The original SN codes read $\chi$ as a special array, and the cross sections were arranged into ``transport tables'' by ``position'' as shown below. Note that the positions containing scattering data give all the source groups that scatter into the same final or ``sink'' group. Even the newer codes retain many features of this structure, and TRANSX input uses terminology based on the table.
A transport table like this is required for each group, Legendre order, and material. The tables may be material ordered or group ordered.
---------------------------------------------------------------------
Position Contents for Group g
---------------------------------------------------------------------
1
... $\sigma_{Eg}$ Response edits
NED
---------- -------------------------- ---------------------
NED+1 $\sigma_{ag}$
NED+2 $\bar{\nu}_g \sigma_{fg}$ Standard edits
NED+3 $\sigma_g$
---------- -------------------------- ---------------------
NED+4
... $\sigma_{g \leftarrow g'}$ Upscatter (g'.gt.g)
NED+NUP+3
---------- -------------------------- ---------------------
NED+NUP+4 $\sigma_{g \leftarrow g'}$ In-group (g'=g)
---------- -------------------------- ---------------------
NED+NUP+5
... $\sigma_{g \leftarrow g'}$ Downscatter (g'.lt.g)
NTABL
---------------------------------------------------------------------
NED = number of extra response edits (NED$\geq$0)
UP = maximum number of upscatter groups (0$\leq$NUP$\leq$NGROUP)
NTABL = table length (NED+4+NUP$\leq$NTABL$\leq$NED+4+NUP+NGROUP)
NGROUP = number of energy groups
IPTOT = NED+3 = position of total cross section
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