Grouping and collapsing data dependent on incident and outgoing energies

This section discusses grouping and collapsing of transfer and fission matrix data. These data are dependent on both incident and outgoing particles' energies. Grouping and collapsing of transfer matrix data are more complicated than is presented here, since either particle number, energy, or number-and-energy of the outgoing particles is conserved during the grouping and collapsing. In this section only particle conserving grouping and collapsing will be discussed. A full discussion of grouping and collapsing of the transfer matrix data can be found in Chapter VI and pages VII-19 to VII-23 of reference [1] and in reference [2].

If M(E, E') is a quantity that is dependent on incident E and outgoing E' energies and f^l(E) is the l-order Legendre flux then the l-order Legendre particle-conserving grouped matrix M_{g, h}^l is calculated as,

$${\displaystyle \int_{E_{g+1}}^{E_g} \int_{E'_{h+1}}^{E'_h} f^l(E) \, M^l(E,E') \, dE \, dE'\over \displaystyle \int_{E_{g+1}}^{E_g} f^l(E) \, dE}$$ (14)

Collapsing this data to new incident and outgoing particle groups, label as g' and h', is calculated as,

$${\displaystyle \sum_{g \in g'} \sum_{h \in h'} \varphi^l_g \, M^l_{g,h} \over \displaystyle \sum_{g \in g'} \varphi^l_g}$$ (15)

Here g $\in$ g' means to sum over all g for which the boundaries of g fall inclusively between the boundaries of g' and h $\in$ h' means to sum over all h for which the boundaries of h fall inclusively between the boundaries of h' except that the end points of h' are extended to include the end points of h so as to conserve outgoing particle number. For example, collapsing the outgoing particle's group from (20.0, 15.0, 12.3, 0.1) to (20.0, 15.0, 12.3) will result in the outgoing particle's collapse group being (20.0, 15.0, 0.1) when collapsing. The incident particle's collapse group is set by calling ndfgroup or ndfcgroup. For the interaction transfer matrix data and the fission transfer matrix data the outgoing particle's collapse group is also that set by calling ndfgroup or ndfcgroup. For transfer matrix data for y_i$\ne$y_o the outgoing particle's collapse group is specified through arguments to the routines dfpmat and ndfcpmat.