10.1} Multigroup neutron transport

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 Transport of neutrons with energies lower than a certain energy is performed
 in FLUKA by a multigroup algorithm.
 The energy boundary below which multigroup transport takes over depends in
 principle on the cross section library used. This energy is 20 MeV for the
 260-group library which is distributed with the code.
 In FLUKA, internally there are two neutron energy thresholds: one for
 high-energy neutrons and one for low-energy neutrons. The high-energy neutron
 threshold represents in fact the energy boundary between continuous and
 discontinuous neutron transport. Starting from this release, the former is
 computed automatically on the basis of the user inputs with options PART-THR
 and/or LOW-BIAS. Please note that PART-THR no longer controls the transition
 energy between model and group tretaments for neutrons, but rather it sets
 the actual lower threshold for neutron transport, regardless if it falls
 in the group regime or not.

 The multi-group technique, widely used in low-energy neutron transport
 programs, consists in dividing the energy range of interest into a
 given number of intervals ("energy groups"). Elastic and inelastic reactions
 are simulated not as exclusive processes, but by group-to-group transfer
 probabilities forming a so-called "downscattering matrix".

 The scattering transfer probability between different groups is
 represented by a Legendre polynomial expansion truncated at the
 (N+1)th term, as shown in the equation:

  Sigma_s(g-->g',mu) = Sum_{i=0,N}(2i+1)/(4pi) P_i(mu) Sigma_i(g-->g')

 where mu = Omega.Omega' is the scattering angle and N is the chosen
 Legendre order of anisotropy.

 The particular implementation used in FLUKA has been derived from that of the
 MORSE program [Emm75] (although the relevant part of the code has been
 completely rewritten). In the FLUKA neutron cross section library, the energy
 range up to 20 MeV is divided into 260 energy groups of  approximately equal
 logarithmic width (31 of which are thermal).
 The angular probabilities for inelastic scattering are obtained by a
 discretisation of a P5 Legendre polynomial expansion of the actual scattering
 distribution which preserves its first 6 moments. The generalised Gaussian
 quadrature scheme to generate the discrete distribution is rather complicated:
 details can be found in the MORSE manual [Emm75]. The result, in the case of a
 P5 expansion, is a set of 6 equations giving 3 discrete polar angles (actually
 angle cosines) and 3 corresponding cumulative probabilities.

 In the library, the first cross section table for an isotope (isotropic
 term P_0) contains the transfer probabilities from each group g to
 any group g': Sum_{g-->g'}/Sum_g, where Sum_g is the sum over all the
 g' (including the "in-scattering" term g' = g). The next cross section
 table provides the P_1 term for the same isotope, the next the P_2
 multigroup cross sections, etc.

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