The multigroup scheme adopted in FLUKA is reliable and much faster than any possible approach using continuous cross sections. However, it is important to remember that there are two rare situations where the group approximation could give bad results. One of such situations may occur when each neutron is likely to scatter only once (e.g. in a very thin foil) before being scored: an artefact then is possible, due to the discrete angular distribution. In practice the problem vanishes entirely, however, as soon as there is the possibility of two or more scatterings: it must be kept in mind, in fact, that after a collision only the polar angle is sampled from a discrete distribution, while the azimuthal angle is chosen randomly from a uniform distribution. In addition, the 3 discrete angles are different for each g --> g' combination and for each element or isotope. Thus, any memory of the initial direction is very quickly lost after just a few collisions. The second possible artefact is not connected with the angular but with the energy structure of the cross sections used. The group structure is necessarily coarse with respect to the resonance structure in many materials. A resonance in a material present in a dilute mixture or as a small piece cannot affect much a smooth neutron fluence (case of so-called "infinite dilution") but if an isotope is very pure and is present in large amounts, it can act as a "neutron sink", causing sharp dips in the neutron spectrum corresponding to each resonance. This effect, which results in a lower reaction rate sigma*phi, is called "self-shielding" and is necessarily lost in the process of cross section averaging over the width of each energy group, unless a special correction is made. Such corrected cross section sets with different degrees of self-shielding have been included in the FLUKA libraries for a few important elements (Al, Fe, Cu, Au, Pb, Bi): but it is the responsibility of the user to select the set with the degree of self-shielding most suitable in each different case. It is worth stressing that non-self-shielded materials are perfectly adequate in most practical cases, because the presence of even small amounts of impurities is generally sufficient to smooth out the effect. On the other hand, in regions of non-resolved resonances the multigroup approach is known to give very good results anyway.
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