Let us suppose an infinite homogeneous mixture of moderator and resonance absorber. Above the resonances the flux will be ф(Е) = ЦЕ (see § 6.1). The reaction rate within a resonance is

/ = J (Та(Е)ф(Е) dE resonance integral,

a resonance integral I, can be defined for each resonance i.

In the resonance region, because of the neutron absorption the flux will not in general follow the ЦЕ behaviour, except if the concentration of resonance absorber is

negligible (infinite dilution). In that case we have

infinite dilution resonance integral

where и is the lethargy.

For multi-group calculations the cross-section for group g is given by

If the flux over the group interval can still be considered to have 1 IE behaviour, considering that

f <t>(E)dE= f Щ=А щ

J A Eg J AEK LL

eqn. (7.1) becomes

If more resonances are included in the energy range of group g their contributions to Is have to be added.

The flux in the resonance region in an homogeneous infinite mixture of moderator and resonance absorber with a homogeneously distributed source of fission neutrons of energy well above the resonance range is given by the slowing-down eqn. (6.7) which in this case takes the formt

where 1 indicates moderator and 0 absorber.

For numerical reasons this equation is usually rewritten in terms of the collision

de"Si, V F(E)-*(£)*,№) and instead of E the lethargy is used as a variable.

It is always possible to solve numerically this equation obtaining the resonance integral and effective group cross sections as in eqn. (7.1) assuming а ЦЕ flux above the resonance region.