We have derived from the Boltzmann equation a new integral equation governing the slowing down of neutrons in a lump, assuming a spatially-uniform neutron flux inside it. In the first approximation we have solved the equation using the asymptotic energy dependence of the neutron flux and proposed a new resonance integral formula. In the limit of both the narrow resonance and the wide resonance, the formula tends to be equal to that derived in the conventional narrow and wide resonance approximations. In the second approximation we calculated effects of the deviation of the Placzek function from its asymptotic form by a method similar to that used by Weinberg and Wigner for homogeneous systems.
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