Pairing Corrections and Spin Cutoff Factors in Exciton Level Densities for Two Kinds of Fermions

Abstract

Pairing corrections in particle-hole (exciton) state-density formulas used in precompound nuclear reaction theories are, strictly speaking, dependent on the nuclear excitation energy U and the exciton number n. A general formula for (U, n)-dependent pairing corrections was derived earlier for the exciton state-density formula for a system of one kind of fermion. A similar derivation is made for a system of two kinds of fermions, a system in which neutrons and protons occupy different sets of single-particle states. In this paper it is shown that the constant-pairing- energy correction used in standard state-density formulas, such as U{sub 0} in Gilbert and Cameron, is a limiting case of the present general (U,n)-dependent results. Spin cutoff factors are calculated using the same pairing theory and parameterized into an explicit (U,n)-dependent function, thereby defining the exciton level-density formula for two kinds of fermions. The results show that the ratios in the exciton level densities in the one-and two-fermion approaches vary with both U and n, thus, most likely leading to differences in calculated compound-to-precompound ratios. However, the differences in the spin cutoff factors in the two cases are found to be rather small.