Pairing Interaction Effects in Exciton Level Densities

摘要

Recent progress in pairing corrections for exciton state-density formulas used in pre-compound nuclear reaction theories is reviewed. These correction factors are, strictly speaking, dependent on the nuclear excitation energy U and the exciton number n. A simple formula for (U,n)-dependent pairing corrections has been derived, based on the BCS pairing equations for constant single-particle spacing, for the exciton state-density formula for one kind of Fermion. It has been shown that the constant-pairing-energy correction used in standard state-density formulas, such U(sub 0) in Gilbert and Cameron, is a limiting case of the general (U,n)-dependent results. Spin cutoff factors with pairing effects were also obtained using the same theory and parameterized into an explicit (U,n)-dependent function, thereby defining a simple exciton level-density formula for applications in quantum mechanical precompound theories. Preliminary results from extending such simple pairing-interaction representations to level-density formulas for two kinds of Fermions are summarized. The results show that the ratios in the exciton level densities in the one-Fermion and two-Fermion approaches vary with both U and n, thus 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. 12 refs., 3 figs.