Nuclear partition functions

Abstract

A nondivergent prescription for the calculation of nuclear partition functions at high temperature is derived. When this is expressed as an integral over nuclear level densities, particle-unstable states in the continuum contribute only if they correspond to increasing scattering phase shifts, so that the disappearance of narrow levels provides a natural energy cutoff and the partition functions saturate at temperatures approaching 1 trillion K. The decreasing phase shifts at higher energies lead to subtractions which would in the infinite temperature limit cancel the bound-state contributions exactly as demanded by Levinson's (1949) theorem. This prescription is applied to the numerical evaluation of high-temperature partition functions for Ni-56 and Fe-56, the sensitivity to various approximations is investigated, and a simple expression is proposed for application to nuclei with unknown parameters. Some astrophysical implications are discussed. In particular, storage of energy in the excited states of a nucleus is emphasized as an important effect during supernova core collapse.