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, particleunstable 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 boundstate contributions exactly as demanded by Levinson's (1949) theorem. This prescription is applied to the numerical evaluation of hightemperature partition functions for Ni56 and Fe56, 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 December 1978
 DOI:
 10.1086/156679
 Bibcode:
 1978ApJ...226..984F
 Keywords:

 Nuclear Astrophysics;
 Nuclear Fusion;
 Nuclei (Nuclear Physics);
 Stellar Interiors;
 Stellar Models;
 Stellar Structure;
 Atomic Excitations;
 Energy Storage;
 Gravitational Collapse;
 Heavy Nuclei;
 High Temperature;
 Iron;
 Nickel;
 Phase Shift;
 Resonance;
 Supernovae;
 Astrophysics;
 Nuclear Reactions:Stellar Interiors