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.
- 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