Nuclear level statistics: extending the shell model theory to higher temperatures
The Shell Model Monte Carlo (SMMC) approach has been applied to calculate level densities and partition functions to temperatures up to ~ 1.5 - 2 MeV, with the maximal temperature limited by the size of the configuration space. Here we develop an extension of the theory that can be used to higher temperatures, taking into account the large configuration space that is needed. We first examine the configuration space limitation using an independent-particle model that includes both bound states and the continuum. The larger configuration space is then combined with the SMMC under the assumption that the effects on the partition function are factorizable. The method is demonstrated for nuclei in the iron region, extending the calculated partition functions and level densities up to T ~ 4 MeV. We find that the back-shifted Bethe formula has a much larger range of validity than was suspected from previous theory. The present theory also shows more clearly the effects of the pairing phase transition on the heat capacity.