Statistical treatment of nuclear clusters in the continuum
Résumé
The evaluation of the subsaturation nuclear equation of state at finite temperature requires a proper state counting of the internal partition sum of nuclei which are immersed in the background of their continuum states. This classical statistical problem is addressed within the self-consistent mean-field approximation, which naturally accounts for isospin and effective mass effects in the nuclear density of states. The nuclear free energy is decomposed into bulk and surface terms, allowing a simple analytical prescription for the subtraction of gas states from the nuclear partition sum, that avoids double counting of unbound single-particle states. We show that this correction leads to a sizable effect in the composition of matter at high temperature and low proton fractions, such as is formed in supernova collapse, early proto-neutron-star evolution, as well as laboratory experiments. Specifically, the energy stored in the internal nuclear degrees of freedom is reduced, as well as the mass fraction of heavy clusters in the statistical equilibrium. The gas subtraction prescription is compared with different phenomenological methods proposed in the literature, based on a high-energy truncation of the partition sum. We show that none of these methods satisfactorily reproduces the gas subtracted level density, if the temperature overcomes ≈4 MeV.
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