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 $\approx 4$ MeV.

The isospin diffusion of the quasi-projectile formed in the Ni 64 , 58 on Ni 64 , 58 reactions in the Fermi energy domain is investigated in the framework of the Boltzmann–Uehling–Uhlenbeck transport model. The well known isospin transport ratio observable is revisited, with the aim of insuring an optimal comparison between experimental data and theoretical calculations and reducing the present uncertainties in the extraction of empirical equation of state parameters. We show that isospin transport ratios are sensitive to all the low order isovector parameters ( E _sym , L _sym and K _sym , but the quantitative results depend on the choice of the isospin sensitive observable. We demonstrate that realistic models of the equation of state, covering the uncertainty that presently affects the theoretical description of neutron stars static observables, can be effectively discriminated by isospin diffusion experiments, provided the neutron to proton ratio of the projectile remnant is precisely measured as a function of centrality.

In this work, the canonical thermodynamical model for nuclear multifragmentation has been updated with a realistic nuclear equation of state. Mass distribution, intermediate mass fragment multiplicity, and isospin sensitive observables have been investigated with a semi-microscopic approach of determining nuclear binding and excitation energies. Production of neutron-rich isotopes as well as isoscaling and isobaric yield ratio parameters have been significantly modified due to inclusion of this realistic nuclear equation of state.