Composition and thermodynamics of nuclear matter with light clusters

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We investigate nuclear matter at a finite temperature and density, including the formation of light clusters up to the $\ensuremath{\alpha}$ particle ($1\ensuremath{\leqslant}A\ensuremath{\leqslant}4$). The novel feature of this work is to include the formation of clusters as well as their dissolution due to medium effects in a systematic way using two many-body theories: a microscopic quantum statistical (QS) approach and a generalized relativistic mean-field (RMF) model. Nucleons and clusters are modified by medium effects. While the nucleon quasiparticle properties are determined within the RMF model from the scalar and vector self-energies, the cluster binding energies are reduced because of Pauli blocking shifts calculated in the QS approach. Both approaches reproduce the limiting cases of nuclear statistical equilibrium (NSE) at low densities and cluster-free nuclear matter at high densities. The treatment of the cluster dissociation is based on the Mott effect due to Pauli blocking, implemented in slightly different ways in the QS and the generalized RMF approaches. This leads to somewhat different results in the intermediate density range of about ${10}^{\ensuremath{-}3}$ to ${10}^{\ensuremath{-}1} \phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$, which gives an estimate of the present accuracy of the theoretical predictions. We compare the numerical results of these models for cluster abundances and thermodynamics in the region of medium excitation energies with temperatures $T\ensuremath{\leqslant}20$ MeV and baryon number densities from zero to a few times saturation density. The effects of cluster formation on the liquid-gas phase transition and on the density dependence of the symmetry energy are studied. It is demonstrated that the parabolic approximation for the asymmetry dependence of the nuclear equation of state breaks down at low temperatures and at subsaturation densities because of cluster formation. Comparison is made with other theoretical approaches, in particular, those that are commonly used in astrophysical calculations. The results are relevant for heavy-ion collisions and astrophysical applications.