We investigate nuclear matter at finite temperature and density, including the formation of light clusters up to the alpha particle 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. 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. We compare the numerical results of these models for cluster abundances and thermodynamics in the region of medium excitation energies with temperatures T <= 20 MeV and baryon number densities from zero to a few times saturation density. The effect of cluster formation on the liquid-gas phase transition and on the density dependence of the symmetry energy is studied. Comparison is made with other theoretical approaches, in particular those, which are commonly used in astrophysical calculations. The results are relevant for heavy-ion collisions and astrophysical applications.Comment: 32 pages, 15 figures, minor corrections, accepted for publication in Physical Review

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A fully covariant approach to a density dependent hadron field theory is presented. The relation between in-medium NN interactions and field-theoretical meson-nucleon vertices is discussed. The medium dependence of nuclear interactions is described by a functional dependence of the meson-nucleon vertices on the baryon field operators. As a consequence, the Euler-Lagrange equations lead to baryon rearrangement self-energies which are not obtained when only a parametric dependence of the vertices on the density is assumed. It is shown that the approach is energy-momentum conserving and thermodynamically consistent. Solutions of the field equations are studied in the mean-field approximation. Descriptions of the medium dependence in terms of the baryon scalar and vector density are investigated. Applications to infinite nuclear matter and finite nuclei are discussed. Density dependent coupling constants obtained from Dirac-Brueckner calculations with the Bonn NN potentials are used, Results from Hartree calculations for energy spectra, binding energies, and charge density distributions of ' 0, ' Ca, and Pb are presented. Comparisons to data strongly support the importance of rearrangement in a relativistic density dependent field theory. Most striking is the simultaneous improvement of charge radii, charge densities, and binding energies. The results indicate the appearance of a new "Coester line" in the nuclear matter equation of state.

A new scheme for testing nuclear matter equations of state (EoSs) at high densities using constraints from neutron star (NS) phenomenology and a flow data analysis of heavy-ion collisions is suggested. An acceptable EoS shall not allow the direct Urca process to occur in NSs with masses below 1.5M , and also shall not contradict flow and kaon production data of heavy-ion collisions. Compact star constraints include the mass measurements of 2.1 ± 0.2M (1σ level) for PSR J0751+1807 and of 2.0 ± 0.1M from the innermost stable circular orbit for 4U 1636-536, the baryon mass-gravitational mass relationships from Pulsar B in J0737-3039 and the mass-radius relationships from quasiperiodic brightness oscillations in 4U 0614+09 and from the thermal emission of RX J1856-3754. This scheme is applied to a set of relativistic EoSs which are constrained otherwise from nuclear matter saturation properties. We demonstrate on the given examples that the test scheme due to the quality of the newly emerging astrophysical data leads to useful selection criteria for the high-density behavior of nuclear EoSs.