Symmetric and asymmetric nuclear matter in the relativistic approach at finite temperatures

Abstract

The properties of hot matter are studied in the frame of the relativistic Brueckner-Hartee-Fock theory. The equations are solved self-consistently in the full Dirac space. For the interaction we used the potentials given by Brockmann and Machleidt. The obtained critical temperatures are smaller than in most of the nonrelativistic investigations. We also calculated the thermodynamic properties of hot matter in the relativistic Hartree-Fock approximation, where the force parameters were adjusted to the outcome of the relativistic Brueckner-HartreeFock calculations at zero temperature. Here, one obtains higher critical temperatures, which are comparable with other relativistic calculations in the Hartree scheme. ͓S0556-2813͑98͒03806-0͔ PACS number͑s͒: 21.65.ϩf, 21.60.Jz, 25.75.Ϫq, 26.60.ϩc The properties of hot and dense nuclear matter play an essential role in the understanding of high-energy heavy-ion collisions, supernova explosions, and protoneutron stars. For that reason the problem of hot nuclear matter has been studied over the past decades in several investigations, which however were predominantly performed within the nonrelativistic scheme ͓1͔, using either effective density dependent interactions ͓1-4͔ or the Brueckner approach ͓1,5-8͔. In the relativistic approach investigations of the equations of state for T 0 are relatively scarce. The majority of such calculations were performed in the relativistic Hartree approximation ͑RH͒, where the extension to finite temperatures is straightforward. Details of this scheme are given, for instance, in Refs. ͓4,9-15͔. More complicated are the relativistic Hartree-Fock ͓14,15͔ and Brueckner-Hartree-Fock approximations ͓16͔, and the application to finite nuclei ͓17͔.In this contribution we will concentrate on the relativistic Brueckner-Hartree-Fock treatment ͑RBHF͒ of symmetric and asymmetric nuclear matter generalizing the formalism as described in Refs. ͓18,19͔ to T 0. The RBHF approach seems to be of special interest, since it is known for Tϭ0 that the resulting equations of state ͑EOSs͒ are much stiffer than their nonrelativistic counterparts ͓20͔. To our knowledge such an investigation has only been performed so far by the Groningen group for symmetric nuclear matter ͓16͔. As described in more detail in Refs. ͓16,18͔, their method uses a nonunique ansatz for the T matrix in terms of five Fermi invariants, which can lead to ambiguous results for the selfenergies ͑see, e.g., Refs. ͓21,22͔͒. In order to avoid this problem we solve, according to the original scheme of the Brooklyn group ͓23͔, the RBHF approximation in the full Dirac space, which is more tedious ͑for a more detailed discussion, see Ref. ͓18͔͒. Since the formal structure of the problem is the same as for Tϭ0, where one has to solve three coupled equations, namely the Dyson equation for the one-body Green's function G, the ͑reduced͒ Bethe-Salpeter equation for the effective scattering matrix T in matter, and the equation for the self-energy ⌺, we will not repeat here the equations. As in Refs. ͓16,1...

Protoneutron stars within the Brueckner-Bethe-Goldstone theory

“…Later, Brueckner calculations (Lejeune et al 1986;Baldo & Ferreira 1999) and chiral perturbation theory at finite temperature (Kaiser et al 2002) confirmed these findings with very similar values of T c . The Van der Waals behavior was also found in the finite-temperature relativistic Dirac-Brueckner calculations of Ter Haar & Malfliet (1986, 1987 and Huber et al (1999), although at a lower temperature.…”

Hot nuclear matter equation of state with a three-body force

“…[12] and T C ≃ 10MeV in Ref. [13]. One possible reason for this discrepancy is the difference between the relativistic effect in the DB approach [27] and the effect of the present microscopic TBF as discussed in Ref.…”

“…Theoretically, considerable effort has been devoted to establishing the EOS of hot symmetric nuclear matter and discussing the critical phenomena [7][8][9][10][11][12][13]. Although almost all the predicted EOSs of infinite symmetric nuclear matter display a typical Van der Waals behavior, the obtained values of the critical temperature T C for the phase transition are distributed in a wide range from 8MeV to 20MeV.…”

The limiting Temperature of hot nuclei from microscopic Equation of State

“…Finite temperature Dirac-Brueckner calculations are quite few in the literature [3,4]. Furthermore, for our analysis we need the free energy as a function of density at small steps of the temperature.…”

“…Phenomenological information on the EoS can be obtained from experimental data on heavy ion collisions at intermediate energies and astrophysical observations on supernovae explosions and neutron stars. The nuclear matter EoS is believed to go through a liquid-gas phase transition, as many theoretical calculations indicate [1][2][3][4]. However, if this phase transition exists, does not possess a direct correspondence in finite nuclei, due to the presence of the Coulomb and finite size effects.…”