Neutron matter properties are calculated both at zero and finite temperature within an extended Brueckner approach using the Paris potential. The binding energy turns out to be very close to the one calculated variationally with the Urbana v14 potential. Particular emphasis is put on the symmetry energy, on the isospin dependence of the mean field and on the effective mass. As an illustration, the masses of neutron stars are calculated. 21.65. +f
PACS:
IntroductionA great deal of interest is currently devoted to the nuclear matter equation of state. The present situation is however rather confuse. To describe it very shortly, conventional analysis of giant monopole in nuclei [1,2], early analysis of heavy-ion collisions neglecting effective mass effects [3,4] and microscopic calculations based on potential models, be them performed in a variational [5] or in a (nonrelativistic [6] or relativistic [7]) perturbative scheme, seem to point to a so-called stiff nuclear matter equation of state, i.e. a sharp increase of the binding energy per particle between P0 and ,-~4po (P0 =normal nuclear matter equilibrium density). On the other hand, reanalysis of nuclear properties in the spirit of the Landau sum rules for Fermi liquids [8], and recent calculations on supernovae explosions [9] seem, on the contrary, to suggest that the equation of state would be much softer. Finally, the masses of known neutron stars favour [10] a stiff nuclear matter equation of state. The last considerations involve asymmetric nuclear matter, for which the theoretical investigations are much less numerous in comparison with the symmetric case. In fact, for purely neutronic matter, there is practically only one very sophisticated microscopic * Work supported by the NATO Grant 025.81 calculation [5], based on the variational method. Here, we want to study the same system by a detailed Brueckner type approach, both at zero and at low temperature, extending so our previous investigations of symmetric nuclear matter [6]. Actually, our purpose is fourfold. First, we want to calculate the binding energy of neutron matter, in order to check whether the agreement between variational and perturbative approaches, observed for N =Z [6], also holds for Z = 0. Second, we want to calculate microscopically the symmetry energy. Third, we investigate the single-particle properties of neutron matter both at T= 0 and T+ 0, especially the neutron effective mass, which can play an important role in supernovae explosions. Fourth, we propose ourselves to use our results to calculate the neutron star mass spectrum. This is for illustrative purpose mainly, since this calculation requires the detailed knowledge of the equation of state at large densities, for which the perturbative approach is inadequate or, at least, on less safe grounds than the variational approach.The paper is organized as follows. Section 2 shortly describes the theoretical frame. Section 3 contains the numerical results for the binding energy, the average nucleon field, the effective mass and...