Nuclear matter within the relativistic-mean-field model involving free-space nucleon-nucleon forces
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CLEI Theory
Nuclear Matter within the Relativistic-Mean-Field Model Involving Free-Space Nucleon–Nucleon Forces B. L. Birbrair* and E. L. Kryshen Petersburg Nuclear Physics Institute, Russian Academy of Sciences, Gatchina, 188350 Russia Received October 6, 2008
Abstract—Masses and radii of neutron stars were calculated within the relativistic-mean-field model by using free-space nucleon–nucleon forces. Multiparticle forces and correlations were taken into account phenomenologically by introducing a nonlinearity in isoscalar channels and three-particle forces in the scalar–isovector channel. PACS numbers: 24.80.+y, 13.75.Cs DOI: 10.1134/S1063778809070072
1. INTRODUCTION Originally, the problem of the equation of state for nuclear matter was almost speculative, but it became very topical after the discovery of neutron stars [1]. The Hartree–Fock–Brueckner method in the nonrelativistic (HFB) [2] and especially in the relativistic (DHFB) [3] version is thought to be an adequate approach to studying this problem since this method, which employs two-body nucleon–nucleon forces determined from a partial-wave analysis of elastic scattering and from the properties of the deuteron, involves no free parameters. In our opinion, however, this approach is hardly adequate for the following reasons. (i) The Brueckner G matrix satisfies the equation of the gas approximation, which is valid under the condition kF /µ 1 (where kF is the Fermi momentum and µ is the mass of the interaction mediator). This condition is invalid from the outset in the case of one-pion exchange even at nuclear densities (kF ∼ = 270 МeV, while µ = mπ = 140 МeV), and the amount of its violation grows monotonically with increasing density, which, in neutron stars, becomes as large as 8n0 (where n0 = 0.16 fm−3 in the equilibrium nuclear-matter density). (ii) Within the HFB and DHFB methods, the interaction is treated as a potential—that is, momentum exchange is taken into account, while energy exchange is disregarded. At the same time, nucleons in the intermediate state are off the Fermi surface, so that their energies may be indefinitely large. But in this case, the energy transfer is commensurate with *
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the momentum transfer, with the result that the original approximation becomes meaningless. This may be demonstrated in the limit where the momenta of intermediate nucleons exceed their masses substantially. (iii) At densities of about 2n0 , hyperons may arise in neutron stars [4]. In that case, the free-parameter independence of the method becomes questionable, because there are no data on free-space hyperon– nucleon or hyperon–hyperon interactions (available data on hypernuclei furnish information about the interaction in nuclear matter at densities of about n0 rather than about the free-space interaction, and there are no grounds to employ this interaction at high densities). (iv) Strong-interaction forces are essentially nonlinear. Therefore, many-body forces act in nuclear matter [5] in addition to two-body forces, the ro
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