Variational Calculations of Asymmetric Nuclear Matter

We report on variational calculations of the energy E(p, ß) of asymmetric nuclear matter having p = p +pp = 0.05 to 0 .35 fm-~, and ß = (P -p~)lp = 0 to l . The nuclear hamiltonian used in this work consists of a realistic two-nucleon interaction, called °i<, that fits the available nucleon-nucleon scattering data up to 425 MeV, and a phenomenological three nucleon interaction adjusted to reproduce the empirical properties of symmetric nuclear matter. The variational many-body theory of symmetric nuclear matter is extended to treat matter with neutron excess . Numerical and analytic studies ofthe ß-dependence of various contributions to the nuclear matter energy show that at p < 0.35 fm -' the ßa terms are very small, and that the interaction energy EI(p, ß) defined as E(p, ß)TF(p, ß), where TF is the Fermi-gas energy, is well approximated by EI o(p)+ß 2EIZ(p) . The calculated symmetry energy at equilibrium density is 30 MeV and it increases from IS to 38 MeV as p increases from 0 .05 to 0 .35 fm -3 . Recently we') [denoted by I henceforth] reported on variational calculations of symmetric nuclear matter with a hamiltonian consisting of a realistic two-nucleon interaction operator called c't4, and a phenomenological three-nucleon interaction (TNI). The vt4 interaction operator is obtained by fitting the deuteron properties and the nucleon-nucleon scattering data in S, P, D and F waves up to 400 MeV [ref. 2)] . By itself the vt4 interaction does not give satisfactory properties of nuclear matter . The TNI is obtained by requiring that the vt4 +TNI model gives the correct energy, density and compressibility of nuclear matter. The contribution of TNI to the ground state energy of nuclear matter is small. The TNI is divided into two parts . One of them, called TNR, generates a density-dependent repulsive twonucleon interaction that is added to the vt4 interaction in nuclear matter calculations. The contribution of the other part is attractive, and it is represented by a function of density, TNA(p , pa) as discussed in I. The i't4+TNI hamiltonian has also been used to study the equation of state of hot and cold nuclear and neutron matter 3) . In this paper we present our studies of the energy E(p, ß) ofcold asymmetric nuclear matter having (p -pP)/p = ß. Symmetric-nuclear andneutron matter are the limiting cases having ß = 0 and 1 respectively . Work supported by NSF PHY78-26582. 1 . Introduction