PHENOMENOLOGICAL NUCLEON-NUCLEON POTENTIALS AND THE EQUATION OF STATE OF NEUTRON STAR MATTER Letter to the Editor G.H. BORDBAR and N. RIAZI Department of Physics, Shiraz University, Shiraz, 71454, Iran Institute for Studies in Physics and Mathematics (IPM), Farmanieh, Tehran, P.O. Box 19395-5531, Iran (Received 11 September 2000; accepted 11 December 2001) Abstract. We have calculated the equation of state of the neutron star matter and some of its prop- erties for a wide range of nucleon-nucleon potentials using the lowest order constrained variational (LOCV) method. It turns out that for the UV 14 + TNI potential, the proton fraction exhibits a peak and falls off at high densities. The equation of state with the UV 14 + TNI potential is seen to be much harder than those with other potentials. The polytropic behaviour of the neutron star matter with various potentials are discussed. Compared with the other methods, the LOCV results show good agreement for densities below 0.7fm -3 . Above this density, however, the differences with other methods are appreciable. 1. Introduction Neutron stars are formed in the gravitational collapse of supernovae with M> 8M ⊙ . The interior part of a neutron star is composed of neutrons, protons, electrons and muons. The core is electrically neutral and is in equilibrium with respect to the weak interaction (beta-stable matter) (Shapiro and Teukolsky, 1983). Within minutes after formation, the matter inside neutron stars rapidly cool by neutrino emission to interior temperatures of less than about 1 MeV (Burrows and Lattimer, 1986). Therfore, to a good approximation, the matter inside can be assumed to be at zero temperature. One of the most interesting applications of the many-body techniques to the astrophysics is the calculation of the properties of the matter inside neutron stars (beta-stable matter). The equation of state of neutron star matter covers a wide range of densities. Having a consistent and reliable equation of state is of particular importance in calculating the mass limit and internal structure of neutron stars (Bombaci, 1996; Prakash et al., 1988). Instead of doing a microscopic calcula- tion, others employ an empirical parabolic approximation. In this approximation, the symmetry energy is expressed in terms of the difference of the energy per particle between pure neutron matter and symmetric nuclear matter (Wiringa et al., 1988; Baldo et al., 1997). In our microscopic calculations, we treat expli- citly the isospin projection (T z ) in the nuclear many-body wave functions. This Astrophysics and Space Science 282: 563–572, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.