Compression modulus of asymmetric nuclear matter

Abstract

The formula for the compression modulus of asymmetric nuclear matter is derived within the framework of the Landau theory of normal Fermi liquids. The net effect of neutron excess is to make nuclear matter at a fixed density ϱ = ϱ n + ϱ p more incompressible. The increase in the compression modulus is well described by the formula K eα 2, with α = (ϱ n − ϱ p ) ϱ and K e ≈ 270 MeV. When the compression modulus is calculated at the equilibrium density of asymmetric nuclear matter, the net increase reads K e eqα 2, with K e eq ≈ 150 MeV. In the case of strongly asymmetric nuclear matter ( ϱ p ⪡ ϱ) corresponding to the liquid interior of neutron stars, the effect of admixture of protons is to make the matter more compressible, as compared to the pure neutron matter case, the decrease of the compression modulus being proportional to the proton fraction.