Equilibrium theory of the nuclear symmetry energy of infinite nuclear matter

A set of generalized nuclear matter curves is calculated as a function of density and ξ = 1−(2Z/A), which maps out the energy versus density plane for 0 ≤ ξ ≤ 1 and determines the nuclear matter equilibrium curve (NMEC) as the locus of their saturation points. The NMEC immediately determines the equilibrium energy and density as a function of the neutron excess, and thereby automatically gives the nuclear symmetry energy. The component parts of the equilibrium energy are also determined, and we find that the average kinetic energy per nucleon is a decreasing function of the neutron excess parameter, so that the contribution of the kinetic energy to the second order coefficient, β2∞, is negative. By noting that the density variation along the NMEC is determined by kFE = k∞(1−F2ξ2 + F4ξ4−… ) f−1 with k∞ = 1.4 f−1, F2 ~ 0.45, and F4 ~ 0.07, we find a general connection between the equilibrium and nonequilibrium symmetry energy coefficients, i.e. β0∞ = β0NE(k∞), β2∞ = β2NE(k∞), β4∞ = β4NE(k∞), etc., where K0(...