Momentum distributions, chemical potential, and free energy of asymmetric nuclear matter using the static fluctuation approximation

Abstract

The Static Fluctuation Approximation (SFA) is used to calculate the momentum distributions, chemical potentials, and Helmholtz (free) energy of asymmetric nuclear matter with the Argonne interaction potential AV₁₈. The results indicate that, as the linear momentum $k\to 0$, the momentum distributions of both neutrons and protons increase with decreasing temperature. Further, in this limit, the momentum distributions increase with increasing number density ρ. In symmetric nuclear matter, the momentum distributions of neutrons and protons are, of course, identical. In contrast, however, in asymmetric nuclear matter, as the isospin-asymmetric parameter increases, the momentum distribution of neutrons increases; whereas that of protons decreases. The chemical potential results show that the Fermi temperature of neutrons is greater than that of protons, i.e., the neutrons remain in the quantum regime at a temperature greater than that for the protons. We also find that, in the low ρ-limit, both protons and neutrons exist in the classical regime. The protons cross over from the classical to the quantum regime at a density greater than that for the neutrons. The Helmholtz energy is calculated as a function of ρ, temperature, and isospin parameter. It increases with ρ, decreases with temperature, and exhibits a parabolic dependence on the isospin parameter.

Our results agree quite well with those of other theoretical approaches. Together with our previous SFA work, the present calculations demonstrate yet again the reliability of this formalism for low-energy, nonrelativistic nuclear matter.