Symmetry Energy and the Isotopic Spin Dependence of the Single-Particle Potential in Nuclear Matter

Abstract

Nuclear matter with a given neutron excess is treated within the frame of the $K$-matrix theory. General expressions for the symmetry energy ${\ensuremath{\epsilon}}_{\mathrm{sym}}$ and the single-particle potential are obtained with the help of the reaction matrix which depends on two different Fermi momenta for neutrons and protons. In particular, an expression for the isotopic spin-dependent part ${U}_{1}$ of the single-particle potential is obtained, and then specialized for single particles at the Fermi surface. With suitable approximations numerical values of ${\ensuremath{\epsilon}}_{\mathrm{sym}}$ and ${U}_{1}$ at the Fermi surface are obtained with the help of the Bruckner-Gammel solution for nuclear matter. The results are: ${\ensuremath{\epsilon}}_{\mathrm{sym}}=64$ MeV, ${U}_{1}({k}_{F})=126$ MeV.