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

Nuclear matter with a given neutron excess is treated within the frame of the K-matrix theory. General expressions for the symmetry energy εsym 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 U₁ of the single-particle potential is obtained, and then specialized for single particles at the Fermi surface. With suitable approximations numerical values of εsym and U₁ at the Fermi surface are obtained with the help of the Bruckner-Gammel solution for nuclear matter. The results are: εsym=64 MeV, U₁(kF)=126 MeV.