Self-energy in a semirealistic model of nuclear matter

A semirealistic parametrization in momentum space is used for the matrix elements of the effective nucleon-nucleon interaction. In this model, the nucleons only interact in a relative $s$-wave state and essentially via an exponential potential. In the Hartree-Fock approximation, algebraic expressions are derived for the self-energy and the effective mass. The strength and the range of the nucleon-nucleon interaction are chosen in such a way that these quantities are in fair agreement with the empirical values. We calculate analytically the frequency dependence of the imaginary part of the polarization and correlation contributions to the self-energy. The real part of these contributions can then be computed very accurately with the help of dispersion relations. Their frequency dependence can most conveniently be described in terms of a frequency mass $\overline{m}$. It is found that $\overline{m}$ has an enhancement peak, typically 30 MeV wide, centered on the Fermi energy. The contributions of the correlation and of the polarization graphs to this local enhancement are disentangled. The contribution to $\overline{m}$ of the polarization graph peaks somewhat above the Fermi energy, and that of the correlation graph somewhat below the Fermiy energy. The total peak is approximately symmetric about the Fermi energy. We identify the range of excitation energy of those core excited states which mainly contribute to the enhancement. The enhancement peak is more pronounced at low density and for long-range interactions. The usual effective mass also displays an enhancement at the Fermi surface. The momentum distribution in the correlated ground state is calculated. The effect of introducing a hard core in the nucleon-nucleon interaction is studied.