Core polarization and the effective interaction between nucleons in a nucleus

Abstract

Core polarization is taken into account to all orders by systematic inclusion of particle-hole scattering, self-screening of phonons and modification of the vertices connecting single-particle to two-particle one-hole states, and single-hole to two-hole one-particle states. Problems of convergence are overcome by converting the sum of perturbation theory diagrams into closed equations. A set of coupled nonlinear equations for the particle-hole interaction is derived and solved, and the solution is used to compute the effect of core polarization to all orders. The self-screening strongly suppresses the RPA enhancement of the core phonons, the net effect being close to TDA phonons, while the vertex modification drastically changes the contributions of the various phonons. The final result for the core polarization is very different from the lowest-order effect for low-lying energy levels, being generally quite small.