Self-Consistent Potential for Individual Particle Motions in the Nuclei with Closed Shells

Abstract

The principle of mass renormalization in the quantum electrodynamics is applied to derive the equations which the potential for the individual particle motions satisfies self-consistently in the nuclei with the doubly closed shells. The potential is to be such that the excitation energy of each single particle (hole) state is invariant when the residual interactions are taken into account. Since this condition is concerned only with the diagonal matrix elements of the potential, the other matrix elements are so determined that the wave functions of the unperturbed ground and single particle (hole) states can best simulate the corresponding perturbed ones. The perturbed ground state is supposed not to have the components with one (particle and hole) pair excitation. Each perturbed single particle (hole) state should have the components of the different unperturbed single particle (hole) states as small as possible. The equations for the potential are given in a form of power series expansion with respect to the two-body interactions and are explicitly written up to the second order. The result turns out to be practically identical with that for the real part of the optical potential. The relation with Sawada's theory in an infinite system is pointed out.