SINGLE PARTICLE DYNAMICS

Abstract

This chapter explores single-particle dynamics. The opening of the 3-quasiparticle continuum at 3Δ sets the energy scale for the enhancement of the effective mass near the Fermi surface of nuclei. The chapter presents an argument that the spreading width of single-particle states, which occur because of coupling with low-lying collective modes, is qualitatively different from the two-body collision mechanism and contributes little to the single-particle lifetime in the sense of the optical model. Nuclear single-particle levels, near the Fermi energy λ, lie much closer together than those that are far from the Fermi surface. The latter are consistent with the results of mean-field theory and are determined by the effective range of nuclear interactions. The increased level density near λ—commonly parameterized as an enhancement of the effective mass—has been traced to retardation effects in single-particle propagation, because of the polarization of the nuclear medium. This enhancement has been discussed in finite nuclei, both in terms of single-particle collisions and in terms of collective dressing of the single-particle propagator. The effect has also been reported in studies of infinite nuclear matter. The range of energies over which the enhancement occurs is a matter of controversy. In nuclear matter, the results depend on perturbation theory diagrams that are taken into account, with no clear intuitive explanation of the range. In the case of finite nuclei, the width of the enhancement has been associated with the energies of low-lying collective excitations. In nuclear matter, the pairing gap determines the region of single-particle energies over which the effective mass is enhanced by retardation effects.