Theory of particle and hole transfer in elastic nucleus-nucleus scattering

Abstract

The optical model description of elastic nucleus-nucleus scattering is generalized to include the transfer of particles and holes in collisions between heavy nuclei which differ only by one or a few nucleons. An elementary model which consists of two identical cores and a valence particle is solved for small valence-particle masses in the molecular two-state approximation. The molecular states of the valence particle are constructed by a linear combination of nuclear orbitals (LCNO). In order to get around the problem of Coriolis coupling the scattering solution is restricted to cases where nuclear states with j ≦ 1 2 or l = 0 are involved. Because of the possible exchange of the valence particle between the two identical cores, even and odd partial waves are scattered by different potentials. The difference is due to exchange potentials which are associated with the molecular states of definite core-permutation symmetry. The result is a characteristic interference pattern in the angular distribution of the elastic cross section. The elementary model is generalized by describing the cores in the framework of Hartree-Fock theory. This description shows that holes can be exchanged like particles. The derivation of an optical core-core potential is given. The exchange potential which is real in the elementary model becomes complex in the general treatment. For the elastic transfer of two particles, two holes or a particle and a hole, four possible approximations are discussed. Correlations between core particles and valence particles or holes can approximately be taken into account by spectroscopic factors in the exchange potentials.