The generator coordinate method for nuclear scattering

Abstract

A generator coordinate description of nucleus-nucleus scattering is formulated. By imposing proper scattering boundary conditions on the Hill-Wheeler integral equation, one can derive an effective nucleus-nucleus potential directly from the basic two-nucleon Hamiltonian. The effective potential is a rather complicated non-local and energy-dependent operator, but it does incorporate both Pauli exchange effects and the occurrence of nuclear shape, size and orientation changes during the collision. The generator coordinate and resonating group descriptions are compared and it is concluded that they are essentially equivalent. However, the generator coordinate approach is a special truncation which is based on semi-classical ideas of collective nuclear motion. Use of generator coordinates leads one to a set of continuous, coupled Lippmann-Schwinger equations in a biorthogonal basis. As a step toward practical solution of these equations, an effective α-α potential including monopole deformation effects is derived using the independent particle model and a simplified two-nucleon potential.