This chapter shows how the interactions in and between channels may be calculated on the basis of some potential model for a few interacting bodies. That is, a Hamiltonian is defined whose matrix elements give rise to channel couplings, also known as transition potentials. The parameters in this Hamiltonian may be found either from structure models (Chapter 5), or from fitting data (Chapter 15). It is also possible to directly fit to experiment the effects of these couplings on the asymptotic amplitudes of the wave functions, and this is the basis of the R-matrix phenomenology discussed in Chapter 10.

Optical potentials

Beforewecan discuss more detailed reaction mechanisms,weneed to see the typical kinds of potentials used for elastic scattering, and also the binding potentials needed to reproduce the usual single-particle structures of nucleons within a nucleus. We will start by describing the most commonly used optical potentials for elastic scattering, expanding on the introduction in Box 3.4.

Typical forms

The interaction potential between a nucleon and a spherical nucleus is usually described by an attractive nuclear well of depth Vr with a radius Rr slightly larger than the nuclear matter radius, and a diffuse nuclear surface.