The imaginary part of the heavy ion optical potential

Abstract

A number of different methods have been proposed for calculating the imaginary part of the Heavy-Ion Optical potential. In some of these a folding type procedure is used. Real and imaginary parts of the optical potential come from folding of the real and imaginary parts of some effective nucleon-nucleon t-matrix with nuclear densities. Another procedure calculates the loss of flux from the incident channel in second order perturbation theory. Green’s function methods give a way of improving the perturbation approach.

In this lecture a different approach based on Feynman’s path integral method is proposed. It is known that semi-classical methods are very useful for calculating heavy-ion scattering. The Feynman method provides a natural link between a complete quantal theory and semi-classical approximations. By writing a path integral expression for the scattering amplitude one obtains a formula relating the imaginary part of the optical potential to the coupling of the elastic channel to various inelastic and reaction channels. In a perturbation approximation this formula is quite analogous to Feshbach’s formula which has been used recently to obtain a long-range optical potential describing the effects of Coulomb excitation on elastic scattering.