Expressions for Form Factors for Inelastic Scattering and Charge Exchange in Plane-Wave, Distorted-Wave, and Coupled-Channels Reaction Formalisms

Abstract

This document is intended to facilitate calculation of inelastic scattering and charge-exchange cross sections in a variety of reaction models, including the plane-wave and distorted-wave approximations and the full coupled-channels treatments. Expressions are given for the coupling potentials between the relevant channels in both coordinate and momentum space. In particular, it is expected that the plane-wave calculations should be useful as a check on the correctness of coupled-channels calculations. The Fourier transform methods used to calculate the plane-wave approximation cross sections are also intended to be used to generate the transition potentials for coupled-channels codes, using a folding model with local effective interactions. Specific expressions are given for calculating transition densities for the folding model in the random phase approximation (RPA).

LDRD Final Report: Surrogate Nuclear Reactions and the Origin of the Heavy Elements (04-ERD-057)

“…Under this LDRD project we have developed a framework and implemented computer codes to study the effects of collectivity and to compare the results with those obtained with the uncorrelated particle-hole model, described in Section 3.5. The description of the formalism has been written up as a technical report [18]. The calculations are carried out by constructing the transition densities for every relevant state in the desired excitation-energy range (roughly 5-30 MeV), and then convoluting the transition density with an effective interaction between the projectile and target nucleus to yield a transition potential.…”