Coulomb wave theory of stripping

Abstract

This paper presents an exact analytic treatment of pure Coulomb distortions in stripping reactions. This first-order theory is analogous to some of the simplest plane-wave theories; the important innovation consists in the use of pure Coulomb waves instead of plane waves to describe the relative motions in both entrance and exit channels. The projectile is considered to be a bound state of two particles, described by a purely asymptotic wave function of the form e − αr / r. The resultant nucleus is considered to be a bound state of the target particle plus a captured particle, described by a wave function of definite orbital angular momentum L, with a radial part which may be taken to be any linear combination of terms of the form r L e − βr / r. The distorted-wave cross sections predicted are found to contain a factor whose leading term has an angular variation identical to that predicted by the analogous plane wave theory. A second factor, which is identical for all values of L, depends only on the energies and the Coulomb parameters of the relative motions; it represents the overall decrease in magnitude due to the Coulomb repulsions in both incident and exit channels. A third factor contains an additional angular dependence due to the distortions. The angular dependence is found to resemble qualitatively the angular dependence of plane wave theories except possibly in the case that the Coulomb parameters are very large in the entrance and the exit channels simultaneously. Detailed formulae are given for cases of L = 0, L = 1 and L = 2. These are so simple that there should be no point in using plane-wave expressions, rather than these Coulomb-wave expressions, for the preliminary evaluation of experimental results showing the usual characteristics of stripping.