Quantal corrections and the WKB approximation of multiple Coulomb excitation

Abstract

For an exact quantal calculation of multiple Coulomb excitation a set of coupled radial differential equations must be solved. The WKB method can be used to facilitate such computations. For large values of the angular momenta the set of coupled radial equations can be approximated by the simpler semiclassical equations. Also for large distances of the projectile from the target nucleus the WKB method simplifies the computation. The earlier suggested symmetrization of the relevant parameters of Coulomb excitation has been proved. For the case of the reorientation effect quantal corrections have been computed numerically for the excitation probability and the angular distribution of the de-excitation γ-rays. The slow convergence of the sum over the orbital momenta in the reaction amplitude can be improved by a method similar to the one used in electron scattering calculations. The numerical computations allow an estimate of the quantal correction for the reorientation effect for all experimental conditions up to a few percent.