A new semi-classical approach to the treatment of elastic scattering and direct reactions

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Abstract
The author considers the short wavelength (semi-classical) limits of the s-matrix for elastic scattering, and the distorted wave Born approximation (DWBA) t-matrix for a direct reaction, and derive some interesting and useful formulae. One result takes the form of an integral representation of the elastic s-matrix which resembles the Poisson sum representation of the exact elastic s-matrix. The main result of this paper is a new approximate expression for the DWBA t-matrix in which the main effects of the distorting potentials are described in terms of average elastic phase shifts. This approximation is applicable in various forms to the treatment of a wide range of direct nuclear and atomic reactions. It possesses a number of attractive and useful features offering some practical advantages over the original quantal expression. In particular the formulae are easy to evaluate and are amenable to detailed interpretation and further analytical approximation. Conditions for their validity are stated and demonstrate their wide range of applicability. More detailed discussion is given of application to peripheral reactions and to Coulomb excitation.