Analytical Proton Transfer Amplitude for Heavy Ion Induced Nuclear Reactions

Abstract

Direct reactions between heavy ions have been studied widely using semi‐classical theories. The Distorted Wave Born Approximation or DWBA has been extensively applied to analyse transfer reaction processes. Initial attempts to gain insights into the simple semi‐classical parametrisation starting from the DWBA had focused mainly on neutron transfer reactions. An analytical formula for the semi‐classical amplitude for the transfer of a single neutron between bound classical orbits states in heavy ion collisions that agrees well with the DWBA calculations has been successfully derived. In this paper, we have successfully derived the corresponding analytical expression for the proton transfer amplitude by using a technique analogous to the transfer of a single neutron between bound states. Our result reduces to the well known expression for the neutron transfer amplitude in the limit that the nuclear charge tends to zero.