On the description of direct nuclear rearrangement reactions using various coupled channel equations

Abstract

The standard description of direct nuclear rearrangement reactions by means of the distorted wave Born approximation (DWBA) or the coupled reaction channel (CRC) method has provided little insight into the role of rearrangement coupling effects in these reactions. Essential to these calculational schemes is the bound state approximation (BSA), i.e., the replacement of the full wave function by product wave functions corresponding to relevant asymptotic channels. The role of the continuum in rearrangement effects is thus ignored. Many-body scattering theory provides a powerful, mathematically correct tool for assessing the validity of these approximate schemes and for improving the treatment of the coupling mechanisms. In this paper we use one of the many-body scattering theories, the channel coupling array (CCA) theory, to study rearrangement coupling effects in the BSA both theoretically and computationally. The results of these calculations are compared with those from the DWBA and the CRC scheme for the transfer reactions 16O(d, p) 17O(2s 1 2 ), 16O(α, 3He) 17O(2s 1 2 ), and 19F( 3He, d) 20He(0 +). The associated elastic cross sections are also determined. Coupling effects are found to be very small in the BSA. They are overestimated considerably in the common “post” form of the CRC equations. In general, the CCA and CRC results are similar in shape and in magnitude. We argue that the exact coupling effects can be much larger and indicate how one could accomodate these large effects in equations having the same structure as the CCA or CRC equations. In such equations the rearrangement effects will mainly reveal themselves either through modified optical potentials, in which case a DWBA procedure — which uses first-order distorted waves — is well justified, or through large coupling potentials in which case higher order CCA or CRC type equations must be used. In the second case, and possibly also in the first case, the effective coupling potentials will be quite different from the short range interaction occurring in the usual DWBA.