Few channel models of nuclear reactions: Distorted-wave Born approximation for light-ion-induced transfer processes.

Abstract

Standard derivations of the distorted wave Born approximation amplitudes for particle-transfer reactions have always left unanswered two fundamental questions: How can one justify cancellation of the typical, one-body, absorptive-potential counter term, and, which Pauli-principle exchange amplitudes correspond to the standard, nonexchange distorted-wave Born approximation amplitude? This paper provides an answer to these questions. This is accomplished by using a particular type of antisymmetrized, N-particle collision theory to describe the transfer processes. For the reaction (b,a), with the mass of a greater than the mass of b, the extended Faddeev theory of the preceding paper is used, while its time-reversal partner, the precursor form of the Bencze-Redish-Sloan equations, is used for the (a,b) case. They lead to almost identical first-order amplitudes. For all the reactions studied herein, it is found that the form of the nonexchange distorted-wave amplitudes---those that are commonly referred to as distorted-wave Born approximation amplitudes---are essentially the same as are used to fit data. This result is achieved without any need to account for cancellation of a counter term, since none appears, implying an absence of so-called core-excitation effects in first order.No formalism other than the extended Faddeev--Bencze-Redish-Sloan--type has yet been found to yield such results. In addition, none of the first-order, Pauli-principle exchange amplitudes predicted by the formalism are of the conventional knockon type: all are either heavy-particle type of exchange amplitudes or heavy-particle plus additional, non-knockon types. There is also no need to cancel a counter term in the exchange amplitudes. For the (p,d) reaction, and certain others, the occurrence of a pure heavy-particle pickup amplitude helps to explain why direct reaction data analyses that rely on a distorted-wave Born approximation amplitude alone, i.e., one without an exchange amplitude, have been successful.The lack of a knockon term also helps to understand the empirical fact that three-particle pickup and not knockon is the mechanism for direct (p,\ensuremath{\alpha}) reactions. In addition to treating first-order amplitudes, a general expression is given for a two-step correction, and an expression for the nonexchange part of the (p,d)-(d,t) portion of the (p,t) two-step amplitude is derived. It is found to contain the same interactions as occur in a similar amplitude recently derived by Austern and Kawai.