Study of Deuteron Stripping Reaction by Coupled Channel Theory. I

Abstract

Close coupling equations for the rearrangement reaction A+d →B+p are derived from a variational principle for reaction amplitude assuming the usual stripping mechanism. The sum of the wave functions of the deuteron and proton channels is used as a trial function. An exact and simple expression for the error introduced into the reaction amplitude is also derived by applying the theory of finite variations. Our variational principle is not affected by the existence of ambiguity in defining the proton and deuteron wave functions of relative motion, which should be carefully considered for rearrangement reaction because of the “non-orthogonality” or channels. The origin of this non-uniqueness and the induced ambiguity in the optical potentials are discussed in connection with the relation between the present method and the method of the projection operators. The interaction kernel consists of two parts, one coming from the usual Vnp+VpA-UpB term and the other due to the non-orthogonality of the initial and final channel wave functions. It is shown that DWBA is obtained only if the whole interaction kernel (not Vnp+VpA-UpB alone) is considered as perturbation. The relation between the present method and the methods of projection operators is discussed.