On the dispersion theory of direct nuclear reactions

Abstract

The Feynman graphs with singularities closest to the physical region of variables are assumed to be responsible for the main contribution to the amplitude of a direct nuclear process. Using the dispersion relations with respect to energy a singular integral equation is obtained for calculating interactions in the initial and final states. This equation admits an accurate solution and simple iteration, the first-order iteration corresponding to the method of distorted waves. It is found that a substantial contribution to the direct process mechanism may come not only from pole graphs corresponding to the Butler mechanism, exchange stripping and heavy pick-up reactions, but from more complex graphs as well. The reactions Be 9(d, n)B 10, Be 9(α, t)B 10 and C 12(d, p)C 13 are considered to illustrate this point. Some reactions of the type (x, yz) and in particular, the “knock out” of nuclear clusters, are analyzed from the same angle.