Collision Matrix for (n, d) and (p, d) Reactions

Abstract

The contributions to ($n, d$), ($p, d$) reactions and their inverses from the pickup and stripping mechanisms are considered as corrections to the compound-nucleus or $R$-matrix theory of nuclear reactions. In an ($n, d$) reaction, for example, the $R$-matrix theory neglects the interaction of the incident neutron with the target-nucleus proton "tails" which extend beyond the nuclear radius. The pickup correction to the collision-matrix component, or reaction amplitude, appears as the matrix element of the neglected interaction involving an exact wave function and the approximate wave function of the compound-nucleus system not having the interaction; a distorted-wave Born approximation is used in which the former exact wave function is replaced by one of the latter type with the appropriate radiation condition. An explicit expression is given for the collision-matrix component which, together with the compound-nucleus contribution, can be substituted directly into the formulas of Blatt and Biedenharn for total reaction cross sections and angular distributions. In general, the angular distributions contain interference terms in addition to the straight pickup and compound-nucleus contributions. If the distorted neutron and deuteron spherical partial waves are assumed to depend only on the angular momenta, and not explicitly on the total spin and the channel spins, the formula of Tobocman is obtained for the pickup contribution, while Butler's formula is obtained if plane waves are used instead of distorted waves. There are discussions of the various approximations, the exchange terms, and the question of the nuclear radius.