Gell-Mann-Goldberger Relation for Reactions of the Form (d,pn)

Abstract

For the breakup of a particle $d$ into its constituents $n$ and $p$ in the field of a nucleus $A$, a Gell-Mann-Goldberger relation is derived for which the first potential excludes the $\mathrm{np}$ interaction. Effects of the recoil and structure of $A$ are neglected. The limit problems that arise in the use of Lippmann-Schwinger equations with three-particle final states are treated for the case of short-range forces, and the discussion is extended to include Coulomb forces. The final exact "post" form of the transition matrix element resembles the distorted-wave Born approximation result given by Huby and Mines, and may be considered a justification of it.