Application of the Burnett-Kroll Soft-Proton Theorem to Nucleon-Nucleon Bremsstrahlung

Abstract

We give an explicit analytic formula for the leading terms in the square of the matrix element for nucleon-nucleon bremsstrahlung in the relativistic, model-independent, soft-photon theory of Nyman. Such a formula should simplify direct and detailed comparisons of this soft-photon theory with experiment and with the predictions of other models. These comparisons have been difficult because Nyman in his original calculation of $\mathrm{NN}\to \mathrm{NN}\gamma$ was forced by the extremely complicated matrix element to use entirely numerical procedures. To obtain an analytic result we have used the Burnett-Kroll theorem, which makes it possible to bypass many of the complications of a straightforward algebraic calculation. We also emphasize the general utility of the Burnett-Kroll theorem as a calculational tool for obtaining in an almost trivial fashion the leading terms in the squares of very complicated radiative matrix elements.