One-Pion-Exchange-Current Contribution to Neutron-ProtonBremsstrahlung

Abstract

The electromagnetic current ${\mathrm{j}}_2^{\mathrm{OPE}}$ due to the exchange of a charged pion between a neutron and a proton is rederived by comparing the bremsstrahlung matrix element computed from the Schrödinger equation with that obtained from the lowest-order Feynman diagrams. No account is taken of renormalization effects or nucleon resonances. The operator $\int d^{3}x{\overrightarrow{\mathrm{j}}}_2^{\mathrm{OPE}}\left(\overrightarrow{\mathrm{x}}\right)e^{-i\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{x}}}$ which is needed for neutron-proton bremsstrahlung calculations is evaluated, and an approximation to it obtained as an expansion in powers of (photon energy)/(pion mass), keeping the first two terms. This is expected to be considerably more accurate than expanding the bremsstrahlung matrix element itself in powers of $k$. The second term in the expansion contributes to ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\leftrightarrow {}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ transitions and may become significant even for small values of $\frac{k}{\mu }$. As a preparation for actual calculations the operator is rewritten in terms of irreducible tensors. The treatment of nonlocalities other than charged-pion exchange is discussed briefly.