Neutron-Electron Interaction in Cutoff Theory

The perturbation-theoretic result for the neutron-electron interaction, as calculated by Salzman in the Chew no-recoil theory, is in serious disagreement with experiment. The main part of the experimental interaction ({~}4.2 kev) is accounted for by the Foldy term (4.08 kev). But the latter is not included in the no-recoil approximation, where one calculates only the electron interaction with the static pion cloud of the physical neutron. For this part of the interaction the no-recoil perturbation result is too large by a factor of at least twenty. We investigate here the possibility that higher order corrections drastically alter the pion cloud charge distribution. Using the techniques developed by Miyazawa, one can express the higher order corrections in terms of weighted integrals over the pion-nucleon interaction cross sections. It is found that the higher order effects indeed reduce the pion cloud contribution, but only by 20 percent. Because of certain ambiguities involved in treating the cutoff function, it cannot be stated that this represents the true content of Chew's theory; but it seems unlikely that any reasonable treatment of the cutoff could reduce the discrepancy much further.