Application of Dispersion Relations to Neutron-Electron Interaction

Abstract

The main part of the neutron-electron interaction is accounted for by the Foldy term (4.08 kev). The most recent experimental value is 4.165 kev. The static charge-cloud term obtained in Chew's no-recoil theory which does not include the Foldy term, therefore, should contribute an interaction of a few hundred ev, whereas Salzman's calculation corresponding to ${f}^{2}=0.08$ would give \ensuremath{\sim}10 kev, which is in serious disagreement with experiment. Treiman and Sachs found that the higher order corrections in the static model reduce the discrepancy by about 20%. We carry out a covariant calculation of the meson current part of the neutron-electron interaction, using dispersion relations derived by Chew et al. under the assumption that the (3,3) resonance dominates the dispersion integral. It is found that the recoil effects of the perturbation part reduce Salzman's perturbation result by 30%, and the higher order corrections including recoil reduce the perturbation result further by about 20%. The final result is 5.7 kev for ${f}^{2}=0.08$. The contribution of the meson current to the anomalous magnetic moment of the nucleon is found to be 2.9 nuclear magnetons for ${f}^{2}=0.08$.