Pseudoscalar Matrix Element in Beta-Decay

Abstract

The interpretation of the $\ensuremath{\beta}$-spectrum of RaE seems to need a mixture of pseudoscalar and tensor interactions. Estimates of the necessary ${G}_{P}$ give ${G}_{P}\ensuremath{\gg}{G}_{T}$ to compensate for the small pseudoscalar matrix element. This matrix element is greatly increased if the nucleon is in a potential which strongly mixes free particle states of positive and negative energies even though the diagonal terms are not large. Such an interaction arises from pseudoscalar meson theory. The pseudoscalar matrix element is calculated for the RaE decay assuming that the nucleons interact through pseudoscalar coupled pseudoscalar mesons. Exchange transitions, in which two nucleons exchange the charge and spin given to the electron and neutrino, predominate. The RaE spectrum can be fitted with ${G}_{P}\ensuremath{\sim}\ensuremath{-}{G}_{T}$. Exchange terms alter other momentum type matrix elements appreciably. Such effects are unimportant for gradient coupled pseudoscalar mesons.