Pseudoscalar Interaction in the Theory of Beta-Decay

Abstract

It is shown that analysis of the pseudoscalar interaction in beta-decay theory results in the appearance of the two sets of nuclear matrix elements, $\ensuremath{\int}{\ensuremath{\theta}}_{p}\ensuremath{\beta}{\ensuremath{\gamma}}_{5} \mathrm{and} \frac{i}{2M}\ensuremath{\int}{\ensuremath{\theta}}_{p}\ensuremath{\sigma}\ifmmode\cdot\else\textperiodcentered\fi{}{\ensuremath{\nabla}},$ ${\ensuremath{\theta}}_{p}$ denoting the angular part of the pseudoscalar lepton covariant and ${\ensuremath{\nabla}}$ the gradient operation on the radial part of this covariant, instead of the single matrix element, $\ensuremath{\int}{\ensuremath{\theta}}_{p}{\ensuremath{\gamma}}_{5}.$As a consequence pseudoscalar interaction correction factors containing derivatives of the lepton wave functions are deduced.