Relativity and the enhancement of the weak axial-charge matrix elements in the lead region.

Abstract

We present a calculation of first-forbidden \ensuremath{\beta}-decay transitions in the lead region using relativistic mean-field and relativistic Hartree approximations to a quantum hydrodynamic model of Serot and Walecka. A formalism for the response of the core to a valence particle or hole in the case of weak transitions is developed and studied for the \ensuremath{\pi}- and \ensuremath{\rho}-meson fields present in the model. Two applications are shown for which the mean-field results show a sizable enhancement of the matrix element. This enhancement is partly quenched by the inclusion of the vacuum corrections. The core response for these cases turns out to be negligible in the long wavelength limit. Altogether, it is concluded that the relativistic effects discriminate against nonrelativistic calculations but, however, are not enough to account for the recently reported discrepancy between shell model analysis of beta-decay rates and the (nonrelativistic) impulse approximation and meson-exchange-current calculations.