First-forbidden beta decay in the lead region and mesonic enhancement of the weak axial current.

Abstract

A shell-model study is made of first-forbidden \ensuremath{\beta} decay and related processes in A=205--212 nuclei. The interactions used are modifications of the Kuo-Herling realistic effective interactions for particles above and holes below $^{208}\mathrm{Pb}$ and a cross-shell G-matrix interaction connecting these two. Large-scale diagonalizations are made of 1p-1h excitations across the double-shell closure at $^{208}\mathrm{Pb}$. The calculations of the first-forbidden rates use effective single-particle matrix elements which incorporate core polarization of the final state to first order. All first-order initial state 1p-1h admixtures are included explicitly in the diagonalization. A least-squares fit of theory to experiment for eighteen \ensuremath{\Delta}J=0 and 1 decay rates was made with two unknowns: (1) an enhancement factor ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{mec}}$ for the rank zero matrix element of ${\ensuremath{\gamma}}_{5}$, and (2) an overall scaling factor for the rank one component of the decay rate. A good fit is achieved yielding ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{mec}}$=2.01\ifmmode\pm\else\textpm\fi{}0.05 and a rank-one scaling factor of 0.97\ifmmode\pm\else\textpm\fi{}0.06. The agreement of the latter with unity indicates a satisfactory understanding of the rank-one component of the decay. The result ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{mec}}$=2.01\ifmmode\pm\else\textpm\fi{}0.05 indicates an enhancement of the matrix element of ${\ensuremath{\gamma}}_{5}$ by 100% over the impulse approximation. A 40% effect is predicted from meson exchange. Thus, a deficiency in the meson-exchange calculation or some further as-yet-unforeseen contribution is suggested. Predictions for twenty other decays in A=205--211 nuclei are compared to experiment and found to be in good general agreement. A calculation of the capture of neutrinos by $^{205}\mathrm{Tl}$ is described in detail.