μ-Meson Capture inLi6Leading to the Ground State ofHe6

Abstract

We calculate the rate of the capture reaction of ${\ensuremath{\mu}}^{\ensuremath{-}}$ mesons in ${\mathrm{Li}}^{6}$ leading to the ${\mathrm{He}}^{6}$ ground state (Godfrey-type reaction), a process which is expected to give more accurate information on the $\ensuremath{\mu}$-capture coupling constants than the capture in nuclei leading to all possible final states. Induced pseudoscalar coupling and Gell-Mann's conserved vector current are taken into account, and numerical results are given assuming a universal weak interaction. The ${\mathrm{Li}}^{6}$ and ${\mathrm{He}}^{6}$ wave functions are taken as shell model states with $\mathrm{LS}$ coupling and configuration mixing. It is found that the capture rate is sensitive to the $p$-shell radius, and for a determination of the latter, the Stanford electron scattering results for ${\mathrm{Li}}^{6}$ have been analyzed taking into account the recoil motion of the $\ensuremath{\alpha}$-particle core; however, the main portion of the radial integral in the theoretical capture rate can be read off the scattering data directly. The capture rate is found to be of the order of 0.4\ifmmode\times\else\texttimes\fi{}${10}^{3}$ ${\mathrm{sec}}^{\ensuremath{-}1}$, its exact value still depending on some assumptions about the coupling.