Muon Capture on Deuteron and 3He

Abstract

The muon-capture reactions $^{2}\mathrm{H}$(${\ensuremath{\mu}}^{\ensuremath{-}},{\ensuremath{\nu}}_{\ensuremath{\mu}}$)$\mathit{nn}$ and $^{3}\mathrm{He}$(${\ensuremath{\mu}}^{\ensuremath{-}},{\ensuremath{\nu}}_{\ensuremath{\mu}}$)$^{3}\mathrm{H}$ are studied with conventional or chiral realistic potentials and consistent weak currents. The initial and final $A=2$ and $A=3$ nuclear wave functions are obtained from the Argonne ${v}_{18}$ or chiral next-to-next-to-next-to leading order (N3LO) two-nucleon potential, in combination with, respectively, the Urbana IX or chiral next-to-next-to leading order (N2LO) three-nucleon potential in the case of $A=3$. The weak current consists of polar- and axial-vector components. The former are related to the isovector piece of the electromagnetic current via the conserved-vector-current hypothesis. These and the axial currents are derived either in a meson-exchange or in a chiral effective field theory ($\ensuremath{\chi}$EFT) framework. There is one parameter (either the $N$-to-$\ensuremath{\Delta}$ axial coupling constant in the meson-exchange model, or the strength of a contact term in the $\ensuremath{\chi}$EFT model) that is fixed by reproducing the Gamow-Teller matrix element in tritium $\ensuremath{\beta}$ decay. The model dependence relative to the adopted interactions and currents (and cutoff sensitivity in the $\ensuremath{\chi}$EFT currents) is weak, resulting in total rates of $392.0\ifmmode\pm\else\textpm\fi{}2.3$ ${\mathrm{s}}^{\ensuremath{-}1}$ for $A=2$, and $1484\ifmmode\pm\else\textpm\fi{}13$ ${\mathrm{s}}^{\ensuremath{-}1}$ for $A=3$, where the spread accounts for this model dependence.