The ${}^3\mathrm{He}({\mu }^{-},{\nu }_{\mu }{)}^3\mathrm{H}$ weak capture is studied using correlated-hyperspherical-harmonics wave functions, obtained from realistic Hamiltonians consisting of the Argonne $v_{14}$ or Argonne $v_{18}$ two-nucleon, and Tucson-Melbourne or Urbana-IX three-nucleon interactions. The nuclear weak charge and current operators have vector and axial-vector components with one- and two-body contributions. The axial-vector current includes the nucleon and $\Delta$ induced pseudoscalar terms, with coupling constants $g_{\mathrm{PS}}$ and $g_{\mathrm{PS}}^{*}$ derived from pion-pole dominance and partially conserved-axial-current hypothesis. The strength of the leading two-body operator is adjusted to reproduce the Gamow-Teller matrix element in tritium $\beta$ decay. The calculated total capture rate is within $\sim 0.5\%$ of the most recent measurement, $1496\pm 4{\sec }^{-1}.$ The predictions for the capture rate and angular correlation parameters $A_v,$ $A_t,$ and $A_{\Delta }$ are found to be only very weakly dependent on the model input Hamiltonian. The variation of the observables with $g_{\mathrm{PS}}$ and $g_{\mathrm{PS}}^{*}$ and the theoretical uncertainties deriving from the model-dependent procedure used to constrain the axial current are investigated.

• Received 3 December 2001

DOI:https://doi.org/10.1103/PhysRevC.66.054003