Muon capture in nuclei: An ab initio approach based on Green's function Monte Carlo methods

An ab initio Green's function Monte Carlo (GFMC) method is introduced for calculating total rates of muon weak capture in light nuclei with mass number A <= 12. As a first application of the method, we perform a calculation of the rate in H-3 and He-4 in a dynamical framework based on realistic two- and three-nucleon interactions and realistic nuclear charge-changing weak currents. The currents include one- and two-body terms induced by pi- and rho-meson exchange, and N-to-Delta excitation, and are constrained to reproduce the empirical value of the Gamow-Teller matrix element in tritium. We investigate the sensitivity of theoretical predictions to current parametrizations of the nucleon axial and induced pseudoscalar form factors as well as to two-body contributions in the weak currents. The large uncertainties in the measured He-4 rates obtained from bubble-chamber experiments (carried out over 50 years ago) prevent us from drawing any definite conclusions. No data exist for H-3, but results are compared to those of a recent Faddeev calculation as a validation of the present GFMC method.