  Searches for neutrinoless-double beta decay rates are crucial in addressing
questions within fundamental symmetries and neutrino physics. The rates of
these decays depend not only on unknown parameters associated with neutrinos,
but also on nuclear properties. In order to reliably extract information about
the neutrino, one needs an accurate treatment of the complex many-body dynamics
of the nucleus. Neutrinoless-double beta decays take place at momentum
transfers on the order of 100 MeV/$c$ and require both nuclear electroweak
vector and axial current matrix elements. Muon capture, a process in the same
momentum transfer regime, has readily available experimental data to validate
these currents. In this work, we present results of {\it ab initio}
calculations of partial muon capture rates for $^3$He and $^6$Li nuclei using
variational and Green's Function Monte Carlo computational methods. We estimate
the impact of the three-nucleon interactions, the cutoffs used to regularize
two-nucleon ($2N$) interactions, and the energy range of $2N$ scattering data
used to fit these interactions.
