This work investigates the muon capture reactions 2H(\mu^-,\nu_\mu)nn and3He(\mu^-,\nu_\mu)3H and the contribution to their total capture rates arisingfrom the axial two-body currents obtained imposing thepartially-conserved-axial-current (PCAC) hypothesis. The initial and final A=2and 3 nuclear wave functions are obtained from the Argonne v_{18} two-nucleonpotential, in combination with the Urbana IX three-nucleon potential in thecase of A=3. The weak current consists of vector and axial components derivedin chiral effective field theory. The low-energy constant entering the vector(axial) component is determined by reproducting the isovector combination ofthe trinucleon magnetic moment (Gamow-Teller matrix element of tritiumbeta-decay). The total capture rates are 393.1(8) s^{-1} for A=2 and 1488(9)s^{-1} for A=3, where the uncertainties arise from the adopted fittingprocedure.
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