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The longitudinal asymmetry induced by parity-violating (PV) components in thenucleon-nucleon potential is studied in the charge-exchange reaction 3He(n,p)3Hat vanishing incident neutron energies. An expression for the PV observable isderived in terms of T-matrix elements for transitions from the {2S+1}L_J=1S_0and 3S_1 states in the incoming n-3He channel to states with J=0 and 1 in theoutgoing p-3H channel. The T-matrix elements involving PV transitions areobtained in first-order perturbation theory in the hadronic weak-interactionpotential, while those connecting states of the same parity are derived fromsolutions of the strong-interaction Hamiltonian with thehyperspherical-harmonics method. The coupled-channel nature of the scatteringproblem is fully accounted for. Results are obtained corresponding to realisticor chiral two- and three-nucleon strong-interaction potentials in combinationwith either the DDH or pionless EFT model for the weak-interaction potential.The asymmetries, predicted with PV pion and vector-meson coupling constantscorresponding (essentially) to the DDH "best values" set, range from -9.44 to-2.48 in units of 10^{-8}, depending on the input strong-interactionHamiltonian. This large model dependence is a consequence of cancellationsbetween long-range (pion) and short-range (vector-meson) contributions, and isof course sensitive to the assumed values for the PV coupling constants.

The parity-violating asymmetry in the 3He(n,p)3H reaction