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

TL;DR

This paper calculates the parity-violating asymmetry in the 3He(n,p)3H reaction at zero incident neutron energy, exploring the effects of different nuclear interaction models and weak coupling constants.

Contribution

It provides a detailed theoretical framework for predicting PV asymmetries using realistic strong and weak interaction models, including hyperspherical-harmonics solutions and perturbation theory.

Findings

Predicted asymmetries range from -9.44 to -2.48 in 10^{-8} units.

Results show large dependence on the choice of interaction models and PV coupling constants.

Cancellations between long-range and short-range contributions significantly affect the asymmetry values.

Abstract

The longitudinal asymmetry induced by parity-violating (PV) components in the nucleon-nucleon potential is studied in the charge-exchange reaction 3He(n,p)3H at vanishing incident neutron energies. An expression for the PV observable is derived in terms of T-matrix elements for transitions from the {2S+1}L_J=1S_0 and 3S_1 states in the incoming n-3He channel to states with J=0 and 1 in the outgoing p-3H channel. The T-matrix elements involving PV transitions are obtained in first-order perturbation theory in the hadronic weak-interaction potential, while those connecting states of the same parity are derived from solutions of the strong-interaction Hamiltonian with the hyperspherical-harmonics method. The coupled-channel nature of the scattering problem is fully accounted for. Results are obtained corresponding to realistic or chiral two- and three-nucleon strong-interaction potentials in combination with either the DDH or pionless EFT model for the weak-interaction potential. The asymmetries, predicted with PV pion and vector-meson coupling constants corresponding (essentially) to the DDH "best values" set, range from -9.44 to -2.48 in units of 10^{-8}, depending on the input strong-interaction Hamiltonian. This large model dependence is a consequence of cancellations between long-range (pion) and short-range (vector-meson) contributions, and is of course sensitive to the assumed values for the PV coupling constants.