Neutron Asymmetry in Polarized Nuclear Muon Capture

A general theoretical framework for neutron emissions due to nuclear muon capture is given in terms of relativistic and nonrelativistic kinematics, which can be applied to the cases where the energies of the final nuclear states belong to the continuous spectrum as well as the discrete one. The consequences of chiral invariance and conserved-vector-current (CVC) theory are taken into account in the formulation. The formulas obtained are compared with conventional ones. In particular, the pioneering work due to Primakoff is re-examined from this general framework. The difference between the CVC theory with the impulse approximation and the nuclear CVC theory is discussed. In the limit of small momentum of the emitted neutrino, the present formalism is related to the conventional $\beta$-decay formalism. The effect of nuclear collective motions on neutron asymmetry is discussed without assuming any detailed nuclear models.