Partial conservation of axial current constraints on pion production or absorption within nonrelativistic nuclear dynamics

We show the necessity of two-nucleon axial currents and associated pion emission or absorption operators for the partial conservation of the axial current (PCAC) nuclear matrix elements with arbitrary nuclear dynamics described by a nonrelativistic Schrodinger equation. As examples we construct such nonrelativistic axial two-body currents in the linear- and the heterotic (g(A) = 1.26) sigma models, with an optional isoscalar vector (omega) meson exchange. The nuclear axial current matrix elements obey PCAC only if the nuclear wave functions used in the calculation are solutions to the Schrodinger equation with the static one-meson-exchange potential constructed in the respective (sigma) model. The same holds true for the nuclear pion production amplitude, since it is proportional to the divergence of the axial current matrix element, by Virtue of PCAC. Thus we found a consistency condition between the pion creation or absorption operator and the nuclear Hamiltonian. We present examples drawn from our models and discuss the implication of our results for one-pion-two-nucleon processes. [S0556-2813(98)00310-0].