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

Abstract

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 Schr\odinger equation. As examples we construct such nonrelativistic axial two-body currents in the linear- and the heterotic ${(g}_{A}=1.26) \ensuremath{\sigma}$ models, with an optional isoscalar vector $(\ensuremath{\omega})$ meson exchange. The nuclear axial current matrix elements obey PCAC only if the nuclear wave functions used in the calculation are solutions to the Schr\odinger equation with the static one-meson-exchange potential constructed in the respective $(\ensuremath{\sigma})$ 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.