Phenomenological interaction currents in nuclear systems

Abstract

Beginning with the differential conservation law for electric charge, the electromagnetic current density operator for a nuclear system is decomposed into one-body and two-body terms. The two-body or interaction current density is further separated into a longitudinal part which is related to the charge exchange part of the nuclear force and a transverse part, depending on the nucleons' dynamical variables, and containing a large number of arbitrary parameters. In determining all the linearly independent irreducible vectors formed from the relative position vectors R i and R k and the nucleon spin vectors σ i and σ k , which may be present in the transverse current density, the method of group characters is used. Along with these spin-space vectors, all linearly independent irreducible spin-space scalars, pseudoscalars, and pseudovectors are also calculated. These linearly independent vectors are then used together with the various symmetry properties of the current density to determine the most general form the transverse current density can assume. In a similar manner, the most general form of the Fourier transform of this current density operator is determined. Lastly, the form of the axial vector weak current density arising from mesonic exchange effects in β-decaying nuclei is derived again by using the spin-space pseudovectors and the various symmetry properties of the weak current density.