Semi-leptonic weak and electromagnetic interactions in nuclei:: Parity violations in electron scattering and weak neutral currents

Abstract

A general result for the difference in differential cross sections for electron scattering between any two nuclear levels with incident longitudinally polarized right- and left-handed electrons is derived. This difference must involve the parity-violating weak interaction at least linearly and can be used to study weak neutral currents as pointed out by Feinberg. A V — A structure for the weak neutral currents is assumed with a semi-leptonic current-current interaction, and the electromagnetic interaction is treated in the one-photon-exchange approximation. The result is expressed in terms of the same set of reduced matrix elements of the multipoles of the nuclear currents which govern all electromagnetic and weak transitions between these levels. A previously developed unified analysis of semi-leptonic weak and electromagnetic interactions in nuclei which determines one-body transition densities, including their spin and spatial dependences, through electron scattering provides nuclear transitions to serve as known analyzers in testing the structure of this part of the weak interaction. Examples are given using Weinberg's model of the weak neutral currents. Feinberg's result for elastic scattering from spin-0 nuclei is rederived and two new examples using previously determined one-body densities are discussed : the 1 +0 → 0 +1 (3.56 MeV) transition in 6Li and the 0 +0 → 1 + 1(15.1 MeV) transition in 12C.