Semileptonic weak and electromagnetic interactions with nuclei: Parity violations in electron scattering and abnormal-parity admixtures in nuclear states

Abstract

We derive an expression for the difference in the differential cross section for the scattering of right- and left-handed longitudinally polarized electrons from nuclei. Our result is applicable to scattering between any two nuclear levels and includes contributions from both the parity-nonconserving weak-electromagnetic interference and from abnormal-parity admixtures in the nuclear states. It is written in terms of the same nuclear matrix elements that govern all semileptonic transitions between the two levels and these matrix elements are examined using a recently developed one-body density matrix analysis of weak and electromagnetic interactions with nuclei. By exploiting the different momentum transfer dependence of the admixture and interference contributions, we find that, for the general cases considered here, the two contributions can be observed independently. In inelastic transitions in even-even nuclei, the admixture terms dominate at low-momentum transfers allowing for a determination of the scale of the parity admixing and a check of other parity-violation experiments. In this limit the contributions from the abnormal-parity admixtures can be investigated by appealing to the long-wavelength limit of the nuclear multipole matrix elements and by specifying the nuclear-state admixing with one overall scale parameter, which may become large in cases of favorable admixing. At higher momentum transfers, the interference terms dominate, permitting an investigation of the weak neutral-current interaction. In elastic scattering, current conservation implies that the leading term of the abnormal-parity nuclear matrix element vanishes; hence, the weak-electromagnetic interference is highly dominant in these cases. These results are illustrated by two examples using a simple parity-violating nucleon-nucleon potential derived from one-pion exchange. We use previously determined one-body transition densities to calculate the asymmetry in the 0 +0 → 1 +1 (15.11 MeV) transition in 12C, and perform a new calculation of the asymmetry in elastic scattering from 13C, determining the one-body transition densities from electron scattering data.