A theoretical analysis of parity violation induced by neutral currents in atomic cesium

Abstract

In this paper we give a theoretical analysis of the parity violation phenomena in nS − n′S transitions in atomic cesium induced by the electron-nucleus neutral-current interaction. The actual observation of parity violation consists in the measurement of an interference between the p.v. electric dipole amplitude E l pv with the electric amplitude induced by a static electric field. Our theoretical work must then include a calculation of the diagonal and non-diagonal polarizabilities of the states of atomic cesium. We have used a one-electron model proposed by Norcross which incorporates some many-body effects like the electric screening induced by the core polarization in a semi-empirical way. Our calculated values of the diagonal and non-diagonal polarizabilities of the nS states are in good agreement with the existing measurements; this confirms the already well-established success of the model in predicting the radiative transitions in cesium. We present theoretical arguments supported by detailed numerical computations showing that the one-particle matrix element of the parity-violating electron-nucleus interaction and the parity-violating electric dipole amplitude E l pv itself weakly depend on the shape of the one-electron potential provided the binding energies of the valence states are reproduced accurately. Furthermore it turns out that because of a compensation mechanism, the parity-violating transition is induced by the radiation field outside the ion core region where the screening can be described simply in terms of the measurable cesium ion polarizability. Our results are then used to extract, from the Ecole Normale Supérieure experiment, a value of the weak charge Q w = −57.1 ± 9.4 (r.m.s. statistical deviation) ± 4.7 (systematic uncertainty). This number is to be compared with the prediction of the Weinberg-Salam model with electro-weak radiative corrections: Q w = −68.6 ± 3.0. A general discussion of the uncertainties of the atomic physics calculations leads to the conclusion that the theoretical error which affects the determination of Q w is not likely to exceed 10 to 15%.