Magnetic dipole and electric quadrupole amplitudes induced by the hyperfine interaction in the Cesium 6S-7S transition and the parity violation calibration

Abstract

A possible way to calibrate the Cesium 6S→7S parity violating electric dipole amplitude E 1 (p.v) is to make use of the ratio E 1 (p.v)/M 1 (h.f) where M 1 (h.f) is the magnetic dipole amplitude induced by the hyperfine interaction V(h.f). We show by evaluating relativistic and many-body effects that M 1 (h.f) is given, to better than 3•10 −3 , by the geometrical mean of the 6S and 7S hyperfine splittings and thus provides a very good calibration of E 1 (p.v.). It one wishes to reach the 1% accuracy, it may be no longer legitimate to ignore the electric quadrupole amplitude E 2 (h.f) which can also be induced by V(h.f). We have shown that E 2 (h.f), computed within a one-particle model, is strongly suppressed by an approximate selection rule. This rule, however, does not work in general for many-body effects. Consequently we have made an estimate of the ratio E 2 (h.f)/M 1 (h.f) to first order in the electron-electron interaction; we have found a value which confirms the necessity of including the quadrupole amplitude E 2 (h.f) in the 6S→7S radiative amplitude, as it is suggested by a recent phenomenological analysis of the experimental data. This quadrupole amplitude E 2 (h.f.) is by itself an interesting quantity since it is governed almost exclusively by man Demonstration de la possibilite de calibrer l'amplitude electrique dipolaire violant la parite E 1 (p.v.) a mieux que 3•10 −3 en utilisant le rapport E 1 (p.v.)/M 1 (h.f.), ou M 1 (h.f.), amplitude dipolaire magnetique induite par l'interaction hyperfine V(h.f.), est donnee par la moyenne geometrique des ecarts hyperfins des etats 6S et 7S, en tenant compte des corrections relativistes et des effets a N corps. A cette precision, necessite d'introduire l'amplitude quadripolaire electrique E 2 (h.f.) que l'on calcule a l'aide d'un modele a une particule: elle est fortement inhibee par une regle de selection approchee, qui ne s'applique pas en general aux effets a N corps