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

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Abstract
A possible way to calibrate the Cesium 6S → 7S parity violating electric dipole amplitude E1 (p.v) is to make use of the ratio E1 (p.v )/M1 (h.f ) where M1 (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 M1 (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 Z1(p.v). It one wishes to reach the 1 % accuracy, it may be no longer legitimate to ignore the electric quadrupole amplitude E2 (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 E2 (h.f)/M1 (h.f) to first order in the electron-electron interaction ; we have found a value which confirms the necessity of including the quadrupole amplitude E2(h.f) in the 6S→7S radiative amplitude, as it is suggested by a recent phenomenological analysis of the experimental data. This quadrupole amplitude E2(h.f) is by itself an interesting quantity since it is governed almost exclusively by many-body effects