Relativistic mean-field approach to anapole moment: Atomic parity-violating hyperfine transitions

Abstract

A generalized formula of nuclear anapole moment is derived using the current relativistic nuclear approach. The Dirac spin magnetization and the anomalous spin magnetization contributions to anapole moment are shown to be proportional to the second moment of respective magnetizations. The valence nucleon effective g_l(g_a) factors in a nucleus are obtained from the different phenomenological generalizations of relativistic nuclear magnetic moment. The unitary transformation approach is used to derive the parity nonconserving (PNC) perturbed wave functions. In the case of g_l parametrization, the anomalous spin magnetization and pion contributions to anapole moment are nearly two and three times the Dirac magnetization contribution respectively; while for g_a parametrization, all the three contributions are of the same order of magnitude. Using these calculated values of anapole moment and available atomic structure data from published literature, the ¹³³Cs PNC hyperfine amplitudes are calculated. The results are closer to the experimental data, particularly when the measured value of Im E1^pv/β is used. The optical rotation angles induced by nuclear spin dependent PNC interaction are also calculated.