Nuclear anapole moments

Nuclear anapole moments are parity-odd, time-reversal-even $E1\mathrm{}$ moments of the electromagnetic current operator. Although the existence of this moment was recognized theoretically soon after the discovery of parity nonconservation (PNC), its experimental isolation was achieved only recently, when a new level of precision was reached in a measurement of the hyperfine dependence of atomic PNC in ${}^{133}\mathrm{Cs}.$ An important anapole moment bound in ${}^{205}\mathrm{Tl}$ also exists. In this paper, we present the details of the first calculation of these anapole moments in the framework commonly used in other studies of hadronic PNC, a meson-exchange potential that includes long-range pion exchange and enough degrees of freedom to describe the five independent $S-P$ amplitudes induced by short-range interactions. The resulting contributions of $\pi ,$ $\rho ,$ and $\omega$ exchange to the single-nucleon anapole moment, to parity admixtures in the nuclear ground state, and to PNC exchange currents are evaluated, using configuration-mixed shell-model wave functions. The experimental anapole moment constraints on the PNC meson-nucleon coupling constants are derived and compared with those from other tests of the hadronic weak interaction. While the bounds obtained from the anapole moment results are consistent with the broad “reasonable ranges” defined by theory, they are not in good agreement with the constraints from the other experiments. We explore possible explanations for the discrepancy and comment on the potential importance of new experiments.