Abstract
A high-precision calculation of the $7s\ensuremath{-}8s$ parity-nonconserving (PNC) transition amplitude in francium, based on a relativistic all-order method, is presented. Our values for the PNC amplitudes in ${}^{223}\mathrm{Fr}$ and ${}^{210}\mathrm{Fr}$ are ${E}_{\mathrm{PNC}}=15.41(17)$ and $14.02(15),$ respectively, in units ${10}^{\ensuremath{-}11}i|e|{a}_{0}(\ensuremath{-}{Q}_{W}/N),$ where ${Q}_{W}$ is the weak charge and N is the neutron number. Spin-dependent contributions to the PNC amplitude are calculated for Fr isotopes with nucleon numbers $A=207,$ 209, 211, and 213. To assess the accuracy of our calculations, we apply the present all-order method to the $6s\ensuremath{-}7s$ PNC amplitude in cesium and obtain a result in close agreement with previous high-precision calculations.
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