Calculation of energy levels,E1 transition amplitudes, and parity violation in francium

Many-body perturbation theory in the screened Coulomb interaction was used to calculate energy levels, E1 trransition amplitudes, and the parity-nonconserving (PNC) E1 amplitude of the 7s-8s transition in francium. The method takes into account the core-polarization effect, the second-order correlations, and the three dominating sequences of higher-order correlation diagrams: screening of the electron-electron interaction, particle-hole interaction, and the iterations of the self-energy operator. The result for the PNC amplitude for ${}_{}{}^{223}{}_{}{}^{}\mathrm{Fr}$ is E1(7s-8s)=(1.59±∼1%)×${10}^{\mathrm{-}10}$ ${\mathit{iea}}_{\mathit{B}}$(-${\mathit{Q}}_{\mathit{W}}$/N), where ${\mathit{Q}}_{\mathit{W}}$ is the weak charge of the nucleus, N=136 is the number of neutrons, e=‖e‖ is the elementary charge, and ${\mathit{a}}_{\mathit{B}}$ is the Bohr radius. Our prediction for the position of the 8s energy level of Fr, which has not been measured yet, is 13 110 ${\mathrm{cm}}^{\mathrm{-}1}$ below the limit of the continuous spectrum. The accuracy of the calculations was controlled by comparison with available experimental data and analogous calculations for cesium. It is estimated to be ∼0.1% for the energy levels and ∼1% for the transition amplitudes.