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

Abstract

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\ifmmode\pm\else\textpm\fi{}\ensuremath{\sim}1%)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}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=\ensuremath{\Vert}e\ensuremath{\Vert} 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 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ 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 \ensuremath{\sim}0.1% for the energy levels and \ensuremath{\sim}1% for the transition amplitudes.