Excitation energies, polarizabilities, multipole transition rates, and lifetimes of ions along the francium isoelectronic sequence

Abstract

Relativistic many-body perturbation theory is applied to study properties of ions of the francium isoelectronic sequence. Specifically, energies of the $7s$, $7p$, $6d$, and $5f$ states of Fr-like ions with nuclear charges $Z=87--100$ are calculated through third order; reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for $7s\text{\ensuremath{-}}7p$, $7p\text{\ensuremath{-}}6d$, and $6d\text{\ensuremath{-}}5f$ electric-dipole transitions; and $7s\text{\ensuremath{-}}6d$, $7s\text{\ensuremath{-}}5f$, and $5{f}_{5∕2}\text{\ensuremath{-}}5{f}_{7∕2}$ multipole matrix elements are evaluated to obtain the lifetimes of low-lying excited states. Moreover, for the ions $Z=87--92$ calculations are also carried out using the relativistic all-order single-double method, in which single and double excitations of Dirac-Fock wave functions are included to all orders in perturbation theory. With the aid of the single-double wave functions, we obtain accurate values of energies, transition rates, oscillator strengths, and the lifetimes of these six ions. Ground state scalar polarizabilities in $\mathrm{Fr}\phantom{\rule{0.2em}{0ex}}\mathrm{I}$, $\mathrm{Ra}\phantom{\rule{0.2em}{0ex}}\mathrm{II}$, $\mathrm{Ac}\phantom{\rule{0.2em}{0ex}}\mathrm{III}$, and $\mathrm{Th}\phantom{\rule{0.2em}{0ex}}\mathrm{IV}$ are calculated using relativistic third-order and all-order methods. Ground state scalar polarizabilities for other Fr-like ions are calculated using a relativistic second-order method. These calculations provide a theoretical benchmark for comparison with experiment and theory.