Blackbody radiation shift, multipole polarizabilities, oscillator strengths, lifetimes, hyperfine constants, and excitation energies in Ca+

Abstract

A systematic study of Ca${}^{+}$ atomic properties is carried out using a high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to $n=7$. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-dipole scalar polarizabilities for the $5s$, $6s$, $7s$, $8s$, $4{p}_{j}$, $5{p}_{j}$, $3{d}_{j}$, and $4{d}_{j}$ states and tensor polarizabilities for the $4{p}_{3/2}$, $5{p}_{3/2}$, $3{d}_{j}$, and $4{d}_{j}$ states in Ca${}^{+}$ are calculated. Methods are developed to accurately treat the contributions from highly excited states, resulting in significant (factor of 3) improvement in the accuracy of the $3{d}_{5/2}$ static polarizability value, $31.8(3){a}_{0}^{3}$, in comparison with the previous calculation [Arora et al., Phys. Rev. A 76, 064501 (2007).]. The blackbody radiation shift of the $4s--3{d}_{5/2}$ clock transition in Ca${}^{+}$ is calculated to be $0.381(4)$ Hz at room temperature, $T=300$ K. Electric-quadrupole $4s--\mathit{nd}$ and electric-octupole $4s--\mathit{nf}$ matrix elements are calculated to obtain the ground-state multipole $E2$ and $E3$ static polarizabilities. Excitation energies of the $\mathit{ns}$, $\mathit{np}$, $\mathit{nd}$, $\mathit{nf}$, and $\mathit{ng}$ states with $n\ensuremath{\leqslant}$ 7 in are evaluated and compared with experiment. Recommended values are provided for the $7{p}_{1/2}$, $7{p}_{3/2}$, $8{p}_{1/2}$, and $8{p}_{3/2}$ removal energies for which experimental measurements are not available. The hyperfine constants $A$ are determined for the low-lying levels up to $n=7$. The quadratic Stark effect on hyperfine structure levels of $^{43}\mathrm{Ca}$${}^{+}$ ground state is investigated. These calculations provide recommended values critically evaluated for their accuracy for a number of Ca${}^{+}$ atomic properties for use in planning and analysis of various experiments as well as theoretical modeling.