High-precision study of Hg$^+$ atomic properties

The systematic study of Hg$^+$ properties is carried out using 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. Third-order many-body perturbation theory calculations are also carried out to establish the size of the higher-order corrections. Excitation energies of the [Xe]$4f^{14}5d^{10}ns$, [Xe]$4f^{14}5d^{10}np$, [Xe]$4f^{14}5d^{10}nd$, [Xe]$4f^{14}5d^{10}n'f$, and [Xe]$4f^{14}5d^{10}n'g$ ($n \leq$ 10, $n' \leq$ 9) states in Hg$^+$ are evaluated. Reduced matrix elements, oscillator strengths, and transition rates are determined for electric-dipole transitions including the $ns$ ($n=6-11$), $np$ ($n=6-10$), $nd$ ($n=6-10$), $nf$ ($n=5-9$), and $ng$ ($n=5-9$) states. Lifetimes of these states, E1 ground state polarizability, and the hyperfine $A$ and $B$ constants of the first low-lying levels up to $n$ = 7 are determined. The quadratic Stark effect on hyperfine structure levels of $^{199}$Hg$^+$ ground state is investigated. These calculations provide critically evaluated recommended values of Hg$^+$ atomic properties.