All-order perturbation calculation of energies, hyperfine constants, multipole polarizabilities, and blackbody radiation shift inSr87+

Abstract

Excitation energies of the $[\mathrm{Kr}]{\mathit{ns}}_{1/2}$, $[\mathrm{Kr}]{\mathit{np}}_{j}$, $[\mathrm{Kr}]{\mathit{nd}}_{j}$, and $[\mathrm{Kr}]{\mathit{nf}}_{j}$ ($n\ensuremath{\leqslant}9$ and $[\mathrm{Kr}]=(1{s}^{2}2{s}^{2}2{p}^{6}3{s}^{2}3{p}^{6}3{d}^{10}4{s}^{2}4{p}^{6}$) in Sr ii are evaluated. First-order, second-order, third-order, and all-order Coulomb energies and first-order and second-order Coulomb-Breit energies are calculated. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to $n=7$. Electric-dipole ($5{s}_{1/2}\ensuremath{-}{\mathit{np}}_{j}$, $n=5--26$), electric-quadrupole ($5{s}_{1/2}\ensuremath{-}{\mathit{nd}}_{j}$, $n=4--26$), and electric-octupole ($5{s}_{1/2}\ensuremath{-}{\mathit{nf}}_{j}$, $n=4--26$) matrix elements are calculated to obtain the ground-state $E1$, $E2$, and $E3$ static polarizabilities. Scalar and tensor polarizabilities for the $5{p}_{j}\ensuremath{-}9{p}_{j}$ and $4{d}_{j}\ensuremath{-}8{d}_{j}$ excited states in Sr ii are also calculated. All the above-mentioned matrix elements are determined using the all-order method. We also investigate the hyperfine structure in $^{87}\mathrm{Sr}$${}^{+}$. The hyperfine $A$ values and $B$ values are determined for the first low-lying levels up to $n=7$. The quadratic Stark effect on hyperfine-structure levels of the $^{87}\mathrm{Sr}$${}^{+}$ ground state is investigated. The calculated shift for the $(F=5,M=0)\ensuremath{\leftrightarrow}(F=4,M=0)$ transition is found to be 0.120(1) Hz/(kV/cm)${}^{2}$. These calculations provide a theoretical benchmark for comparison with the experiment and theory. A careful study of uncertainty of our calculations is carried out for the transition-matrix elements, line strengths, transition rates, lifetimes, polarizabilities, and the Stark shift coefficient.