All-order perturbation calculation of energies, hyperfine constants, multipole polarizabilities, and blackbody radiation shift in ${}^{87}\mathrm{Sr}$${}^{+}$

Excitation energies of the $[\mathrm{Kr}]{\mathit{ns}}_{1/2}$, $[\mathrm{Kr}]{\mathit{np}}_j$, $[\mathrm{Kr}]{\mathit{nd}}_j$, and $[\mathrm{Kr}]{\mathit{nf}}_j$ ($n⩽9$ and $[\mathrm{Kr}]=(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^6$) 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 ($5s_{1/2}-{\mathit{np}}_j$, $n=5–26$), electric-quadrupole ($5s_{1/2}-{\mathit{nd}}_j$, $n=4–26$), and electric-octupole ($5s_{1/2}-{\mathit{nf}}_j$, $n=4–26$) matrix elements are calculated to obtain the ground-state $E1$, $E2$, and $E3$ static polarizabilities. Scalar and tensor polarizabilities for the $5p_j-9p_j$ and $4d_j-8d_j$ 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 $(F=5,M=0)\leftrightarrow (F=4,M=0)$ 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.