Hyperfine structure of the $4s$, $4p$, and $3d$ states in ${\mathrm{Ca}}^{+}$ evaluated by many-body perturbation theory

The hyperfine structure of the $4s$, $4p$, and $3d$ states in ${\mathrm{Ca}}^{+}$ has been evaluated with the use of many-body perturbation theory. Core-polarization and correlation effects have been included by solving inhomogeneous one- and two-particle differential equations. By solving these equations iteratively, these effects have been treated also to higher orders. Certain correlation effects have been accounted for by modifying the valence orbitals to approximate "Brueckner orbitals." Relativistic effects were estimated on the basis of relativistic calculations including core polarization. The final results for ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ca}$ are $A\left(4^2{S}_{\frac{1}{2}}\right)=-819\mathrm{}$ MHz, $A\left(4^2{P}_{\frac{1}{2}}\right)=-148\mathrm{}$ MHz, $A\left(4^2{P}_{\frac{3}{2}}\right)=-30.9\mathrm{}$ MHz, $\frac{B\left(4^2{P}_{\frac{3}{2}}\right)}{Q}=155\mathrm{}$ MHz/b, $A\left(3^2{D}_{\frac{3}{2}}\right)=-52\mathrm{}$ MHz, $\frac{B\left(3^2{D}_{\frac{3}{2}}\right)}{Q}=68\mathrm{}$ MHz/b, $A\left(3^2{D}_{\frac{5}{2}}\right)=-5.2\mathrm{}$ MHz, and $\frac{B\left(3^2{D}_{\frac{5}{2}}\right)}{Q}=97\mathrm{}$ MHz/b.