Calculation of isotope shifts and King plot nonlinearities in Ca$^+$

Many-body perturbation theory is implemented in order to calculate the isotope shifts of $4s$, $4p_{1/2}$, $4p_{3/2}$, $3d_{3/2}$, and $3d_{5/2}$ energy levels of Ca$^+$, for even isotopes $A=$40, 42, 44, 46, 48. The results are presented for mass shift and field shift, as well as for higher-order field shifts, quadratic mass shift, nuclear polarization correction, and the cross term between field and mass shifts. Additionally, we examine King-plot nonlinearities introduced by the higher-order isotope-shift corrections to the combinations of $3d_{3/2}\rightarrow 4s$, $3d_{5/2}\rightarrow 4s$, and $4p_{1/2}\rightarrow 4s$ transitions. For these transitions, second-order mass shift and nuclear polarization correction are identified as the dominant sources of King plot nonlinearity.