Calculation of isotope shifts and King-plot nonlinearities in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>Ca</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:math>

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