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

TL;DR

This paper uses many-body perturbation theory to calculate isotope shifts in calcium ion energy levels and investigates the nonlinearities in King plots caused by higher-order isotope-shift effects.

Contribution

It provides detailed calculations of isotope shifts including higher-order effects and analyzes their impact on King plot nonlinearities in Ca$^+$.

Findings

Second-order mass shift and nuclear polarization are main sources of King plot nonlinearity.

Higher-order isotope-shift corrections significantly affect the interpretation of isotope shift data.

The study enhances understanding of isotope shift contributions in calcium ions.

Abstract

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.