Unexpectedly large difference of the electron density at the nucleus in the 4p $^2$P$_{1/2,3/2}$ fine-structure doublet of Ca$^+$

TL;DR

This study measures isotope shifts in calcium ions using photon recoil spectroscopy, revealing a significant J-dependent field shift difference that challenges existing theoretical predictions and provides benchmarks for atomic structure calculations.

Contribution

The paper reports the first high-precision measurement of the splitting isotope shift in Ca$^+$, highlighting a larger-than-predicted ratio of field shift constants and advancing atomic structure theory.

Findings

Resolved isotope shift differences between D1 and D2 lines.

Extracted a larger-than-expected ratio of field shift constants.

Provided benchmark data for relativistic atomic structure calculations.

Abstract

We measured the isotope shift in the $^2$S$_{1/2}$-$^2$P$_{3/2}$ (D2) transition in singly-ionized calcium ions using photon recoil spectroscopy. The high accuracy of the technique enables us to resolve the difference between the isotope shifts of this transition to the previously measured isotopic shifts of the $^2$S$_{1/2}$-$^2$P$_{1/2}$ (D1) line. This so-called splitting isotope shift is extracted and exhibits a clear signature of field shift contributions. From the data we were able to extract the small difference of the field shift coefficient and mass shifts between the two transitions with high accuracy. This J-dependence is of relativistic origin and can be used to benchmark atomic structure calculations. As a first step, we use several ab initio atomic structure calculation methods to provide more accurate values for the field shift constants and their ratio. Remarkably, the high-accuracy value for the ratio of the field shift constants extracted from the experimental data is larger than all available theoretical predictions.