Comprehensive Inclusion of Higher-order Ca$^+$ Isotope Shifts in the King's Plot Yields an Order Improvement on the $e^-$-$n$ Coupling Limit

TL;DR

This paper refines the analysis of isotope shifts in calcium ions by including higher-order effects, leading to a tenfold improvement in constraining hypothetical electron-neutron interactions beyond the Standard Model.

Contribution

It introduces a comprehensive method to include higher-order isotope shift effects in the King's plot, significantly improving limits on new physics interactions.

Findings

Higher-order effects are crucial for accurate isotope shift analysis.

The study achieves an order of magnitude better constraint on electron-neutron coupling.

Comparison of computational approaches reveals significant differences in second-order parameters.

Abstract

By critically evaluating higher-order nonlinear effects to the isotope shifts (ISs) in the low-lying transition frequencies of the singly charged calcium ion, stringent constraint on the electron-neutron coupling due to a hypothetical boson describing physics beyond the Standard Model is inferred. It shows an order magnitude difference compared to the previously reported limit demonstrating importance of higher-order effects in the analysis of nonlinearity in the King's plot. The first-order IS parameters and enhancement factor ($D$) were evaluated using two complementary approaches in the relativistic coupled-cluster theory framework: namely finite-field (FF) and analytical response (AR) approaches. Extraction of the second-order IS parameters in the FF approach show numerical instabilities, so they are determined in the AR approach. Comparison of these factors with previous calculation shows substantial differences in the magnitudes. However, $D$ values from both the FF and AR approaches display excellent agreement. We also show explicitly roles of electron correlation effects in the evaluation of $D$ values accurately.