Relativistic effects in search for new intra-atomic force with isotope shifts

TL;DR

This paper investigates how relativistic effects influence the search for new intra-atomic forces via isotope shifts, revealing that relativistic calculations are crucial for accurate interpretation and proposing a method to mitigate standard model background effects.

Contribution

It demonstrates the importance of relativistic wave functions in accurately estimating isotope shift nonlinearities and suggests using specific atomic states to improve new physics searches.

Findings

Relativistic effects significantly increase predicted nonlinearity in isotope shifts.

Nonrelativistic calculations underestimate the nonlinearity for mediator masses > 1 MeV.

Using p_{3/2} states can reduce standard model background in new physics searches.

Abstract

Isotope shift of atomic spectra is considered as a probe of new interaction between electrons and neutrons in atoms. We employ the method of seeking a breakdown of King's linearity in the isotope shifts of two atomic transitions. In the present work, we evaluate the magnitudes of the nonlinearity using relativistic wave functions and the result is compared with that of nonrelativistic wave functions in our previous work. It turns out that the nonrelativistic calculation underestimates the nonlinearity owing to the new interaction in the mass range of the mediator greater than 1 MeV. Further, we find that the nonlinearity within the standard model of particle physics is significantly magnified by the relativistic effect in the $\text{p}_{1/2}$ state. To get rid of this obstacle in the new physics search, we suggest to avoid $\text{p}_{1/2}$, and use $\text{p}_{3/2}$ instead for example.