The dual King relation

TL;DR

The paper introduces the dual King relation, a new linear relation among isotope pairs in atomic spectroscopy, which provides constraints on nuclear factors and helps test higher order isotope shifts and new physics.

Contribution

It presents the dual King relation, a novel linear relation that exchanges roles of electronic and nuclear factors, offering new constraints without additional fit parameters.

Findings

The dual King relation is mathematically equivalent to the original King relation.

It constrains isotope dependence ratios independent of electron wave functions.

It can be used to test for unknown higher order isotope shifts and constrain new light bosons.

Abstract

We introduce a new linear relation in the isotope shifts of atomic spectroscopy. While the famous King relation is the linear relation among the different transitions, the new one is the linear relation among the different isotope pairs. Since we obtain this relation by exchanging the roles of the electronic and the nuclear factors in the original relation, we call it the dual King relation. This relation shows us similar information to the original King relation without including new fit parameters when we measure the isotope shifts of many transitions. In the dual King relation, the fit coefficients consist of the nuclear factors. Then, the fit results give us constraints to the ratios of the isotope dependence independent of the electron wave functions. This helps us to test the origin of unknown higher order isotope shifts. We show that the dual King relation can also be employed to constrain the weakly interacting light new boson at the same level as the original King relation.