The sensitivity of hyperfine structure to nuclear radius and quark mass variation

TL;DR

This paper investigates how atomic hyperfine structures depend on nuclear radius and quark masses, providing formulas and calculations to help constrain possible variations of fundamental constants over time.

Contribution

It derives an analytical formula linking hyperfine structure to nuclear radius and quark masses, tested with relativistic calculations for several atoms.

Findings

Derived an analytical dependence of hyperfine structure on nuclear radius and quark mass.

Validated the formula with relativistic Hartree-Fock calculations for multiple atoms.

Enables using atomic clock and quasar data to constrain quark mass variation.

Abstract

To search for the temporal variation of the fundamental constants one needs to know dependence of atomic transition frequencies on these constants. We study the dependence of the hyperfine structure of atomic $s$-levels on nuclear radius and, via radius, on quark masses. An analytical formula has been derived and tested by the numerical relativistic Hartree-Fock calculations for Rb, Cd$^+$, Cs, Yb$^+$ and Hg$^+$. The results of this work allow the use of the results of past and future atomic clock experiments and quasar spectra measurements to put constrains on time variation of the quark masses.