Atomic Clock States of Thulium have Near-Zero Electric Quadrupole Moment

TL;DR

This paper presents a highly accurate computational method for atomic electric quadrupole moments, demonstrating that thulium's clock transition states have near-zero EQM, which is significant for precision measurements and atomic clock development.

Contribution

The paper introduces a relativistic configuration interaction method for calculating atomic EQMs, applied to thulium, revealing its ground state has an exceptionally small EQM.

Findings

Thulium's clock states have near-zero electric quadrupole moments.

The method achieves high accuracy with full quadruple excitations.

Implications for other atoms with unpaired f electrons are discussed.

Abstract

A method for highly accurate calculations of atomic electric quadrupole moments (EQM) is presented, using relativistic general-excitation-rank configuration interaction wavefunctions based on Dirac spinors. Application to the clock transition states of the thulium atom employing up to full Quadruple excitations for the atomic wavefunction yields a final value of $Q_{zz}({^2F}_{7/2}) = 0.07 \pm 0.07$ a.u., establishing that the thulium electronic ground state has an exceptionally small EQM. A detailed analysis of this result is presented which has implications for EQMs of other atoms with unpaired $f$ electrons.