Theoretical study of HfF$^+$ for the electron EDM search

TL;DR

This theoretical study provides detailed calculations of electronic states, properties, and lifetimes of HfF$^+$, supporting its use in electron EDM experiments by revealing its electronic structure and effective electric field.

Contribution

It offers ab initio relativistic calculations of HfF$^+$ electronic states, electric fields, hyperfine constants, and lifetimes, advancing understanding for EDM search applications.

Findings

HfF$^+$ has a deeply bound ground state with $D_e=6.4$ eV.

The $^3 riangle_1$ state has a lifetime of about 0.4 seconds.

Effective electric field on the electron is calculated as $5.84*10^{24}$ Hz/e·cm.

Abstract

We report ab initio relativistic correlation calculations of potential curves and electric dipole transition moments for ten low-lying electronic states, effective electric field on the electron, hyperfine constants and radiative lifetimes for the $^3\Delta_1$ state of cation of the heavy transition metal fluoride HfF$^+$, which it is suggested to be used in experiments to search for the electric dipole moment of the electron. It is obtained that HfF$^+$ has deeply bound $^1\Sigma^+$ ground state; its dissociation energy is $D_e=6.4$ eV. The $^3\Delta_1$ state is obtained as the relatively long-lived, with lifetime equal to about 0.4 s.,first excited state lying about 0.2 eV higher. The calculated effective electric field, $E_{eff}=W_d|\Omega|$, acting on an electron in this state is $5.84*10^{24} Hz/{e*cm}$. The obtained hyperfine constants are $A_{\parallel}= -1239$ MHz for the $^{177}$Hf nucleus and $A_{\parallel}= -58.1$ MHz for the $^{19}$F nucleus.