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

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.