Zeeman interaction in $^3\Delta_1$ state of HfF$^+$ to search for the electron electric-dipole-moment

摘要

We report the theoretical investigation of the suppression of magneticsystematic effects in HfF$^+$ cation for the experiment to search for theelectron electric dipole moment. The g-factors for $J = 1$, $F=3/2$,$|M_F|=3/2$ hyperfine levels of the $^3\Delta_1$ state are calculated asfunctions of the external electric field. The lowest value for the differencebetween the g-factors of $\Omega$-doublet levels, $\Delta g = 3 \times10^{-6}$, is attained at the electric field 7 V/cm. The body-fixed g-factor,$G_{\parallel}$, was obtained both within the electronic structure calculationsand with our fit of the experimental data from [H. Loh, K. C. Cossel, M. C.Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science {\bf342}, 1220 (2013)]. For the electronic structure calculations we used acombined scheme to perform correlation calculations of HfF$^+$ which includesboth the direct 4-component all-electron and generalized relativistic effectivecore potential approaches. The electron correlation effects were treated usingthe coupled cluster methods. The calculated value $G_{\parallel}=0.0115$ agreesvery well with the $G_{\parallel}=0.0118$ obtained in the our fittingprocedure. The calculated value $D_{\parallel}=-1.53$ a.u. of the moleculeframe dipole moment (with the origin in the center of mass) is in agreementwith the experimental value $D_{\parallel}=-1.54(1)$ a.u. [H. Loh, Ph.D.thesis, Massachusetts Institute of Technology (2006)].