Zeeman interaction in ${}^3{\Delta }_1$ state of HfF${}^{+}$ to search for the electron electric-dipole-moment

Abstract

We report the theoretical investigation of the suppression of magnetic systematic effects in HfF${}^{+}$ cation for the experiment to search for the electron 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 as functions of the external electric field. The lowest value for the difference between the g-factors of $\Omega$-doublet levels, $\Delta g=3\times 10^{-6}$, is attained at the electric field 7 V/cm. The body-fixed g-factor, $G_{\parallel }$, was obtained both within the electronic structure calculations and 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 {\bf 342}, 1220 (2013)]. For the electronic structure calculations we used a combined scheme to perform correlation calculations of HfF${}^{+}$ which includes both the direct 4-component all-electron and generalized relativistic effective core potential approaches. The electron correlation effects were treated using the coupled cluster methods. The calculated value $G_{\parallel }=0.0115$ agrees very well with the $G_{\parallel }=0.0118$ obtained in the our fitting procedure. The calculated value $D_{\parallel }=-1.53$ a.u. of the molecule frame dipole moment (with the origin in the center of mass) is in agreement with the experimental value $D_{\parallel }=-1.54(1)$ a.u. [H. Loh, Ph.D. thesis, Massachusetts Institute of Technology (2006)].

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• Many body study of $g$-factor in boron-like argon
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• Towards High Performance Relativistic Electronic Structure Modelling: The EXP-T Program Package
• Rovibrational structure of the Ytterbium monohydroxide molecule and the $\mathcal{P}$,$\mathcal{T}$-violation searches
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• Enhanced nuclear spin dependent parity violation effects using the 199HgH molecule
• Accurate Evaluation of $\mathcal{P}$,$\mathcal{T}$-odd Faraday Effect in Atoms of Xe and Hg
• HfF${}^{+}$ as a candidate to search for the nuclear weak quadruple moment
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• Accurate numerical evaluation of systematics in the experiment for electron electric dipole moment measurement in HfF${}^{+}$