Zeeman interaction in the Δ13 state of HfF+ to search for the electron electric dipole moment
AbstractA theoretical study devoted to suppression of magnetic systematic effects in HfF+ cation for an experiment to search for the electron electric dipole moment is reported. The g factors for J=1, F=3/2, |MF|=3/2 hyperfine levels of the Δ13 state are calculated as functions of the external electric field. The minimal value for the difference between the g factors of Ω-doublet levels, Δg=3×10−6, is attained at the electric field 7 V/cm. The body-fixed g factor, G∥, was obtained both within the ab initio electronic structure calculations and with our fit of the experimental data [H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science 342, 1220 (2013)SCIEAS0036-807510.1126/science.1243683]. For the electronic structure calculations we used a combined scheme to perform correlation calculations of HfF+, which includes both the direct four-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∥=0.0115 agrees very well with the G∥=0.0118 obtained with our fitting procedure. The calculated ab initio value D∥=−1.53 a.u. for the molecule-frame dipole moment (with the origin in the center of mass) is in agreement with the experimental datum D∥=−1.54(1) a.u. [H. Loh, Ph.D. thesis, Massachusetts Institute of Technology, 2006.].