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Register a new userHfF$^+$ as a candidate to search for the nuclear weak quadruple moment
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Nuclei with a quadrupole deformation such as $^{177}$Hf have enhanced weak quadrupole moment which induces the tensor weak electron-nucleus interaction in atoms and molecules. Corresponding parity non-conserving (PNC) effect is strongly enhanced in the $^3Delta_1$ electronic state of the $^{177}$HfF$^+$ cation which has very close opposite parity levels mixed by this tensor interaction. In the present paper we perform relativistic many-body calculations of this PNC effect. It is shown that the tensor weak interaction induced by the weak quadrupole moment gives the dominating contribution to the PNC effects in $^{177}$HfF$^+$ which significantly exceeds contributions of the vector anapole moment and the scalar weak charge. The anapole and the weak charge can contribute due to the nonadiabatic mechanism proposed here. Therefore, corresponding experiment will allow one to separate the tensor weak PNC effect from the other PNC effects and to measure the quadrupole moment of the neutron distribution which gives the dominating contribution to the weak quadrupole moment.
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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 $^3Delta_1$ 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)].
The energy splitings for $J = 1$, $F=3/2$, $|M_F|=3/2$ hyperfine levels of the $^3Delta_1$ electronic state of $^{180}$Hf$^{19}$F$^+$ ion are calculated as functions of the external variable electric and magnetic fields within two approaches. In the first one transition to the rotating frame is performed, whereas in the second approach the quantization of rotating electromagnetic field is performed. Calculations are required for understanding possible systematic errors in the experiment to search for electron electric dipole moment (eEDM) on $^{180}$Hf$^{19}$F$^+$ ion.
It is demonstrated that the TaN molecule is the best candidate to search for T,P-violating nuclear magnetic quadrupole moment (MQM), it also looks promising to search for other T,P-odd effects. We report results of coupled-cluster calculations of T,P-odd effects in TaN produced by the Ta nucleus MQM, electron electric dipole moment (EDM), scalar$-$pseudoscalar nucleus$-$electron interactions, also of the molecule-axis hyperfine structure constant and dipole moment. Nuclear calculations of $^{181}$Ta MQM are performed to express the T,P-odd effect in terms of the strength constants of T,P-odd nuclear forces, proton and neutron EDM, QCD parameter $theta$ and quark chromo-EDM.
We use (1+1$$) resonance-enhanced multiphoton photodissociation (REMPD) to detect the population in individual rovibronic states of trapped HfF$^+$ with a single-shot absolute efficiency of 18%, which is over 200 times better than that obtained with fluorescence detection. The first photon excites a specific rotational level to an intermediate vibronic band at 35,000-36,500 cm$^{-1}$, and the second photon, at 37,594 cm$^{-1}$ (266 nm), dissociates HfF$^+$ into Hf$^+$ and F. Mass-resolved time-of-flight ion detection then yields the number of state-selectively dissociated ions. Using this method, we observe rotational-state heating of trapped HfF$^+$ ions from collisions with neutral Ar atoms. Furthermore, we measure the lifetime of the $^3Delta_1$ $v=0,, J=1$ state to be 2.1(2) s. This state will be used for a search for a permanent electric dipole moment of the electron.
Autoionization of Rydberg states of HfF, prepared using the optical-optical double resonance (OODR) technique, holds promise to create HfF+ in a particular Zeeman level of a rovibronic state for an electron electric dipole moment (eEDM) search. We characterize a vibronic band of Rydberg HfF at 54 cm-1 above the lowest ionization threshold and directly probe the state of the ions formed from this vibronic band by performing laser-induced fluorescence (LIF) on the ions. The Rydberg HfF molecules show a propensity to decay into only a few ion rotational states of a given parity and are found to preserve their orientation qualitatively upon autoionization. We show empirically that we can create 30% of the total ion yield in a particular |J+,M+> state and present a simplified model describing autoionization from a given Rydberg state that assumes no angular dynamics.
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