An accurate determination of the effective electric field (E eff ) in YbF is important, as it can be combined with the results of future experiments to give an improved new limit for the electric dipole moment of the electron. We report a relativistic coupled-cluster calculation of this quantity in which all the core electrons were excited. It surpasses the approximations made in the previous reported calculations. We obtain a value of 23.1 GV/cm for E eff in YbF with an estimated error of less than 10%. The crucial roles of the basis sets and the core excitations in our work are discussed.The electric dipole moment (EDM) of a nondegenerate system arises from violations of both the parity (P) and the time-reversal (T) symmetries [1]. T violation implies charge parity (CP) violation via CPT theorem [2]. In general, CP violation is a necessary condition for the existence of the EDMs of physical systems, and, in particular, atoms and molecules. Paramagnetic atoms and molecules are sensitive to the EDM of the electron (eEDM) [3], which is an important probe of the physics beyond the standard model [4]. The eEDM arising from CP violation could also be related to the matter-antimatter asymmetry in the universe [5]. A number of studies using atoms have been performed during the past few decades to extract an upper limit for the eEDM [6]. In general, for heavy polar molecules, the effective electric field experienced by an electron (E eff ) obtained from relativistic molecular calculations can be several orders of magnitude larger than that in atoms [7]. Therefore, the experimental observable (i.e., the shift in energy because of the interaction of the electric field with the eEDM) is also several orders of magnitude larger. Owing to the high sensitivity of the eEDM in molecules, there has been a considerable increase in interest in this field during the past decade The aim of the present work is to calculate E eff in YbF using a rigorous relativistic many-body method, which is more accurate than the methods used in the previous calculations. The method we have chosen is the four-component relativistic coupled-cluster (RCC) method, which is arguably the current gold standard for calculating the electronic structure of heavy atoms and diatomic molecules [18].The electron EDM interaction Hamiltonian in a molecule can be written as [19] Here, d e is the eEDM of an electron,  is one of the Dirac matrices, and  are the Pauli spin matrices. i is the index of summation labelling for electrons and N e is the total number of electrons. E int is the electric field acting on an electron in a molecule. The quantity that is of experimental interest in the search for the eEDM is an energy shift (E) of a particular state owing to the interaction Hamiltonian given in Eq.(1). This can be expressed as

In this paper we propose to utilize the X 2 g (ν,N,F,M) = (0,0,1/2, ±1/2) → (1,0,1/2, ±1/2) or (2,0,1/2, ±1/2) transition of N 2 + (I = 0) to test variations of the proton-to-electron mass ratio. The X 2 g ground state exhibits no quadrupole shift and the Zeeman shift of the N = 0 → N = 0 transition is exactly zero. Because N 2 + is nonpolar, systematic level shifts such as Stark shifts induced by trap electric field or blackbody radiation are very small and the thermalization of the rotational states is inhibited. This eases the requirements on the experimental setup significantly. Employing Raman transitions at the "magic" wavelength the (0,0,1/2, ±1/2) → (1,0,1/2, ±1/2) or (2,0,1/2, ±1/2) transition frequency can be measured very precisely.

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Transition frequencies of cold molecules must be accurately evaluated to test the variance in the protonto-electron mass ratio. Measuring the X 2 (v,N) = (0,0) → (1,0) transition frequency of optically trapped 174 Yb 6 Li molecules is a promising method for achieving this goal. The Stark shifts induced by trap and probe (for the Raman transition) lasers are eliminated by choosing appropriate frequencies (magic frequencies) during the construction of the optical lattice. In the far-off resonance region, the Stark shift is found to be less than 10 −16 even when the laser frequencies are detuned from the magic frequencies by ∼1 MHz.

We report a series of quantum-chemical calculations for the ground and some of the low-lying excited states of an isolated LiYb molecule by the spin-orbit multistate complete active space second-order perturbation theory (SO-MS-CASPT2). Potential energy curves, spectroscopic constants, and transition dipole moments (TDMs) at both spin-free and spin-orbit levels are obtained. Large spin-orbit effects especially in the TDMs of the molecular states dissociating to Yb((3)P(0,1,2)) excited states are found. To ensure the reliability of our calculations, we test five types of incremental basis sets and study their effect on the equilibrium distance and dissociation energy of the ground state. We also compare CASPT2 and CCSD(T) results for the ground state spectroscopic constants at the spin-free relativistic level. The discrepancies between the CASPT2 and CCSD(T) results are only 0.01 Å in equilibrium bond distance (R(e)) and 200 cm(-1) in dissociation energy (D(e)). Our CASPT2 calculation in the supermolecular state (R=100 a.u.) with the largest basis set reproduces experimental atomic excitation energies within 3% error. Transition dipole moments of the super molecular state (R=100 a.u.) dissociating to Li((2)P) excited states are quite close to experimental atomic TDMs as compared to the Yb((3)P) and Yb((1)P) excited states. The information obtained from this work would be useful for ultracold photoassociation experiments on LiYb.

Electronic open-shell ground-state properties of selected alkali-metal-alkaline-earth-metal polar molecules are investigated. We determine potential energy curves of the (2)Σ(+) ground state at the coupled-cluster singles and doubles with partial triples (CCSD(T)) level of electron correlation. Calculated spectroscopic constants for the isotopes ((23)Na, (39)K, (85)Rb)-((40)Ca, (88)Sr) are compared with available theoretical and experimental results. The variation of the permanent dipole moment (PDM), average dipole polarizability, and polarizability anisotropy with internuclear distance is determined using finite-field perturbation theory at the CCSD(T) level. Owing to moderate PDM (KCa: 1.67 D, RbCa: 1.75 D, KSr: 1.27 D, RbSr: 1.41 D) and large polarizability anisotropy (KCa: 566 a.u., RbCa: 604 a.u., KSr: 574 a.u., RbSr: 615 a.u.), KCa, RbCa, KSr, and RbSr are potential candidates for alignment and orientation in combined intense laser and external static electric fields.

The relativistic coupled-cluster method is applied to calculate the magnetic dipole hyperfine constant ''A'' of the 6s 1/2 , 6p 1/2 , 6p 3/2 , and 5d 3/2 states of singly ionized barium. After the inclusion of two-body correlation effects into the computation of the hyperfine matrix elements, the accuracy of the obtained values was significantly increased compared to earlier computations. Based on these numbers and earlier calculations of the electric dipole transitions and excitation energies, an estimate for the accuracy of the ͉͓5 p 6 ͔6s 1/2 ͘ →͉͓5p 6 ͔5d 3/2 ͘ parity-nonconserving electric dipole transition amplitude is carried out. The results suggest that for the first time, to our knowledge, a precision of better than 1% is feasible for this transition amplitude.An experiment to observe parity nonconservation ͑PNC͒ in a single trapped and laser cooled ion was proposed by Fortson about a decade ago ͓1͔. Initial steps towards the realization of such an experiment on Ba ϩ have been taken and the results were reported recently ͓2͔.Relativistic many-body calculations have been performed for the parity-nonconserving electric dipole amplitude for the ͉͓5 p 6 ͔6s 1/2 ͘→͉͓5p 6 ͔5d 3/2 ͘ transition in 137 Ba ϩ ͓3,4͔.

We present quantum-chemical calculations for the ground and some low-lying excited states of isolated LiCa and LiSr molecules using multi-state complete active space second-order perturbation theory (MS-CASPT2). The potential energy curves (PECs) and their corresponding spectroscopic constants, obtained at the spin-free (SF) and spin-orbit (SO) levels, agree well with available experimental values. Our SO-MS-CASPT2 calculation at the atomic limit (R = 100 a.u.) with the largest basis set reproduces experimental atomic excitation energies within 3% for both LiCa and LiSr. In addition, permanent dipole moments and transition dipole moments at the SF level are also obtained. Rovibrational calculations of the ground and selected excited states, together with the spontaneous emission rates, demonstrate that the formation of ultracold LiCa and LiSr molecules in low-lying vibrational levels of the electronic ground state may be possible.