Fourier-transform spectroscopy and global deperturbation treatment of the A1Σu+ and b3Πu states of K2 in the entire bound energy range.

Rotationally resolved Fourier-transform spectra of laser-induced fluorescence A1Σu+∼b3Πu→X1Σg+ of K2 molecules were recorded and analyzed, yielding 4053 term values of the spin-orbit (SO) coupled A ∼ b complex of the 39K2 isotopologue with ∼0.01 cm-1 accuracy. Their compilation with 1739 term values from previously published sources allowed them to cover the energy range [9955, 17 436] cm-1 from the bottom of the lower-lying b3Πu state up to the vicinity of the atomic asymptote 4s2S12 + 4p2P12, with a rotational quantum number J ∈ [0, 149]. The experimental data were processed by a direct 6 × 6 coupled-channel (CC) deperturbation treatment, which accounted explicitly for both SO and electronic-rotational interactions between all six e-symmetry states: A1Σu+(0u+), b3Πu(0u+,1u,2u), c3Σu(1u), and B1Πu(1u). The initial parameters of the global deperturbation model have been estimated in the framework of ab initio electronic structure calculations applying multi-reference configuration-interaction and coupled-clusters methods. The interatomic potentials analytically defined for A and b states, as well as SO-splitting of the triplet b state and A ∼ b SO-coupling functions, have been particularly refined to fit the 5792 term values of the 39K2 isotopologue, whereas the rest parameters were fixed on their ab initio values. The resulting mass-invariant parameters of the 6 × 6 CC model reproduced the overall rovibronic term energies of the A ∼ b complex of 39K2 with accuracy, which is well within the experimental errors. The quality of the deperturbation analysis was independently confirmed by comparison with the present obtained 705 and 14 term values of respective 39K41K and 41K2 isotopologues, as well as by agreement between measured and predicted relative intensity distributions in long A ∼ b → X(vX) band progressions. This deperturbation analysis provided the refined dissociation energy Tdis = 17 474.569(5) cm-1 and the long-range coefficient C3Σ = 5.501(4) × 105 cm-1 Å3 relevant to the non-relativistic atomic limit 4s + 4p. The derived Tdis yielded the accurate well depth De = 4450.910(5) cm-1 for the ground X1Σg+ state, whereas the new C3Σ value yielded the improved estimates for atomic K(4p2P12;32) radiative lifetimes, τ12 = 26.67(3) and τ32 = 26.32(3) ns.

Observation and modeling of bound-free transitions to the X1Σ+ and a3Σ+ states of KCs.

The oscillation continuum in laser-induced fluorescence spectra of bound-free c3Σ+ → a3Σ+ and (4)1Σ+ → X1Σ+ transitions of the KCs molecule was recorded by a Fourier-transform spectrometer and modeled under the adiabatic approximation. The required interatomic potentials for ground a3Σ+ and X1Σ+ states were reconstructed in an analytical Chebyshev-polynomial-expansion form in the framework of the regularization direct-potential-fit procedure based on the simultaneous consideration of experimental line positions from Ferber et al. [Phys. Rev. A 80, 062501 (2009)] and the present ab initio calculation of short-range repulsive potential data. It was proved that the repulsive part over the dissociation limit of the derived a3Σ+ potential reproduces the experiment better than the potentials reported in the literature. It is also shown that all empirical and semi-empirical potentials available for the X1Σ+ state reproduce the bound-free (4)1Σ+ → X1Σ+ spectrum with equal quality in the range of observations.

Theoretical study of the Coriolis effect in LiNa, LiK, and LiRb molecules.

The non-adiabatic electronic matrix elements, LΠΣ(R), that arise from the spin-conserving electron-rotational interactions between all mΣ+ and mΠ states, where multiplicity m = 1, 3, converging to the lowest three dissociation limits of Li-containing alkali diatomics, LiM (M = Na, K, Rb), were calculated ab initio up to large internuclear distances, R. The required electronic wavefunctions were obtained within the framework of the multi-reference configuration interaction treatment of the two-valence-electron problem constructed using small-core scalar-relativistic effective core potentials and l-independent core-polarization potentials. A least squares analysis of the ab initio functions at large internuclear distances in conjunction with long-range perturbation theory (LRPT) revealed three different asymptotic behaviors of the LΠΣ(R → +∞)-functions: const. + ß[n]/Rn, characterized by n = -1, 3 and 6. The asymptotic coefficients ß[n], extracted from the point-wise ab initio data, were found to be in agreement with their LRPT counterparts, which were evaluated analytically using the relevant atomic parameters. The mass dependence of the LΠΣ matrix elements was investigated analytically and numerically. To confirm the reliability of the LΠΣ(R)-functions and interatomic potentials at small and intermediate distances, the empirical q-factors available for the D1Π-states of all LiM molecules studied were compared with their theoretical counterparts derived from the present ab initio data.

A first principles study of the spin-orbit coupling effect in LiM (M = Na, K, Rb, Cs) molecules.

The spin-orbit (SO) interactions in low-lying electronic states of the LiM (M = Na, K, Rb, Cs) molecular series are studied through ab initio calculations of potential energy curves and SO coupling matrix elements as functions of the interatomic distance, R. Two different approaches are employed: (a) the Fock-space relativistic coupled-cluster calculations (FS-RCC) which directly yield full relativistic energies, Urel(R); the SO coupling functions, ξso(R), are extracted a posteriori through projecting scalar-relativistic wave functions onto the subspaces spanned by their full-relativistic counterparts; (b) the evaluation of the scalar-relativistic electronic energies, Usr(R), and relevant ξso(R) functions using the configuration interaction method with core-valence correlation accounted for using core polarization potentials (CI-CPP). The SO-free potentials and SO coupling functions obtained within the framework of both approaches are in good agreement with each other and their prior theoretical and empirical counterparts.

Long-range behavior of the transition dipole moments of heteronuclear dimers XY (X, Y = Li, Na, K, Rb) based on ab initio calculations.

The ab initio electronic transition dipole moments (ETDMs) of heteronuclear dimers XY (X, Y = Li, Na, K, Rb) were calculated between the ground and excited states converging to the lowest three dissociation limits. The spin-allowed ETDMs were evaluated in a wide range of interatomic distances, R, by means of the quasi-relativistic electronic wave functions obtained by the multi-reference configuration interaction method. The inner-shell electrons (2 electrons for Li and Na atoms, and 10 and 28 for K and Rb, respectively) were described using the non-empirical shape-consistent effective core potentials. The l-independent core polarization potentials of each atom were used to take core-polarization and core-valence correlation effects into account. The long-range behavior of both singlet-singlet X1Σ+-(2,3)1Σ+;(1,2)1Π and triplet-triplet a3Σ+-(2,3)3Σ+;(1,2)3Π transition moments is perfectly fitted at large R-distance by the asymptotic formula of X. Chu and A. Dalgarno, Phys. Rev. A: At., Mol., Opt. Phys., 2002, 66, 024701: , where the coefficient ß is equal to 2 and -1 for the Σ-Σ and Σ-Π transitions, respectively. The n2S-n2P transition moments, dA, and dynamic polarizabilites, αB, of the alkali atoms in the n2S state extracted from the present molecular calculations coincide with their empirical and ab initio counterparts to within a few percent.

Fourier-transform spectroscopy and deperturbation analysis of the spin-orbit coupled A(1)Σ(+) and b(3)Π states of KRb.

Fourier-transform A(1)Σ(+) - b(3)Π â†’ X(1)Σ(+) laser-induced fluorescence spectra were recorded for the natural mixture of (39,41)K(85,87)Rb isotopologues produced in a heatpipe oven. Overall 4200 rovibronic term values of the spin-orbit coupled A(1)Σ(+) and b(3)Π states were determined with an uncertainty of about 0.01 cm(-1) in the energy range [10 850, 14 200] cm(-1) covering rotational quantum numbers J' ∈ [3, 280]. Direct deperturbation analysis of the A ∼ b complex performed within the framework of the A(1)Σ(+) ∼ b(3)ΠΩ=0,1,2 coupled-channel approach reproduced experimental data with a standard deviation of 0.004 cm(-1). Initial parameters of the internuclear potentials and spin-orbit coupling functions along with the relevant transition dipole moments were obtained by performing the quasi-relativistic electronic structure calculations. The mass-invariant molecular parameters obtained from the fit were used to predict energy and radiative properties of the A ∼ b complex for low J levels of (39)K(85)Rb as well as for (41)K(87)Rb isotopologues, allowing us to identify the most reasonable candidates for the stimulated Raman transitions between the initial uppermost vibrational levels of the a(3)Σ(+) and X(1)Σ(+) states, the intermediate levels of the A ∼ b complex, and the lowest absolute ground X(1)Σ(+)(v = 0, J = 0) state.

Direct coupled-channels deperturbation analysis of the A(1)Σ(+) ∼ b(3)Π complex in LiCs with experimental accuracy.

We have carried out the direct deperturbation analysis of about 780 rovibronic term values of the strongly spin-orbit (SO) coupled A(1)Σ(+) and b(3)Π states of the (7)Li(133)Cs molecule recorded by polarization labelling spectroscopy technique. The explicit A(1)Σ(+) ∼ b(3)ΠΩ=0,1,2 coupled-channels treatment allowed us to reproduce 95% experimental term values with a standard deviation of 0.05 cm(-1) which is close to the accuracy of the present experiment. The initial potential energy curves (PECs) of the mutually perturbed states and SO matrix elements were ab initio evaluated in the basis of the spin-averaged wave functions. The empirically refined PECs and SO functions, along with the theoretical transition dipole moments, were used to predict energy and radiative properties of the A ∼ b complex for low J levels of both (7)Li(133)Cs and (6)Li(133)Cs isotopologues. The reasonable candidates for the stimulated Raman transitions between initial Feshbach resonance states, the mixed levels of the A ∼ b complex, and absolute ground X(1)Σ(+) (v = 0 and J = 0) state were identified.

Extended Fourier-transform spectroscopy studies and deperturbation analysis of the spin-orbit coupled A1Σ+ and b3Π states in RbCs.

The article presents a study of the strongly spin-orbit coupled singlet A(1)Σ(+) and triplet b(3)Π states of the RbCs molecule, which provide an efficient optical path to transfer ultracold molecules to their rovibrational ground state. Fourier-transform A(1)Σ(+) - b(3)Π â†’ X(1)Σ(+) and (4)(1)Σ(+) → A(1)Σ(+) - b(3)Π laser-induced fluorescence (LIF) spectra were recorded for the natural mixture of the (85)Rb(133)Cs and (87)Rb(133)Cs isotopologues produced in a heat pipe oven. Overall 8730 rovibronic term values of A(1)Σ(+) and b(3)Π states were determined with an uncertainty of 0.01 cm(-1) in the energy range [9012, 14087] cm(-1), covering rotational quantum numbers J ∈ [6, 324]. An energy-based deperturbation analysis performed in the framework of the four A(1)Σ(+) - b(3)Π(Ω = 0, 1, 2) coupled-channels approach reproduces 97% of the experimental term values of both isotopologues with a standard deviation of 0.0036 cm(-1). The reliability of the deperturbed mass-invariant potentials and spin-orbit coupling functions of the interacting A(1)Σ(+) and b(3)Π states is additionally proved by a good reproduction of the A - b → X and (4)(1)Σ(+) → A - b relative intensity distributions. The achieved accuracy of the A - b complex description allowed us to use the latter to assign the observed (5)(1)Σ(+) → A - b and (3)(1)Π â†’ A - b transitions. As is demonstrated, LIF to the A - b complex becomes as informative as to the ground X(1)Σ(+) state, which is confirmed by comparing the results of (4)(1)Σ(+) state analysis based on (4)(1)Σ(+) → A - b LIF with the data from V. Zuters et al. [Phys. Rev. A 87, 022504 (2013)] based on (4)(1)Σ(+) → X LIF.

Fourier-transform spectroscopy of (4)1Σ+ → A1Σ+ - b3Π, A1Σ+ - b3Π â†’ X1Σ+, and (1)3Δ1→b3Π(0±) transitions in KCs and deperturbation treatment of A1Σ+ and b3Π states.

High resolution Fourier-transform spectroscopy data of term values in the spin-orbit (SO) coupled first excited A(1)Σ(+) and b(3)Π states in KCs were obtained from (4)(1)Σ(+) → A(1)Σ(+) - b(3)Π, A(1)Σ(+) - b(3)Π â†’ X(1)Σ(+), and (1)(3)Δ1→b(3)Π(0(±)) spectra of laser-induced fluorescence (LIF). About 3000 new rovibronic term values of the A(1)Σ(+) and b(3)Π(Ω) states were obtained with an uncertainty about 0.01 cm(-1) and added to the previously obtained 3439 term values in Kruzins et al. [Phys. Rev. A 81, 042509 (2010)] and 30 term values of the b(3)Π(0(+)) state levels below the A(1)Σ(+) state in Tamanis et al. [Phys. Rev. A 82, 032506 (2010)]. The data field was extended considerably, going down to vibrational level v(b) = 0 and up in energy to 13,814 cm(-1), as compared to previously achieved v(b) = 14 and E = 13,250 cm(-1). Overall 6431 e-symmetry term values of (39)K(133)Cs were included in 4 × 4 coupled-channel deperturbation analysis. The analytical Morse-Long-Range (MLR) function yielded empirical diabatic potentials for the A(1)Σ(+) and b(3)Π(0(+)) states while the morphing of the SO ab initio points [J. T. Kim et al., J. Mol. Spectrosc. 256, 57 (2009)] provided the empirical diagonal and off-diagonal SO functions. Overall 98.5% of the fitted term values were reproduced with a rms (root mean square) uncertainty of 0.004 cm(-1). The reliability of the model is proved by a good agreement of predicted and measured term values of the (41)K(133)Cs isotopologue, as well as of measured and calculated intensities of (4)(1)Σ(+) → A(1)Σ(+) - b(3)Π LIF progressions. Direct-potential-fit of low-lying v(b) levels of the b(3)Π(0(-)) component yielded the MLR potential which represents the 204 f-symmetry experimental term values with a rms uncertainty of 0.002 cm(-1). The Ω-doubling of the b(3)Π0 sub-state demonstrates a pronounced vb-dependent increase.

Ab initio long-range interaction and adiabatic channel capture model for ultracold reactions between the KRb molecules.

The coefficients at the lowest-order electrostatic, induction, and dispersion terms of the anisotropic long-range potential between the two KRb((1)Σ(+)) molecules are evaluated through the static and dynamic molecular properties using the ab initio coupled cluster techniques. Adiabatic channel potentials for the ground-state molecules are obtained and used for the numerical quantum capture probability calculations in the spirit of the statistical adiabatic channel models. Capture rate coefficients for indistinguishable (polarized) and distinguishable (unpolarized) molecules at temperatures below 10 µK agree well with those computed with the simple isotropic dispersion R(-6) potential, but underestimate the measured ones [Ospelkaus et al., Science 327, 853 (2010)] up to a factor of 3. Preliminary assessment of the effects of higher-order long-range terms, retardation of dispersion forces, and magnetic dipole-dipole interaction does not offer any clear perspectives for drastic improvement of the capture approximation for the reactions studied.

Fourier transform spectroscopy and direct potential fit of a shelflike state: application to E(4)1Σ(+) KCs.

The paper presents high-resolution experimental study and a direct potential construction of a shelflike state E(4)(1)Σ(+) of the KCs molecule converging to K(4(2)S) + Cs(5(2)D) atomic limit; such data are of interest for selecting optical paths for producing and monitoring cold polar diatomics. The collisionally enhanced laser induced fluorescence (LIF) spectra corresponding to both spin-allowed E(4)(1)Σ(+) → X(1)(1)Σ(+) and spin-forbidden E(4)(1)Σ(+) → a(1)(3)Σ(+) transitions of KCs were recorded in visible region by Fourier transform spectrometer with resolution of 0.03 cm(-1). Overall about 1650 rovibronic term values of the E(4)(1)Σ(+) state of (39)K(133)Cs and (41)K(133)Cs isotopologues nonuniformly covering the energy range [16987, 18445] cm(-1) above the minimum of the ground X-state were determined with the uncertainty of 0.01 cm(-1). Experimental data field is limited by vibrational levels v' ∈ [2, 74] with rotational quantum numbers J' ∈ [1, 188]. The closed analytical form for potential energy curve (PEC) based on Chebyshev polynomial expansion (CPE) was implemented to a direct potential fit (DPF) of the experimental term values of the most abundant (39)K(133)Cs isotopologue. Besides analyticity, regularity, correct long-range behavior, and nice convergence properties, the CPE form demonstrated optimal balance on flexibility and constraint for the DPF of a shelflike state aggravated by a limited data set. The mass-invariant properties of the CPE PEC were tested by the prediction of rovibronic term values of the (41)K(133)Cs isotopomer which coincided with their experimental counterparts with standard deviation of 0.0048 cm(-1). The CPE modeling is compared with the highly flexible pointwise inverted perturbation approach model, as well as with conventional Dunham analysis of restricted data set v' ≤ 50. Reliability of the empirical PEC is additionally confirmed by good agreement between the calculated and experimental relative intensity distributions in the long E(v') → X(v") LIF progressions.

Analogue of oscillation theorem for nonadiabatic diatomic states: application to the A (1)Sigma(+) and b (3)Pi states of KCs.

Relative intensity measurements in the high resolution A (1)Sigma(+) approximately b (3)Pi--> X (1)Sigma(+) laser induced fluorescence spectra of the KCs molecule highlighted a breakdown of the conventional one-dimensional oscillation theorem (L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Pergamon, New York, 1965). For strongly spin-orbit coupled A (1)Sigma(+) and b (3)Pi states the number of nodes n(A) and n(b) of the non-adiabatic vibrational eigenfunctions phi and phi corresponding to the v-th eigenstate differs essentially from their adiabatic counterparts. It is found, however, that in the general case of two-component states with wavefunctions phi and phi coupled by the sign-constant potential operator V(12) not equal 0: (1) the lowest state v = 0 is not degenerate; and (2) the arithmetic mean of the number of nodes n(1) and n(2) of phi and phi never exceeds the ordering number v of eigenstate: (n(1) + n(2))/2

Experimental and theoretical studies of lambda doublings and permanent electric dipoles in the low-lying 1pi states of NaCs.

We present experimental data on the electric permanent dipole moments d(v',J') and lambda splittings (q factors) in the quasidegenerate (3) 1pi(e/f) state of the NaCs molecule over a wide range of the vibrational (v') and rotational (J') quantum numbers by using the combination of dc Stark mixing and electric radio frequency-optical double resonance methods. Within the experimental (3) 1pi state v' ranged from v' = 0 to 34, q values exhibited a pronounced decrease from 7.91x10(-6) to 0.47x10(-6) cm(-1), while absolute value(d) values varied between 8.0 and 5.0 D. Experimental evaluation yielded small d values about 1 D for D2 1pi state v' < 3 levels. The experiment is supported by ab initio electronic structure calculations performed for the (1-3) 1pi states of NaCs by means of the many-body multipartitioning perturbation theory of potential energy curves, permanent dipole, and angular coupling matrix elements for the lowest singlet states. The predicted d values reproduce their experimental counterparts within the measurement errors while theoretical q factors reproduce the measured v' dependence being, however, systematically overestimated by ca. 1x10(-6) cm(-1). The present NaCs data are compared with those of the NaK and NaRb molecules.