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.

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.

Fourier-transform spectroscopy and potential construction of the (2)(1)Π state in KCs.

The paper presents an empirical pointwise potential energy curve (PEC) of the (2)(1)Π state of the KCs molecule constructed by applying the Inverted Perturbation Approach routine. The experimental term values in the energy range E(v', J') ∈ [15 407; 16 579] cm(-1) involved in the fit were based on Fourier-Transform spectroscopy data obtained with 0.01 cm(-1) accuracy from the laser-induced (2)(1)Π â†’ X(1)Σ(+) fluorescence spectra. Buffer gas Ar was used to facilitate the appearance of rotation relaxation lines in the spectra, thus enlarging the (2)(1)Π data set and allowing determination of the Λ-splitting constants. The data set included vibrational v' ∈ [0, 28] and rotational J' ∈ [7, 274] quantum numbers covering about 67% of the potential well. The present PEC reproduces the overall set of data included in the fit with a standard deviation of 0.5 cm(-1). The obtained value of the Λ-doubling constant q = + 1.8 × 10(-6) cm(-1) for J' > 50 and v' ∈ [0, 6] is in an excellent agreement with q = + 1.84 × 10(-6) cm(-1) reported in Kim, Lee, and Stolyarov [J. Mol. Spectrosc. 256, 57-67 (2009)].

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 and description of low-lying energy levels in the B(1)(1)Π state of RbCs.

The Fourier transform spectrometer with resolution of 0.03 cm(-1) was applied to disperse the diode laser induced B(1)(1)Π â†’ X(1)Σ(+) fluorescence spectra of the RbCs molecule in a heat pipe. The presence of buffer gas (Ar) produced in the spectra the dense pattern of collision-induced rotation relaxation lines, thus enlarging the B(1)(1)Π data set, allowing to determine the Λ-splitting constants and to reveal numerous local perturbations. In total, 2664 term values for (85)Rb(133)Cs and (87)Rb(133)Cs in the energy range from 13,770 to 15,200 cm(-1) were obtained with accuracy about 0.01 cm(-1). A pointwise potential energy curve (PEC) based on inverted perturbation approach was constructed in the R-range from 3.35 to 9.00 Å for less perturbed vibrational levels v' ε [0, 35] and compared with ab initio calculations. The data included in the fit were reproduced by present PEC with standard deviation (sd) 0.95 cm(-1). More systematic over rotational levels J(') ε [6, 228] data set was obtained for v' ε [0, 2]. These data were reproduced by the obtained PEC with sd of 0.08 cm(-1). The energy of PEC's minimum Te = 13,746.65 cm(-1), as well as other main molecular constants were determined.

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.

B1(1)Π state of KCs: high-resolution spectroscopy and description of low-lying energy levels.

The diode laser induced B(1)(1)Π â†’ X(1)Σ(+) fluorescence spectra of the KCs molecule were recorded by Fourier-transform spectrometer with resolution of 0.03 cm(-1). Buffer gas Ar was used to facilitate appearance of rotation relaxation lines in the spectra, thus enlarging the B(1)(1)Π dataset, allowing one to determine the Λ-splitting constants and to reveal numerous local perturbations. A dataset was systematically obtained for B(1)(1)Π vibrational levels ν(') ∈ [0; 5] nonuniformly covering rotational levels with J(') ∈ [7; 233]. For ν(') ∈ [0; 3], the less-perturbed data of f-components were included in the fit. A pointwise potential energy curve (PEC) based on the inverted perturbation approach, as well as the Dunham coefficients, was obtained and compared with ab initio calculations; in particular, the energy of the PEC's minimum T(e) = 14,044.918(6) cm(-1) was determined. Both approaches allowed us to reproduce the vast majority of data used in the fit with accuracy of 0.02 cm(-1). Tentative molecular constants for several vibrational levels of the near lying C(3)(1)Σ(+) state were estimated.

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

The ground electronic state of KCs studied by Fourier transform spectroscopy.

We present here the first analysis of laser induced fluorescence (LIF) of the KCs molecule obtaining highly accurate data and perform a direct potential construction for the X (1)Sigma(+) ground state in a wide range of internuclear distances. KCs molecules were produced by heating a mixture of K and Cs metals in a heat pipe at a temperature of about 270 degrees C. KCs fluorescence was induced by different laser sources: the 454.5, 457.9, 465.8, and 472.7 nm lines of an Ar(+) laser, a dye laser with Rhodamine 6G dye (excitation at around 16 870 cm(-1)), and 850 and 980 nm diode lasers (11 500-11 900 and 10 200-10 450 cm(-1) tuning ranges, respectively). The LIF to the ground state was recorded by a Bruker IFS-125HR Fourier transform spectrometer with a spectral resolution of 0.03 cm(-1). Particularly, by applying the 850 nm laser diode we were able to observe LIF progressions to very high vibrational levels of the ground state close to the dissociation limit. The present data field contains 7226 term values for the ground state X (1)Sigma(+) and covers a range from v(")=0 to 97 with J(") varying from 12 to 209. More than 10 000 fluorescence lines were used to fit the ground state potential energy curve via the inverted perturbation approach procedure. The present empirical potential extends up to approximately 12.6 A and covers more than 99% of the potential well depth, it describes most of the spectral lines with an accuracy of about 0.003 cm(-1) and yields a dissociation energy of 4069.3+/-1.5 cm(-1) for the ground state X (1)Sigma(+). First observations of the triplet ground state a (3)Sigma(+) of KCs are presented, and preliminary values of few main molecular constants could be derived.

The B 1Pi state of NaCs: high resolution laser induced fluorescence spectroscopy and potential construction.

The lowest (1)Pi state of the NaCs molecule, the B(1)(1)Pi state, was studied using a dye laser for inducing fluorescence that was resolved by a high resolution Fourier-transform spectrometer. The presence of argon buffer gas yielded rich rotational relaxation spectra allowing to enlarge the data set for the B(1)(1)Pi state, to obtain Lambda-splittings and to reveal numerous local perturbations. 543 weakly perturbed energy levels for rotational quantum numbers from J(')=5 to 168 and vibrational quantum numbers from v(')=0 to 25, which cover about 87% of the potential well depth, were used for a direct pointwise fit of the potential energy curve applying the inverted perturbation approach method. The resulting potential reproduces the term values for v(')=0-7 with an experimental accuracy of about 0.01-0.02 cm(-1), whereas for v(')=8-25 the deviations increase due to the perturbations, going to the order of 1 cm(-1); an extrapolation is made to the dissociation asymptote.

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.

High resolution spectroscopy and potential determination of the (3)1Pi state of NaCs.

The (3)(1)Pi state of the NaCs molecule was studied by high resolution Fourier-transform spectroscopy. The (3)(1)Pi-->X (1)Sigma(+) laser induced fluorescence was excited by an Ar(+) ion laser or by a single-mode frequency-doubled cw Nd:YAG laser. The presence of argon buffer gas yielded rich rotational relaxation spectra allowing to enlarge the data set for the (3)(1)Pi state term values, as well as to observe Lambda splittings in a wide range of vibrational (v(')) and rotational (J(')) quantum numbers. The data field includes about 820 energy levels of (3)(1)Pi NaCs in the range from v(')=0 to 37 and from J(')=3 to 190, which corresponds to ca. 95% of the potential well depth. Direct fit of the potential energy curve to the level energies is realized using the inverted perturbation approach method; a set of Dunham coefficients is also presented.