Inverted Perturbation Approach Research Articles

The double minimum E(3)[formula omitted] state in Cs[formula omitted]

The double minimum E1Σu+ state in caesium dimer was investigated by analysing spectra of the E1Σu+← X1Σg+ band system, simplified by polarisation labelling. A total of 6727 rotationally resolved transitions to levels situated in the inner well and above the internal barrier were identified and a potential energy curve allowing to reproduce their energies was constructed using the Fourier grid Hamiltonian and inverted perturbation approach methods. The unambiguity of the potential curve in view of lack of data related to levels located in the outer well is discussed.

Study of the 71Π u state of sodium dimer by polarisation labelling spectroscopy

Two-colour polarisation labelling experiment measuring excitation spectra of Na in the spectral range 34, 600−39, 400 cm has furnished observation of the previously unknown electronic state. The excited state is characterised by a set of Dunham coefficients describing the f parity levels up to vibrational level v = 28 and the corresponding potential energy curve is constructed by the inverted perturbation approach method. Molecular parameters determined in the fit include ± 0.03 cm, ± 0.03 cm and ± 0.001 Å.

Relativistic treatment of alkaline earth dimers in the presence of non-central molecular potential in N-dimensions

Abstract Within the framework of relativistic theory, N-dimensional non-central Morse potential as anharmonic model is considered thoroughly to describe the internuclear motion of alkaline earth dimers in the different electronic states. We illustrate the surface plots of alkaline earth dimers to examine the effect of angular potential, due to existence of molecular systems in which spherical symmetry disappears. Also, the contribution of angle dependent interaction to the relativistic energy spectra has been investigated in N-dimensions. We determine the relativistic vibrational transition frequencies in the lower vibrational states for the X 1 Σ g + ground state of 24 Mg 2 , 40 Ca 2 , 24 Mg 40 Ca and A 1 Σ u + excited state of 88 Sr 2 alkaline earth diatomic molecules. The theoretical results have been compared with Rydberg-Klein-Rees (RKR) and the inverted perturbation approach (IPA) experimental data. We also discussed the validity of Pekeris approximation around the equilibrium distance as well as the repulsive and attractive regions for alkaline earth dimers.

Determination of the C(3)1Σ+ state potential energy curve in KCs molecule based on polarisation labelling spectroscopy data

The C(3)1Σ+ state of KCs molecule was studied experimentally employing the polarisation labelling spectroscopy (PLS) technique. The experiment extended the prior knowledge of the state adding more than 40 vibrational levels to the previously existing data. A pointwise potential energy curve was constructed for the investigated state with the inverted perturbation approach (IPA) method, basing on experimentally determined energies of over 1300 rovibrational levels.

Fitting an experimental potential energy curve for the 10(0+)[43Π0] electronic state of NaCs.

We present experimentally determined potential energy curves for the 10(0+)[43Π0] electronic state of NaCs. The 10(0+)[43Π0] state exhibits a double-minimum structure, resulting in a distinctive bound-free fluorescence signature. The perturbation facilitated optical-optical double resonance method was used to obtain Doppler-free excitation spectra corresponding to rovibrational transitions to the 10(0+)[43Π0] state. Spectroscopic constants were determined to summarize data belonging to inner well, outer well, and above the barrier regions of the electronic state. The Rydberg-Klein-Rees and inverted perturbation approach methods were used to construct a potential which reproduces the experimental rovibrational energies within a root-mean-square deviation of 2.33 cm-1. An alternative to the pointwise potential approach was also used to determine the potential energy curve by directly fitting an expanded Morse oscillator functional form. Advantages between the two approaches as they apply to double minimum wells are discussed.

Double-minimum 3 Σu+1 state in Rb2 : Spectroscopic study and possible applications for cold-physics experiments

The double-minimum 3 $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}+}$ state in $^{85}\mathrm{Rb}_{2}$ and $^{85}\mathrm{Rb}\phantom{\rule{0.16em}{0ex}}^{87}\mathrm{Rb}$ was investigated by analyzing rotationally resolved spectra of the 3 $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}+}\ensuremath{\longleftarrow}\mathrm{X}^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ band system simplified by polarization labeling. A total of 3665 transitions to rovibrational levels located in the inner well and above the internal barrier were identified and an accurate potential energy curve of the state reaching up to $R\ensuremath{\approx}21$ \AA{} was constructed using the inverted perturbation approach, making this state the best characterized double-minimum state in alkali dimers. The possibility of formation of ultracold rubidium dimers in the absolute ground state by photoassociation into levels of the 3 $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}+}$ state above the internal barrier followed by spontaneous or stimulated emission is discussed.

Spectroscopic study of the C(3)[formula omitted] ← X[formula omitted] and c(2)[formula omitted] ← X[formula omitted] transitions in KCs molecule

We present an experimental investigation of the C(3)1Σ+ and c(2)3Σ+ states of KCs using two-colour polarisation labelling spectroscopy (PLS) technique. Pointwise potential energy curves are generated for both states using the inverted perturbation approach (IPA) method. The experimental pointwise potentials and molecular constants Te, ωe and Re are compared with theoretical calculations.

Energy and radiative properties of the (3)Π1 and (5)Σ+1 states of RbCs: Experiment and theory

We combined high-resolution Fourier-transform spectroscopy and large-scale electronic structure calculation to study energy and radiative properties of the high-lying (3)1{\Pi} and (5)1{\Sigma}+ states of the RbCs molecule. The laser-induced (5)1{\Sigma}+(4)1{\Sigma}+(3)1{\Pi}-A(2)1{\Sigma}+ b(1)3{\Pi} fluorescence (LIF) spectra were recorded by the Bruker IFS-125(HR) spectrometer in the frequency range {\nu} 5500 to 10000cm-1 with the instrumental resolution of 0.03 cm-1. The rotational assignment of the observed LIF progressions, which exhibit irregular vibrational-rotational spacing due to strong spin-orbit interaction between A1{\Sigma}+ and b3(\Pi) states was based on the coincidences between observed and calculated energy differences. The required rovibronic term values of the strongly perturbed A-b complex have been calculated by a coupled-channels approach for both 85Rb133Cs and 87Rb133Cs isotopologs with accuracy of about 0.01 cm-1, as demonstrated in A. Kruzins et al. [J. Chem. Phys. 141, 184309 (2014)]. The experimental energies of the upper (3)1(\Pi) and (5)1{\Sigma}+ states were involved in a direct-potential-fit analysis performed in the framework of inverted perturbation approach. Quasirelativistic ab initio calculations of the spin-allowed (3)1{\Pi},(5)1{\Sigma}+- (1-4)1{\Sigma}+(1-3)1{\Pi} transition dipole moments were performed. Radiative lifetimes and vibronic branching ratios of radiative transitions from the (3)1{\Pi} and (5)1{\Sigma}+ states were evaluated. To elucidate the origin of the {\Lambda}-doubling effect in the (3)1{\Pi} state, the angular coupling (3)1{\Pi}-(1-5)1{\Sigma}+ electronic matrix elements were calculated and applied for the relevant q-factors estimate. The intensity distributions simulated for the particular (5)1{\Sigma}+(3)1{\Pi}-A-b LIF progressions have been found to be remarkably close to their experimental counterparts.

Interatomic potentials of van der Waals dimers Hg2 and Cd2: Probing discrepancies between theory and experiment

Results of new all-electron ab initio calculations and revisit of experimental studies of the interatomic potentials of lower-lying ungerade excited and ground electronic energy states of the Hg2 and Cd2 van der Waals complexes are used as probes of discrepancies between theory and experiment. From simulations of the previously and presently measured LIF excitation and dispersed emission spectra new analytical representations of the excited- and the ground-state interatomic potentials are proposed. An inverted perturbation approach was also used to improve the studied interatomic potentials. The comparison of the new ab-initio calculated potentials with the results of the analyses illustrates an improve theory-to-experiment agreement for such a demanding system like Hg2 or Cd2.

Polarisation labelling spectroscopy of the 51Π state in KCs molecule

We present an experimental investigation of the 51Π state of KCs using the polarisation labelling spectroscopy technique. A pointwise potential energy curve was constructed from 1146 energy levels with use of the inverted perturbation approach.

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 → 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)].

Potential construction of the B(1)1 Π state in KCs based on Fourier-Transform spectroscopy data

The paper presents an empirical pointwise potential energy curve (PEC) of the extensively perturbed B(1)1Π state of the KCs molecule constructed by applying an Inverted Perturbation Approach routine. The experimental term values in the energy range E(v′,J′)∈[14071;15502]cm−1 involved in the fit were based on Fourier-Transform spectroscopy data obtained with 0.01cm−1 accuracy from laser-induced B(1)1Π→X1Σ+ fluorescence spectra in the present work (654 term values) combined with 520 term values from Birzniece et al. (2012) . The data set included vibrational v′∈[0,35] and rotational J′∈[7,233] quantum numbers covering about 85% of the potential well. The present fit reproduces the data included in the fit with a standard deviation 0.94cm−1. The empirical PEC contains an inflection at about R=4.1 Åthat reflects the avoided crossing of two Ω=1 states corresponding to B(1)1Π and c(2)3Σ+ states as predicted by ab initio calculations.

Experimental investigation of the 61Σ+ ‘shelf’ state of KCs

We report the first experimental observation of the 61Σ+ state in the KCs molecule. Polarization labelling spectroscopy technique was applied to determine energies of about 1000 rovibrational levels in this state, most of them strongly perturbed by the neighbouring 43Π state levels. The inverted perturbation approach was used to construct the irregular potential energy curve of the 61Σ+ state. It is compared with the recent theoretical calculations to show that Hund's coupling case (a) is proper for description of this state.

The 41Σ+ electronic state of LiCs molecule

The 41Σ+ state of LiCs molecule is observed experimentally for the first time. The inverted perturbation approach (IPA) method is used to derive the potential energy curve of the state from the measured spectra. The experiment is accompanied by theoretical calculations of adiabatic potentials for excited states in LiCs including 41Σ+, performed with the MOLPRO program package. The irregular shape of the 41Σ+ state potential predicted by theory is confirmed in the experiment.

Polarisation labelling spectroscopy of the D1Π state in Na7Li molecule

We report the first experimental observation of the D(2)1Π state in the NaLi molecule. Polarisation labelling spectroscopy technique is applied to observe transitions to all vibrational levels in this state, save v=0. The inverted perturbation approach method is used to construct a pointwise potential curve for the D state, which has a small barrier (9.3cm−1) to dissociation, located at 7.98Å.

Fourier-transform spectroscopy and description of low-lying energy levels in the B(1)1Π 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 → 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.

On the [formula omitted] state of the KCs molecule

The polarization labeling spectroscopy technique is used to study high vibrational levels of the 41Σ+ state in KCs molecule up to vibrational level v=91, located 27cm−1 below the atomic asymptote. Basing on energies of rovibrational levels measured in this work supplemented by the data from earlier experiment by Busevica et al. [J. Chem. Phys. 134 (2011) 104307] and employing the pointwise Inverted Perturbation Approach algorithm, we construct the potential energy curve of the 41Σ+ state in the range 3.61–15.1Å and extend it to the dissociation limit using a theoretical long-range tail.

B(1)1Π state of KCs: High-resolution spectroscopy and description of low-lying energy levels

The diode laser induced B(1)(1)Π → 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.

The 4 1Σ+ electronic state of KLi molecule

The 4 1 Σ + state in KLi, characterized by a potential energy curve of irregular shape, is investigated experimentally. Spectra of the 4 1 Σ + ← X 1 Σ + band system, simplified by polarization labelling, are recorded and analyzed. The Inverted Perturbation Approach method is used to construct the exotic molecular potential of the 4 1 Σ + state. The result is compared with the prediction of theoretical calculations.