B1Π State Research Articles

Potential energy curve for B1Π state of 85Rb133Cs obtained via genetic algorithm

We adopt the genetic algorithm to fit the potential energy curve for B1Π state of 85Rb133Cs molecule based on the data of rovibrational energy levels, which were observed previously by Fourier-transform spectroscopy and photoassociation spectroscopy. We explore the effect of different hyperparameter settings on the evolutionary process and final results to optimise the performance of the algorithm. Finally, the fitting procedure can reproduce the rovibrational levels with an error less than 0.06 cm−1 compared to the experimental data.

Investigation on the fine and hyperfine structure of the [formula omitted] state in KRb

The hyperfine structure of the transitions in the (X,v′′=0→(B,c),v′=2) band system in 39K85Rb and 39K87Rb is studied by using several selective Doppler-free spectroscopy techniques. Significant splitting of the line profiles is observable for the B1Π state levels coupled to the c3Σ+ levels through spin–orbit interactions. The splitting is the result from an interplay between spin–spin, spin–rotation, spin–orbit interactions and the Fermi-contact interaction between the electron’s spin and the nuclear spins. Energy shifts of the perturbed levels were analyzed and modeled within the effective Hamiltonian approach. Molecular and coupling constants were determined, which successfully model the experimental observations. Although the highest experimental resolution of 50 MHz was not sufficient to resolve entirely the hyperfine structure, the model successfully explains the line broadening in 39K85Rb and the line splitting in 39K87Rb.

Radiative properties of the six lowest–lying triplet and four lowest–lying singlet states of boron nitride molecule

This study addresses the transition properties of the X3Π, A3Σ+, B3Σ–, C3Π, D3Π, E3Σ+, a1Σ+, b1Π, c1Δ, and d1Σ+ states of the boron nitride molecule. The potential energy curves and transition dipole moments are calculated using the complete active space self–consistent field method, followed by the valence internally contracted multireference configuration interaction approach. The radiative lifetimes are of the order of 10–8 s for the E3Σ+ state, 10–7–10–8 s for the C3Π state, 10–7 s for the D3Π and d1Σ+ states, 10–6 s for the c1Δ state, 10–5–10–6 s for the B3Σ– state, and 10–5 s for the A3Σ+ and b1Π states. The C3Π – X3Π and E3Σ– – X3Π transitions are strong, followed by the D3Π – X3Π, D3Π – B3Σ–, E3Σ– – A3Σ+, d1Σ+ – a1Σ+, and d1Σ+ – b1Π transitions. The spin–forbidden transitions from the a1Σ+ and b1Π states to the X3Π state are calculated and confirmed to be weak. The radiative lifetimes of all the vibrational levels are approximately 10–1 s for the a1Σ+0+ state. The contribution of the b1Π – X3Π transition to the radiative lifetimes of the b1Π state is sufficiently insignificant to be considered negligible. The Franck–Condon factors, Einstein A coefficients, and band origins of all the spontaneous vibronic emissions from all these transitions involved herein are calculated. The distribution of the radiative lifetime varying with rotational angular quantum number J is investigated at J ≤ 70 for a certain vibrational level υ of the A3Σ+, B3Σ–, C3Π, D3Π, E3Σ+, b1Π, and c1Δ states when υ ≤ 15. The transition properties reported in this study can provide useful guidelines for future investigations, both experimentally and theoretically.

Transition probabilities of the seven lowest–lying singlet states of the AlN radical

In this study, the potential energy curves are calculated for the a1Σ+, b1Π, c1Δ, d1Σ+, e1Π, f1Δ, and g1Σ− states of the AlN radical. The transition dipole moments between them are computed. The rotationless radiative lifetimes of the vibrational levels are found to be approximately several µs for the d1Σ+ and g1Σ− states, on the order of several hundred ns for the e1Π state, and one-tenth to several µs for the deep well of the f1Δ state. These results suggest that the spontaneous emissions originated from these states occur readily. The rotationless radiative lifetimes of the vibrational levels are on the order of 10–100 µs for the c1Δ state, 1000 µs for the vdW minimum of the f1Δ state, and 10–1000 µs for the b1Π state. In addition, the rotationless radiative lifetimes of these states decrease with the increasing vibrational level. This result suggests that the spontaneous emissions generated from these states at lower levels should be difficult to occur. The Einstein coefficients of spontaneous emissions from the d1Σ+–a1Σ+, d1Σ+–b1Π, e1Π–a1Σ+, e1Π–b1Π, and g1Σ−–b1Π systems, as well as from the f1Δ state to the b1Π and c1Δ states are large, indicating that the emissions of these systems can be measured readily via spectroscopy. The Einstein coefficients of the e1Π–d1Σ+ transition are very small and the emissions originating from the vdW minimum of the f1Δ state are very weak, predicting that these transitions are very difficult to be detected in spectroscopy experiments.

Laser spectroscopy of the X1Σ+ and B1Π states of the LiRb molecule

We have studied the X1Σ+ and B1Π states of 7Li85Rb using Laser Induced Fluorescence (LIF) Spectroscopy and Fluorescence Excitation Spectroscopy (FES). We extract molecular constants for levels v″=0–2 of the X1Σ+ state and levels v′=0–20 of the B1Π state. For the B1Π state, we have observed rotational perturbations in the e-parity component of the v′=2 level, and determined the dissociation energy. We discuss implications of our measurements in finding efficient photoassociation pathways for production of ultracold ground state LiRb molecules, and their detection via state selective ionization.

Analytical potential energy function and spectroscopy parameters for B1\Pi state of KH

Multi-reference configuration interaction is used to produce potential energy curves (PECs) for the excited B1Π state of KH molecule. To investigate the correlation effect of core-valence electrons, five schemes are employed which include the different correlated electrons and different active spaces. The PECs are fitted into analytical potential energy functions (APEFs). The spectroscopic parameters, ro-vibrational levels, and transition frequencies are determined based on the APEFs and compared with available experimental and theoretical data. The molecular properties for B1Π obtained in this letter, which are better than those available in literature, can be reproduced with calculations using the suitable correlated electrons and active space of orbitals.

Investigation of the B1Π state in NaCs by polarisation labelling spectroscopy

We present experimental observation of the B1Π state in NaCs molecule converging to the Na (32S1/2)+Cs (62P3/2) states of separated atoms. The two-colour polarisation labelling spectroscopy technique was applied to the B1Π←X1Σ+ band system. The data field for the B state consists of rovibrational levels with v=0–52 and J=13–51, the last vibrational level located ca. 7.6m−1 below the atomic asymptote. The data were incorporated into a fit of a potential energy curve to the level energies using the Inverted Perturbation Approach (IPA) method. The resulting potential, extending between R=2.4 and 24.8Å, is employed to partially assign the existing photoassociation spectra of NaCs.

Influence of a Feshbach resonance on the photoassociation of LiCs

We analyze the formation of ultracold 7Li133Cs molecules in the rovibrational ground state through photoassociation into the B1Π state, which has recently been reported (Deiglmayr et al 2008 Phys. Rev. Lett. 101 133004). Absolute rate constants for photoassociation at large detunings from the atomic asymptote are determined and are found to be surprisingly large. The photoassociation process is modeled using a full coupled-channel calculation for the continuum state, taking all relevant hyperfine states into account. The enhancement of the photoassociation rate is found to be caused by an ‘echo’ of the triplet component in the singlet component of the scattering wave function at the inner turning point of the lowest triplet a3Σ+ potential. This perturbation can be ascribed to the existence of a broad Feshbach resonance at low scattering energies. Our results elucidate the important role of couplings in the scattering wave function for the formation of deeply bound ground state molecules via photoassociation.

Ab initio calculations of accurate dissociation energy and analytic potential energy function for the second excited state B 1 Π of 7 LiH

The reasonable dissociation limit of the second excited singlet state B1Π of 7LiH molecule is obtained. The accurate dissociation energy and equilibrium geometry of the B1Π state are calculated using a symmetry-adapted-cluster configuration–interaction method in full active space. The whole potential energy curve for the B1Π state is obtained over the internuclear distance ranging from about 0.10 nm to 0.54 nm, and has a least-square fit to the analytic Murrell–Sorbie function form. The vertical excitation energy is calculated from the ground state to the B1Π state and compared with previous theoretical results. The equilibrium internuclear distance obtained by geometry optimization is found to be quite different from that obtained by single-point energy scanning under the same calculation condition. Based on the analytic potential energy function, the harmonic frequency value of the B1Π state is estimated. A comparison of the theoretical calculations of dissociation energies, equilibrium interatomic distances and the analytic potential energy function with those obtained by previous theoretical results clearly shows that the present work is more comprehensive and in better agreement with experiments than previous theories, thus it is an improvement on previous theories.

Laser-assisted ultracold lithium-hydride molecule formation: stimulated versus spontaneous emission

We investigate the feasibility of forming ultracold LiH from a mixture of the ultracold atomic gases, by using B1Π as an intermediate state in the photoassociation process. Using accurate molecular potential energy curves and dipole transition moments, we calculate and compare two possible schemes to populate vibrational levels of the ground electronic state, X1Σ+: (1) two-photon stimulated radiative association and (2) excitation to bound levels of the B1Π state, followed by spontaneous emission to the X1Σ+ state. With laser intensities and atomic densities that are easily attainable experimentally, we find that significant quantities of molecules can be formed in various v, J levels of the electronic ground state. We examine the spontaneous emission cascade which takes place from the upper vibrational levels on a time scale of milliseconds. We discuss the issue of back-stimulation for the two-photon process and ways to mitigate it. Because photon emission in the cascade process does not contribute to trap loss, a sizable population of molecules in v = 0 can be achieved.

Laser spectroscopy of YBr: rotational analysis of the B1Π—X1Σ system

The (ν,0) bands, for ν = 0–5, of the B1Π-X1Σ transition of YBr between 806.2–891.2 nm have been studied using the technique of laser vaporization/reaction with supersonic cooling and laser-induced fluorescence spectroscopy. Spectra of both the Y79Br and Y81 Br isotopic molecules were observed and analysed. A least-squares fit of all the measured line positions yielded vibrational and rotational constants for the B1Π state. The equilibrium bond length of the B1Π state is determined to be 2.622 5(2) Å.

Photodissociation of NaH using time-dependent fourier grid method

We have solved the time dependent Schrodinger equation by using the Chebyshev polynomial scheme and Fourier grid Hamiltonian method to calculate the dissociation cross section of NaH molecule by 1-photon absorption from the X1Σ+ state to the B1Π state. We have found that the results differ significantly from an earlier calculation [1] although we have used the same set of potential energy curves [2].

Near-Infrared Laser Spectroscopy of TiS: The b1Π–X3Δ Transition

Laser-induced fluorescence spectrum of TiS in the 769–863 nm region has been recorded and analyzed. The TiS molecule was produced using the technique of laser vaporization/reaction with supersonic cooling. Twenty-one weak subbands have been assigned as being due to b1Π–X3Δ, B3Π0–X3Δ1, and C3Δ–X3Δ transitions. Strong evidence shows that the b1Π state is responsible for perturbing the v = 0, 1, and 2 levels of the C3Δ1 subband. The molecular constants of the b1Π state have been determined as follows: Te = 10 589.47 cm−1, ωe = 542.14 cm−1, ωexe = 3.16 cm−1, Be = 0.19568 cm−1, and αe = 0.00085 cm−1. The spin–orbit interaction between the b1Π (v = 2 and 3) and C3Δ (v = 1 and 2) levels is discussed in terms of configuration interaction occurring between the b1Π from the 11ς1 5π1 configuration and the 1Π from the 5π1 1δ1 configuration, and the C3Δ state from 12ς1 1δ1 configuration.

The Electric Dipole Moment of the B1Π State of ZrO

A laser ablation source combined with a time-of-flight mass spectrometer has been constructed. The static electric field in the mass spectrometer gives rise to a first-order Stark effect splitting from which the permanent electric dipole moment of the B1Π state (v = 0) of 90ZrO is determined and found to be 3.43 ± 0.07 D. The X1Σ and B1Π states are further investigated and comparisons with the results from ab initio calculations are made.

Electronic Spectra of YOH and YOD in the Visible Region: Strong Vibronic Coupling between the B1Π and C1Σ+ States

Laser excitation spectra of yttrium monohydroxide, YOH, have been recorded in the 500–625 nm wavelength region. Rotational analysis of bands of YOH and YOD has shown that the ground state is X1Σ+, with the structure r0(Y–O) = 1.9486 Å, r0(O–H) = 0.9206 Å; the bending frequency (ν2, π) is 313.73 cm−1 (237.43 cm−1 in YOD) and the Y–O stretching frequency (ν3, ς+) is 673.83 cm−1 (655.34 cm−1). Two excited electronic states have been identified; they are assigned as B1Π (16 449 cm−1) and C1Σ+ (18 509 cm−1). Unusually strong vibronic coupling through the bending vibration occurs between these two states, which causes their vibrational structures to be highly irregular; assignments have only been possible following extensive wavelength-resolved fluorescence experiments. The vibronic coupling raises the bending frequency of the C1Σ+ state to 457 cm−1 and reduces that of the lower Born–Oppenheimer component of the B1Π state (which has A′ symmetry in the Cs point group) to the extent that the molecule becomes nonlinear, with a potential barrier at the linear configuration of about 120 cm−1. The presence of the potential barrier is clearly demonstrated by the level structure of YOD, where the Σ+ vibronic component of the 010 vibrational level (linear molecule notation) lies 1.4 cm−1below the 000 level. The upper Born–Oppenheimer component, which has A″ symmetry, is unaffected; its bending frequency is similar to that of the ground state. Perturbations occur in both the B1Π and C1Σ+ states; some of these represent local interactions between the two of them, but others are caused by higher vibrational levels of lower-lying “dark” electronic states. Over 40 ground state vibrational levels have been identified for both YOH and YOD from the wavelength-resolved fluorescence spectra.

The [formula omitted] and [formula omitted] states of KLi

The polarization labelling spectroscopy technique is used to study the B1Π←X1Σ+ and C1Σ+←X1Σ+ band systems of the KLi molecule. Accurate molecular constants are derived for the B and C states from a Dunham expansion. For the B1Π state our analysis covers more than 99% of the potential well depth and provides a precise value for its dissociation energy. This also allows dissociation energies of the ground X1Σ+ state and excited C1Σ+ state to be determined.

Molecular beam optical Stark spectroscopy of YF

The molecular-beam-optical Stark spectrum of the B1Π(v=0)−X 1Σ+(v=0) band system of YF has been recorded and analyzed. The permanent electric dipole moment μ and the magnetic hyperfine parameter a for the B1Π state were experimentally determined to be 2.96(4) D and 146.8(3) MHz and the experimentally determined value for μ(X 1Σ+) is 1.82(8) D. The sign of the magnetic hyperfine parameter indicates that the major contribution to the B1Π state is from a⋅⋅⋅πδ configuration. The determined μ(X 2Σ+) value is compared with theoretical predictions and the ratio μ(X 1Σ+)/μ(B 1Π) is rationalized in terms of plausible molecular orbital descriptions for the two electronic states.

High resolution laser spectroscopy of the B 1Π−X 1∑+ transition of 23Na39K, and the perturbation between the B 1Π and c 3∑+ states

The Doppler-free laser polarization spectrum of the B1Π −X1∑+ transition of 23Na39K was measured, and the molecular constants of the B1Π state of v=0∼16 were determined. The perturbation between the B1Π(v=8) and the c3∑+(v=22) levels at small J were studied in detail. By comparing the observed line intensities of the B1Π(v=16, J=14) −X1∑+(v″=0∼50, J=13 and 15) transition with the calculated Franck–Condon factors, the dependence of the transition dipole moment on the internuclear distance was determined. Absolute vibrational numbering of the c3∑+ state was done by comparing the calculated Franck–Condon factors with the observed line intensities of the c3∑+ −a3∑+ transition.

High-resolution spectroscopy and photophysics of refractory molecules at low temperature: The C1Σ+-X1Σ+ system of ZrO

This paper shows that the technique of laser vaporization in conjunction with supersonic cooling and laser induced fluorescence is well suited for studies of the spectroscopy and photophysics of diatomic molecules of refractory character. In particular, the technique has been used to investigate the C1Σ+-X1Σ+ band system of ZrO. Rotational temperatures of ca. 25–35 K have been achieved. Fluorescence lifetimes of single rotational levels of C1Σ+ (v = 0, 1) are reported together with those of the vibrational levels v = 0, 1, 2,and 3 of the B1Π state. In light of these results, the photophysics of the C1Σ+ state is discussed. In addition, the Franck-Condon factors and oscillator strengths for the vibronic transitions C1Σ+-X1Σ+ (0 → 0, 1, 2) and (1 → 0, 1, 2, 3) have been determined. A comparison with calculations is given. The 0-0 band of the C1Σ+-X1Σ+ band system has been reinvestigated under higher resolution (∼120 MHz). All five isotopic species (90ZrO, 91ZrO, 92ZrO, 94ZrO, 96ZrO) have been clearly resolved, even for the R head, and data up to J = 29 are reported. Rotational constants and band origins for the X1Σ+ (v = 0) and C1Σ+ (v = 0) states of all five isotopic species have been evaluated. In the cases of 90ZrO, 94ZrO, and 96ZrO, comparisons with previous work are given and discussed. Advantages and disadvantages of the laser vaporization-supersonic cooling technique over conventional high-temperature methods for spectroscopic studies are also given.

Observations on the B1Π state of the NaK molecule

The lowest 1Π state of the NaK molecule, B(1) 1Π, which dissociates to Na (2S1/2) + K (2P3/2), has been studied in three ways: (i) by laser-induced fluorescence recorded at high resolution by Fourier-transform spectrometry, (ii) by dye-laser excitation spectroscopy, and (iii) by observations of the effect of an electric field, which mixes the e and f parity levels of the B1Π state. The B state is subject to numerous small perturbations, many of which arise from interactions with a triplet state, c3Σ+, and these interactions modify the extent of e–f mixing and thus the relative intensities of R and P lines on one hand and the Q lines on the other. These observations of the Stark effect enable perturbation maxima to be located and thus allow relatively unperturbed energy levels to be identified. Constants from these levels of B1Π have been determined from a weighted least squares fit to 1776 lines of the B1Π – X1Σ+ transition as follows:[Formula: see text]