Perturbation-facilitated Optical-optical Double Resonance Research Articles

Analysis of the hyperfine structure of the [formula omitted][formula omitted] and [formula omitted] states of [formula omitted]Li[formula omitted]Li

We report on our theoretical analysis of the hyperfine splitting in the spectra of the 13Δg,23Πg, and 33Σg+ triplet states of 6Li7Li, which were experimentally observed in 2002 (Li et al.) by means of Perturbation Facilitated Optical-Optical Double Resonance (PFOODR) spectroscopy. In our previous work, both homonuclear and heteronuclear molecules were analyzed. However, in this work, we theoretically investigate an isotope-substituted homonuclear molecule for the first time and demonstrate the application of our approach to this case. In our model, we reproduce the major stages of the excitation–de-excitation schemes by considering the mixed nature of the intermediate A1Σu+∼b3ΠΩu singlet–triplet states, whereby the three components of the Ω=0,1,2 basis states might contribute to the hyperfine splitting. We compute the contributions from all components of the mixed states. We present physical models for all triplet states under study, along with the obtained parameters of the analyzed molecular system and the simulation results. Additionally, we describe the principal steps of the computational algorithm in detail.

Perturbation-facilitated detection of the first quintet-quintet band in C2

The first high-spin transition in C2 (1 (5)Πu - 1 (5)Πg) is observed by perturbation-facilitated optical-optical double resonance spectroscopy. The experiment is performed by applying unfolded two-color resonant four-wave mixing. C2 radicals in the initial a (3)Πu, v = 5 state are produced by using a discharge source in a molecular beam environment. The final quintet state is excited via intermediate "gateway" states exhibiting both substantial triplet and quintet character due to a perturbation between the 1 (5)Πg, v = 0 and the d (3)Πg, v = 6 states. Fifty seven rotational transitions in the P, Q, and R branches of all spin sub-states are measured and yield accurate molecular constants of the newly found upper level 1 (5)Πu. In addition, satellite transitions (ΔJ ≠ ΔN) are observed and allow an accurate determination of the spin-orbit constant. The results are compared with high-level ab initio computations at the multi-reference configuration interaction level of theory. The high-lying quintet state is found to be predissociative and displays a shallow potential that accommodates three vibrational levels only.

The hyperfine structure analysis of the K223Σg+ state

Abstract Fine and hyperfine structures observed in the perturbation facilitated optical–optical double resonance (PFOODR) excitation spectra of the K 2 2 3 Σ g + state are analyzed within a model of the isolated multiplet using the case b βS basis. It is concluded that Fermi contact and spin–spin interactions play the leading role. The values of the interaction constants are derived from their fitting to the experimental data.

Nonadiabatic coupling in the 3Π3 and 4Π3 states of NaK

The excited 3 (3)Pi and 4 (3)Pi electronic states of the NaK molecule exhibit an avoided crossing, leading to the anomalous behavior of many features of the rovibrational energy levels belonging to each state. A joint experimental and theoretical investigation of these states has been carried out. Experimental measurements of the vibrational, rotational, and hyperfine structure of numerous levels of the 3 (3)Pi state were recently obtained using the Doppler-free, perturbation-facilitated optical-optical double resonance technique. Additional measurements for the 4 (3)Pi state as well as bound-free emission spectra from selected 3 (3)Pi, 4 (3)Pi, and mixed 3 (3)Pi to approximately 4 (3)Pi rovibrational levels are reported here. A model is also presented for calculating the mixed rovibrational level energies of the coupled 3 (3)Pi-4 (3)Pi system, starting from a 2x2 diabatic electronic Hamiltonian. The 3 (3)Pi and 4 (3)Pi potential curves and the coupling between them are simultaneously adjusted to fit the observed rovibrational levels of both states. The energy levels of the potential curves determined by the fit are in excellent agreement with experiment. The nonadiabatic coupling is sufficiently strong to cause an overall shift of 2-3 cm(-1) for many rovibrational levels as well as somewhat larger shifts for certain pairs of 3 (3)Pi to approximately 4 (3)Pi levels that would otherwise be very close together.

New Observation of Na2 43g+ State by Pulsed Perturbation Facilitated OpticalOptical Double Resonance Spectroscopy

Sixty-five new vibronic levels of the Na2 43g+ state have been observed in the 3390035200 cm1 energy region above the potential minimum of the ground state by pulsed perturbation facilitated opticaloptical double resonance (PFOODR) fluorescence excitation spectroscopy. These new data fill the gap between the low-v levels mainly observed by continuous wave (CW) PFOODR spectroscopy and the high-v levels above the 3s + 3d limit observed by pulsed PFOODR with predissociation detection. Molecular constants are fitted below potential shelf around the 3s + 3d atomic limit with previously published data (mainly observed by CW PFOODR) and these new data. RKR potential curve has been calculated with the new constants. The constants are: Te = 32127.090 cm1; e = 121.4099(0.20720) cm1; Be = 0.116287(0.0002300) cm1; Re = 3.551 A. An error of the RKR potential curve of J. Chem. Phys. 108, 7707 (1998) is corrected.

The NaK 1(b)ΠΩ=3 state hyperfine structure and the 1(b)ΠΩ=3∼2(A)Σ+1 spin–orbit interaction

We have measured the hyperfine structure of mutually perturbing rovibrational levels of the 1(b) 3Pi0 and 2(A) 1Sigma+ states of the NaK molecule, using the perturbation-facilitated optical-optical double resonance method with copropagating lasers. The unperturbed 1(b) 3Pi0 levels are split into four hyperfine components by the Fermi contact interaction bFIS. Mixing between the 1(b) 3Pi0 and 2(A) 1Sigma+ levels imparts hyperfine structure to the nominally singlet component of the perturbed levels and reduces the hyperfine splitting of the nominally triplet component. Theoretical analysis relates these observations to the hyperfine splitting that each 1(b) 3Pi0 level would have if it were not perturbed by a 2(A) 1Sigma+ level. Using this analysis, we demonstrate that significant hyperfine splitting arises because the 1(b) 3Pi0 state cannot be described as pure Hund's case (a). We determine bF for the 1(b) 3Pi0 levels and also a more accurate value for the magnitude of the singlet-triplet spin-orbit coupling HSO=[1(b) 3Pi0(vb,J)(H(SO))2(A) 1Sigma+(vA,J). Using the known spectroscopic constants of the 1(b) 3Pi state, we obtain bF=0.009 89+/-0.000 27 cm(-1). The values of (H(SO)) are found to be between 2 and 3 cm(-1), depending on vb, vA, and J. Dividing (H(SO)) by calculated vibrational overlap integrals, and taking account of the 1(b) 3Pi(Omega) rotational mixing, we can determine the magnitude of the electronic part H(el) of H(SO). Our results yield (H(el))=(16.33+/-0.15) cm(-1), consistent with our previous determinations using different techniques.

Observation and analysis of the 2g(1D) ion-pair state of I2: the g/u mixing between the 1u(1D) and 2g(1D) states.

We report the analysis of the 2g(1D) ion-pair state of I2 by perturbation-facilitated optical-optical double resonance. The present study began with the observation of the 2g(1D)-A' 3Pi(2u) emission at around 230 nm during the analysis of the ultraviolet emissions originating form the 1u(1D) ion-pair state. The identification of this new transition helped us to specify the wavelengths for detecting the 2g(1D) state by emission, and also to estimate its absolute position. The intermediate states used to observe the 2g(1D) state were the B 3Pi(0u(+))-b' 2u mixed states by the hyperfine interaction, which allowed us to combine the X 1Sigmag(+) ground state with the 2g(1D) state in the (1+1) photon excitation following the optical selection rules for one-photon transitions: 2g(1D)<--b' 2u-B 3Pi(0u(+))<--X 1Sigmag(+). Our analysis covered the 2g(1D) state in the 0< or =v< or =12 and 9< or =J< or =40 ranges. The molecular constants and Rydberg-Klein-Rees (RKR) potential of the 2g(1D) state were reported. We discussed the occurrence of the 2g(1D)-A' 3Pi(2u) emission, when exciting to the 1u(1D) v=0 state, and attributed it to the g/u mixing between the 2g(1D) and 1u(1D) states by the hyperfine interaction. The effect of the perturbation on measured line intensities and lifetimes was evident.

The [formula omitted] state of Na 2: observation and assignment

The v=2–21 levels of the Na 2 6 3 Σ g + state have been observed by perturbation facilitated optical–optical double resonance (PFOODR) spectroscopy. The vibrational numbering is confirmed by simulation of the 6 3 Σ g +→a 3 Σ u + bound-free transition. Molecular constants and RKR potential curve of the 6 3 Σ g + state are reported. Perturbations of the 6 3 Σ g + state are discussed.

Experimental observation of Autler–Townes splitting of the Na 2[formula omitted] mixed levels

The Autler–Townes (A–T) splittings of the A 1 Σ u +∼ b 3 Π u mixed levels of Na 2 have been experimentally studied by pulsed laser perturbation facilitated optical–optical double resonance (PFOODR) spectroscopy. A pump laser was used to excite the A 1 Σ u +(v A ′,J ′)∼ b 3 Π u (v b ′,J ′)← X 1 Σ g +(v″,J″=J ′±1) transition and a probe laser was used to probe the A–T splitting of the A 1 Σ u +∼ b 3 Π u mixed levels by further exciting from the intermediate levels to the 2 3 Π g state and monitoring the 2 3 Π g → a 3 Σ u + violet fluorescence. When the pump laser frequency was held fixed to a frequency between the A 1 Σ u +(v A ′,J ′)← X 1 Σ g +(v″,J″=J ′±1) and b 3 Π u (v b ′,J ′)← X 1 Σ g +(v″,J″=J ′±1) transitions, three OODR excitation lines were observed: one line via the A 1 Σ u +(v A ′,J ′) intermediate level, one line via the b 3 Π u (v b ′,J ′) intermediate level, and between these lines, a “ creeper” line via a new superposition intermediate state. The relative intensities of the three lines vs. the detuning of the pump laser frequency, the intensities of the pump and probe lasers and the buffer gas pressure were studied.

Observation of the K2 4 3Δ g state by cw perturbation-facilitated optical–optical double resonance spectroscopy

This paper reports for the first time both, an experimental observation and theoretical calculations of the K 2 4 3Δ g state. For the experiment we used cw perturbation-facilitated optical–optical double resonance (PFOODR) spectroscopy. A single mode Ti-sapphire laser and a dye laser served as the pump and probe lasers, respectively. A total of 55 PFOODR signals have been assigned to the 4 3Δ g ← b 3Π u transitions. Absolute vibrational numbering was determined by using quantum defect analysis combined with comparing observed intensities with calculated Franck–Condon factors (FCF). For the former we used known parameters from the 2 3Δ g state since the 2 3Δ g and the 4 3Δ g states belong to the same Rydberg series. We report here our experimental and calculated spectroscopic constants, the corresponding RKR potential energy curve, the Franck–Condon table for the 4 3Δ g ↔ b 3 Π u system, as well as a comparison with the theoretical potential energy curve. The T e value is found to be 28408.938(52) cm −1.

Perturbation-facilitated optical-optical double resonance spectroscopy of the h0u−(3P1) and H1u(3P1) ion-pair states of I2

Perturbation-facilitated optical-optical double resonance spectroscopy has been applied to study the h0u−(3P1) and H1u(3P1) ion-pair states of I2 correlating with I−(1S)+I+(3P1). The intermediate states used were the g/u parity mixed states found in the B 3∏(0u+)−X 1∑g+ absorption spectrum near the dissociation limit. We identified several B 3∏(0u+)∼3∏(0g−) coupled states by hyperfine interactions for the first time. These states had the 0u+ and 0g− double-faced character and facilitated to combine the X 1∑g+ ground state with the h0u−(3P1) state in the (1+1) photon excitation scheme following the optical selection rules for one-photon transition. We also accessed the H1u(3P1) state through the B 3∏(0u+)∼c1g mixed state, and elucidated the heterogeneous coupling between the h0u−(3P1) and H1u(3P1) states. Our analyses covered the region of about 48 200 to 50 300 cm−1, and gave the molecular parameters of the h0u−(3P1) state valid for v=0–17 and those of the H1u(3P1) state for v=0–20. The Π3(0g−) state used as an intermediate state was analyzed through the dispersed h0u−(3P1)−3∏(0g−) emission in conjunction with the Franck–Condon factor calculations, and the principle spectroscopic constants of the Π3(0g−) state were reported.

The hyperfine structure of the 1 3Δg state of Na2

The hyperfine spectra of the Na2 1 3Δg state have been recorded with sub-Doppler continuous wave (CW) perturbation facilitated optical–optical double resonance (PFOODR) spectroscopy via A 1∑u+∼b 3∏u mixed intermediate levels. The rotational lines into the N=14–51 levels of the 1 3Δg state observed previously [J. Mol. Spectrosc. 134, 50 (1989)] have four components for transitions between symmetric rotational levels or five components for transitions between antisymmetric rotational levels and the hyperfine coupling belongs to Hund’s case bβS. For the low-N levels observed later, however, the hyperfine spectra are much more complicated. We have worked out the matrix elements of the molecular Hamiltonian in the case bβS basis. After taking into consideration spin–orbit, spin–spin, and spin–rotation interactions, we obtained a set of molecular constants for the Na2 1 3Δg state, with which we can reproduce the hyperfine spectra of both high- and low-N rotational levels.

Enhanced Access to the Dark Triplet States of 7Li2 through New Singlet–Triplet A1Σ+u ∼ b3Πu Perturbation Window Levels: Perturbation-Facilitated Optical–Optical Double Resonance Study of the 23Σ+g State

Two new pairs of singlet–triplet A1Σ+u ∼ b3Πu mixed levels of 7Li2 have been observed and used here as “window” levels in cw perturbation-facilitated optical–optical double-resonance (PFOODR) experiments. Previously, only one b3Πu vibrational level, v = 19, was known to mix with the singlet A1Σ+uv = 13 level, resulting in three perturbed A ∼ b pairs [L. Li, T. An, T.-J. Whang, A. M. Lyyra, W. C. Stwalley, R. W. Field, and R. A. Bernheim, J. Chem. Phys. 96, 3342 (1992)]. The scarcity of window levels and the resulting difficulty in accessing the dark triplet states of Li2 is caused by the weak spin–orbit interaction of Li2. The two new mixed b3Πuv = 15 and 22 levels reported here enhance access to the dark triplet state manifold through expansion of the Franck–Condon overlap factor range. Furthermore, the earlier range of accessible rotational levels, N = 5, 7, and 10, is now expanded to include N = 8 and N = 16, thereby allowing for more reliable determination of the excited triplet states rotational structure. To demonstrate the importance of the new A1Σ+u ∼ b3Πu mixed levels, we have studied the 23Σ+g state by cw PFOODR fluorescence excitation spectroscopy. New molecular constants and RKR potential curve have been determined. As previously reported [L. Li, G. Lazarov, and A. M. Lyyra, J. Mol. Spectrosc. 191, 387 (1998)], the 23Σ+g state interacts with the repulsive 13Πg state by L-uncoupling and predissociates. We show that some 23Πg levels predissociate accidentally by the 13Πg state via the 23Σ+g state through L-uncoupling.

The 43Πg State of Na2: Vibrational Numbering and Hyperfine Structure

The Na2 43Πg state has been studied by continuous-wave (cw) perturbation-facilitated optical–optical double resonance (PFOODR) fluorescence excitation and resolved fluorescence spectroscopy. The absolute vibrational numbering was determined by resolved fluorescence to the a3Σ+u state. The OODR excitation lines of the 43Πg (Kv, N) ← b3Πu (Kvb′, J′) ∼ A1Σ+u (KvA′, J′) ← X1Σ+g (Kv", J") transitions show hyperfine splittings, and the hyperfine coupling scheme of the upper 43Πg levels is case bβS. Although this 43Πg state dissociates to the 3p + 3p atomic limit, it is a Rydberg state at a small internuclear distance, and the hyperfine splitting is caused mainly by the Fermi contact interaction of the ςg3s valence electron with the nuclei. The Fermi contact constant was determined to be bF = 218.3 ± 3.9 MHz.

The High-Lying Vibrational Levels and Dissociation Energy of the a3Σ+u State of 7Li2

Perturbation-facilitated optical–optical double resonance (PFOODR) has been used to access the 23Πg state of 7Li2 via the excitation scheme using two single-mode tunable lasers. The selected () mixed level provides a gateway through which the triplet manifold can be accessed. Fluorescence from single rovibrational levels of 23Πg to the state was detected at high resolution using a Fourier transform spectrometer. Transitions to v = 0–9 in the state were observed, covering the potential well almost to the dissociation limit. The data were analyzed using a near dissociation expansion (NDE) technique and the resulting vibrational and rotational parameters were used to calculate a new RKR potential curve which reproduced the observed energy levels to within a rms error of 0.02 cm−1. The following parameters were obtained for the state: D0 = 301.829 ± 0.015 cm−1, De = 333.69 ± 0.10 cm−1, Te = 8183.12 ± 0.12 cm−1.

New Vibrational Numbering and Potential Energy Curve for the 33ΠgElectronic State of the Li2Molecule

An experimental study of the 33Πgelectronic state of7Li2, using the Perturbation–Facilitated Optical–Optical Double Resonance (PFOODR) technique, was recently reported [A. Yiannopoulouet al., J. Chem. Phys.103, 5898, (1995)]. However, due to the very small number of known7Li2A1Σ+u∼b3Πuwindow levels, only 13 ro-vibrational levels (spanning a range of vibrational levels designated υx− 1 to υx+ 3 in that reference) could be observed. Dunham coefficients, based on the assignment υx= 7, were found to fit the observed term values and give a qualitative fit to the intensities of the first six lines of the 33Πg(υ = υx,N= 11) →b3Πuemission spectrum. However, due to the limited number of levels used in the fit, both the absolute vibrational numbering and the 33ΠgRKR potential curve obtained from the Dunham coefficients, must be considered to be uncertain. In the present work, we show that the previously reported 33ΠgRKR curve is unable to reproduce the experimental intensity distribution in the7Li233Πg(υx= 7,N= 11) →a3Σ+uemission continuum. We report new experimental data for the7Li233Πg(υx+ 1,N= 11) →a3Σ+ubound-free continuum and discrete 33Πg(υx± 1,N= 11) →b3Πuspectra obtained using the PFOODR experimental technique. We demonstrate that the correct vibrational numbering and an improved RKR potential curve can be obtained by analyzing the experimental term values in combination with all observed bound-free and discrete spectra. Finally, term values for four6Li233Πgro-vibrational levels were obtained using PFOODR spectroscopy. The measured isotope shifts confirm the absolute vibrational numbering obtained from the present analysis.

Predissociation of the Na2 4 3Σg+ state

The Na2 4 3Σg+ state dissociates adiabatically to the 3s+4p atomic limit. The vibrational levels of the 4 3Σg+ state below the 3s+3d atomic limit were observed previously by perturbation facilitated optical–optical double resonance (PFOODR) fluorescence excitation spectroscopy. Vibrational levels above the 3s+3d atomic limit are found to be predissociated and transitions into these levels have been observed by detecting atomic Na 3d→3p fluorescence. The predissociation is due to the interaction with the continuum of the 2 3Πg state (direct as well as accidental predissociation via bound vibrational levels of the 3 3Πg state). The potential energy curve of the 4 3Σg+ state has been constructed.

Predissociation of the Na2 3 3Πg and other triplet states

The Na2 3 3Πg state adiabatically dissociates to the 3s+4p atomic limit. The 3 3Πg levels below the 3s+3d atomic limit have been observed by perturbation facilitated optical–optical double resonance (PFOODR) fluorescence excitation spectroscopy. Energy levels above the 3s+3d atomic limit cannot be observed by detecting molecular fluorescence but are observable by detecting atomic 3d→3p fluorescence. The 3 3Πg state interacts with the 3s+3d 2 3Πg state. At lower energy this interaction is responsible for many perturbations between bound vibrational levels of these two states. Above the 3s+3d limit, as a result of this interaction, the 3 3Πg state is strongly predissociated and the linewidths of levels close to the 3s+3d limit are about 22 cm−1. The predissociation interaction is due to an avoided crossing between the adiabatic 2 3Πg and 3 3Πg states at R≈2.85 Å. Weak predissociation of the 4 3Σg+ and 2 3Δg states are also observed and discussed.

The 23Πg–b3Πuand 13Δg–b3ΠuTransitions in7Li2: Analysis of theb3ΠuState forv= 0–27

Two double resonance techniques, perturbation facilitated optical–optical double resonance (PFOODR) and collision induced fluorescence (CIF), have been used to excite the 23Πg(PFOODR only) and 13Δgstates of7Li2. Fluorescence from each of these states to theb3Πustate has been studied at high resolution using Fourier transform spectroscopy. Transitions were observed and analyzed up tov= 27 in theb3Πustate, and the PFOODR and CIF data have been combined to give an improved set of Dunham coefficients from which an RKR potential has been calculated. Predissociation by thea3Σu+state, which broadens and shifts the b3Πulevels, has been studied in detail. The level shifts tov= 27 have been calculated and the observed values are shown to follow the theoretically predicted pattern. The isotope effect on the predissociation has also been examined. The 13Δgstate has been analyzed for 0 ≤v≤ 25 and molecular constants and an RKR potential have been calculated.

New measurements of the a3 Σ+u state of K2 and improved analysis of long-range dispersion and exchange interactions between two K atoms

Resolved fluorescence from the K2 43 Σ+g state to the a3 Σ+u state has been measured by the perturbation-facilitated optical–optical double resonance (PFOODR) technique. Data have been fit to an improved set of molecular constants for the a3 Σ+u state. In particular, the new Te value for this state has been determined as 4197.935±0.047 cm−1, nearly 1.8 cm−1 higher than previously reported. By combining the new results for the a3 Σ+u state and the recent results for the ground X1 Σ+g state [J. Chem. Phys. 103, 3350 (1995)], we report in this paper an improved analysis of long-range dispersion and exchange interactions between two K atoms and of the X1 Σ+g and a3 Σ+u state dissociation energies De of 4450.674±0.072 cm−1 and 252.74±0.12 cm−1, respectively.