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We report results of an experimental study of the changes in the alignment of the rotational angular momentum of diatomic molecules during elastic collisions. The experiment involved collisions of diatomic lithium molecules in the A1Σu+ excited electronic state with noble gas atoms (helium and argon) in a thermal gas phase sample. Polarized light for excitation was combined with the detection of polarization-specific fluorescence in order to achieve magnetic sublevel state selectivity. We also report results for rotationally inelastic collisions of Li2 in the lowest lying rotational levels of the A1Σu+v=5 vibrational state with noble gas atoms.

We report calculations of the spin–orbit energy as a function of internuclear distance R within the b 3∏u state of K2, and between the b 3∏0u and A 1∑u+ states, together with new spectroscopic data on the b state and previously unpublished data on the A state. Both the new data and previous data are fitted to Hamiltonian parameters using the discrete variable representation (DVR) method. The DVR matrix includes nonrelativistic Born–Oppenheimer potentials and spin–orbit interactions, which are scaled to match the known asymptotic limits and to best fit the experimental data. We report fitted Dunham coefficients that yield the A and b state potentials by means of the Rydberg–Klein–Rees method. These parameters thus take into account second-order spin–orbit perturbation shifts (from the vibrational levels of these two states) which are normally not considered in band-by-band fits to spectroscopic data.

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.

The repulsive a 3Σu+ state potential of the Na2 molecule is determined by applying the IPA (inverse perturbation approach) of V. S. Ivanov and V. B. Sovkov [Chem. Phys. 213, 295 (1996)] to the analysis of the Na2 2 2Σg+ (v=15, N=27, and v=5, N=39)→a 3Σu+ continua observed in the work of T. J. Whang et al. [J. Mol. Spectrosc. 160, 411 (1993)]. The resulting a 3Σu+ state potential is close to the ab initio potential within the experimental error, but its right branch deviates from the RKR–Le Roy–Bernstein potential function of the a 3Σu+ state shallow well reported in E.-J. Friedman-Hill and R. W. Field [J. Chem. Phys. 96, 2444 (1992)]. The transition moment function M(R) of the 2 3Σg+−a 3Σu+ transition is also obtained from the analysis of the spectra and compared to the ab initio one. The same 2 3Σg+ (v=15, N=27)→a 3Σu+ experimental spectrum is used for investigating abilities of the WKB nodes method, the FCF phase method, and the method of the accurate equation for the potential in terms of the transitio...

CW optical–optical double resonance has been employed to study the upper portion of the G 1Πg state of 7Li2. The use of fluorescence and ion detection enabled the observation of vibrational levels ranging from v=20 to 48 and rotational levels ranging from J=1 to 25. For optical–optical double resonance experiments the Franck–Condon factors between these levels and useful A 1Σu+ state levels (levels that can be reached from the thermally populated levels of the ground state) were exceedingly small. The sensitive ionization detection made possible observation of this upper, anharmonic region of the potential. From the data a Rydberg–Klein–Rees potential curve was constructed which represents over 99% of the potential well depth. A C5 coefficient has been calculated and represents the first experimental determination of a long range coefficient for a doubly excited state in diatomic lithium.

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 A. Weak predissociation of the 4 3Σg+ and 2 3Δg states are also observed and discussed.

State‐to‐state collision energy transfer in the 2 3Πg, 3 3Πg, 3 3Σ+g, 1 3Σ−g, and 1 3Δg states and from singlet to triplet states of 7Li2 has been studied experimentally by continuous wave optical–optical double resonance (OODR) resolved fluorescence spectroscopy. Propensity rules of collision‐induced transitions within a triplet state have been observed. When a rovibrational (v,J) level of the F 1Σ+g or G 1Πg state was excited by OODR transition, fluorescence from high‐lying triplet gerade states to the a 3Σ+u and/or b 3Πu states was always observed. This indicates that population can transfer from F 1Σ+g and G 1Πg states to triplet states by collision. Irrespective of the J of the initially excited singlet level, the most intense fluorescence from the triplet state will occur at the N or J corresponding to that of the F 1Σ+g (and/or G 1Πg)∼3Λg mixed levels. Molecular population moves to the mixed levels and then transfers to the triplet state. This clearly indicates that singlet–triplet mixed levels pla...

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.

The hyperfine structure of the b 3Πu, 2 3Πg, and 3 3Πg states of 7Li2 has been studied by continuous wave perturbation facilitated optical–optical double resonance fluorescence excitation spectroscopy. The b 3Πu state has case bβJ coupling scheme. The hyperfine splittings of the two perturbed b 3Πu v=19, N=10, J=11e, s, F1 and v=19, N=5, J=4e, a, F3 levels were resolved and hyperfine constants determined to be +9.90 MHz and −20.94 MHz, respectively. Fermi contact is the main source of the hyperfine interaction and bF(b 3Πu)=+107 MHz has been obtained. The coupling schemes of different 2 3Πg levels are different: N=4, 6 levels observed from the b 3Πu v′=19, N′=5, J′=4e, a, F3 intermediate level and the N=10 levels observed via the b 3Πu v′=19, N′=10, J′=11e, s, F1 intermediate level have case bβJ coupling; the N=5 levels observed via the b 3Πu v′=19, N′=5, J′=4e, a, F3 intermediate level and the N=9, 11 levels observed from the b 3Πu v′=19, N′=10, J′=11e, s, F1 intermediate level are closer to case bβS cou...

The A 1Σ+u state of 7Li2 has been studied using all optical triple resonance spectroscopy. Vibrational levels v=27–62 and rotational levels ranging from J=0 to 27 have been observed. This represents a region between previous data from single photon experiments and new data from cold atom photoassociative spectroscopy. Our data was fit to a Dunham expansion and the resulting molecular constants reproduce most observed energies to within 0.050 cm−1. A Rydberg–Klein–Rees potential curve has also been constructed and the calculated eigenvalues are in good agreement with observed energies.

The (2p+2p) 2 3Πg and (2s+3p) 3 3Πg states of 7Li2 have been studied both experimentally and theoretically. Vibrational levels v=0–41 of the 2 3Πg state and v=6–10 of the 3 3Πg state have been observed by perturbation facilitated optical–optical double resonance (PFOODR) spectroscopy. Our ab initio calculations show that the 2 3Πg state, although dissociating into 2p+2p atomic limit, is a Rydberg state and strongly mixed with the (2s+3p) 3 3Πg and (2s+3d) 4 3Πg Rydberg states. Our theoretical calculations show good agreement with our experimental results.

The 4 3Σ+g, 3 3Πg, and 2 3Δg states of K2 have been studied by perturbation facilitated optical–optical double resonance spectroscopy for the first time. Molecular constants of those states are derived and compared with theoretical calculations. Varying the trial vibrational quantum numbers of these upper states, absolute vibrational quantum number assignments are obtained by comparison between the observed resolved fluorescence intensities and the calculated Franck–Condon factors. The Rydberg–Klein–Rees potential curves are constructed and compared with theoretical calculations. Finally, the observation of the lowest ‘‘dark’’ vibrational levels of the b 3Πu state by resolved fluorescence from the 2 3Δg state confirmed the absolute vibrational numbering of this state and allowed refinement of the b 3Πu molecular constants.

This paper reports the experimental observation of the 2 3Σ+g, 3 3Σ+g, and 4 3Σ+g states of 7Li2 by cw perturbation facilitated optical–optical double resonance spectroscopy. Molecular constants and RKR potential curves have been obtained. Our experimental Te and Re for the 2 3Σ+g state are 27 297.45(16) cm−1 and 3.0797(18) A, respectively, and for the 3 3Σ+g state are 31 043.93(53) cm−1 and 3.0378(19) A, respectively. The above values are in very good agreement with theoretical calculations. Hyperfine splitting for both states has been resolved. Both states follow Hund’s case (bβS) hyperfine coupling scheme. The experimental Fermi contact parameter, bF, is approximately 96±2 MHz for the 2 3Σ+g state and 95.6±3 MHz for the 3 3Σ+g state. These values are in good agreement with the previously obtained value 98.6±4 MHz [Li et al., J. Chem. Phys. 96, 3342 (1992)]. One level of the 4 3Σ+g state has been observed and its hyperfine structure has been resolved and characterized with Hund’s coupling case (bβS).

This paper reports the first experimental observation of the doubly excited valence (2p+2p)3Σ−g state of 7Li2. We used cw perturbation‐facilitated optical–optical double resonance (PFOODR) fluorescence excitation and resolved fluorescence spectroscopic techniques. All the observed levels have been detected through perturbations by the 2 3Πg state. The deperturbed primary molecular constants of this 1 3Σ−g state are Te=34 045.354(43) cm−1, ωe=216.820(37) cm−1, Be=0.673 69(47) cm−1, Re=2.670 81(94) A, and De=4279.306(43) cm−1. The equilibrium internuclear distance of the 1 3Σ−g state is smaller than that of the X 1Σ+g ground state.

State‐to‐state collision‐induced transitions within the Na2 b 3Πu state have been studied by a sub‐Doppler optical–optical double resonance (OODR) technique employing cw, single mode dye lasers for the PUMP and PROBE steps. The main experimental results are (1) strong Ω‐conservation is observed when a low‐J 3Π0 or 3Π1 parent level is initially prepared (we are unable to prepare low‐J 3Π2 levels). This Ω‐conservation relaxes as J increases. (2) e/f parity conservation (i.e., propensity for even ΔJ changes in homonuclear molecules) is observed at low‐J within the 3Π0 manifold. This propensity for e/f‐conservation relaxes rapidly as J increases. (3) The e/f parity conservation rule observed within the 3Π0 manifold is observed not to apply to the collision‐induced transitions within the 3Π1 manifold. At low‐J, ΔJ=±1, e→f transitions are even stronger than ΔJ=±2, e→e transitions. (4) At higher‐J, for example J=16, neither Ω‐conservation nor e/f‐conservation within the 3Π0 manifold are observed. These results a...

The changes in the hyperfine quantum number (F’) that accompany collision‐induced ΔJ, ΔΩ, and Δ(e/f‐parity) transitions in the Na2 b 3Πu‐state have been studied by sub‐Doppler, cw, perturbation‐facilitated optical–optical double resonance (PFOODR) spectroscopy. The Na2 is contained in a heat pipe oven at ∼1 Torr and the primary collision partner is Na(3s 2S). The PUMP laser selectively excites a single b 3Π0u v’=12, J’=43e, s or 44e, a rotational level, the parent level. All F’ hyperfine components of the parent J’ level are directly populated by the PUMP laser, but with different velocity projections relative to the laser propagation direction. Thus each parent hf component is labeled by its longitudinal velocity. As the PROBE laser is scanned through various 2 3ΠΩg v=2, J←b 3ΠΩ’u v’=12, J’ transitions, sub‐Doppler hyperfine structure can be resolved on each parent and daughter rotational line in the PFOODR fluorescence excitation spectrum. The collisional propensity rule ΔF=ΔJ is obeyed for (s, a permut...

We present here the best qualitative and quantitative illustration to date of the perturbation ‘‘gateway’’ effect in collision‐induced transitions between two mutually perturbing electronic states. The gateway effect, as described by Gelbart and Freed [Chem. Phys. Lett. 18, 470 (1973)], is a suggestion that all collision‐induced transfer of population between two electronic states proceeds through a small number of isolated‐molecule eigenstates which are of mixed electronic character, the ‘‘gateway levels,’’ and that the rates for such gateway‐mediated processes are related to the mixing fractions in the gateway levels. The gateway levels here are the Na2 A 1Σu+ v’=26∼b 3Π2u v’=28 J’=16e,a‐symmetry levels which are significantly mixed owing to an extremely small spin–orbit perturbation matrix element (the neighboring J’=15 and 17e,s‐symmetry levels are essentially free of mixing). A cw optical–optical double resonance (OODR) scheme is used to PUMP a single parent level and PROBE single daughter and grandd...

The Na2 b 3Πu state has been studied by the continuous wave (cw) all‐optical triple resonance (AOTR) technique. The AOTR technique used here corresponds to a perturbation‐facilitated optical–optical double resonance (PFOODR) excitation through A 1Σu+∼b 3Πu mixed intermediate levels from the ground state to the 2 3Πg state and stimulated emission pumping (SEP) of the 2 3Πg→b 3Πu transition. This sub‐Doppler high‐resolution PFOODR‐SEP technique has allowed us to reach many b 3Πu levels (Ω=0, 1, 2, perturbed and unperturbed, including low v below the A 1Σu+ potential minimum and higher vibrational levels up to v=57). Based on these new high resolution data and previous results from high resolution spectroscopy, we have determined a new set of deperturbed molecular constants from the b 3Πu state up to v=57, the corresponding RKR potential energy curve and the A 1Σu+∼b 3Πu spin–orbit interaction constants. This represents an example of a powerful and general technique for observing a ‘‘dark’’ (e.g., triplet) p...

Rydberg states of the potassium dimer in the 28 430–29 080 cm−1 and 30 030–30 500 cm−1 regions above the ground state X1Σ+g minimum have been studied using the perturbation facilitated optical–optical double resonance technique (PFOODR). Energy levels in these energy regions have been assigned to both triplet and singlet gerade states based on excitation pattern information as well as intensity considerations. Resolved fluorescence from a mixed triplet–singlet 43Πg ∼1Πg upper state to the ground triplet state a 3Σ+u has been used to construct a potential energy curve for the a 3Σ+u state which is in excellent agreement with recent theoretical results. Since this electronic state and the ground singlet state X1Σ+g share the same dissociation limit, we have determined the dissociation energy for the potassium dimer to be De=4450±2 cm−1.

Using resolved fluorescence from a 1Σ+g Rydberg state to the A 1Σ+u state of K2, we have observed the lowest vibrational levels (v’≤12) of the A 1Σ+u state. Levels v’=21 to 62 (well beyond the previously known v’=12 to 18 region) were observed using the polarization optical–optical double resonance technique. Molecular constants and a Rydberg–Klein–Rees (RKR) potential energy curve based on these constants are given. Franck–Condon factors for the K2, A 1∑+u–X 1∑+g system based on this new A 1Σ+u potential are also given.

Sets of experimental data on the Cs(2) a(3)Σ(u)(+) and 1(g) (3(3)Π(1g)) states, including the bound-bound and bound-free fluorescence spectra, are analyzed simultaneously to produce the potential energy curves of both states in the form of the Morse long range multiparameter function. The attractive branch of the a(3)Σ(u)(+) state potential is improved relative to the one reported in our earlier work [F. Xie, V. B. Sovkov, A. M. Lyyra, D. Li, S. Ingram, J. Bai, V. S. Ivanov, S. Magnier, and L. Li, J. Chem. Phys. 130, 051102 (2009)], in which the data on this state alone were analyzed. Besides, the new potential of this state also includes the repulsive branch in the range spanned by the bound-free fluorescence spectra. We have not found experimental evidence of the double minimum character of the 3(3)Π(1g) state potential, predicted by ab initio calculations, at least up to v = 8. This fact testifies that the upper state observed is better described by the Hund coupling case (c), in which the case (a) electronic basis states are intermixed by the strong spin-orbit interaction.

Collisional satellite lines with |ΔJ| ≤ 58 have been identified in recent polarization spectroscopy V-type optical-optical double resonance (OODR) excitation spectra of the Rb(2) molecule [H. Salami et al., Phys. Rev. A 80, 022515 (2009)]. Observation of these satellite lines clearly requires a transfer of population from the rotational level directly excited by the pump laser to a neighboring level in a collision of the molecule with an atomic perturber. However to be observed in polarization spectroscopy, the collision must also partially preserve the angular momentum orientation, which is at least somewhat surprising given the extremely large values of ΔJ that were observed. In the present work, we used the two-step OODR fluorescence and polarization spectroscopy techniques to obtain quantitative information on the transfer of population and orientation in rotationally inelastic collisions of the NaK molecules prepared in the 2(A)(1)Σ(+)(v' = 16, J' = 30) rovibrational level with argon and potassium perturbers. A rate equation model was used to study the intensities of these satellite lines as a function of argon pressure and heat pipe oven temperature, in order to separate the collisional effects of argon and potassium atoms. Using a fit of this rate equation model to the data, we found that collisions of NaK molecules with potassium atoms are more likely to transfer population and destroy orientation than collisions with argon atoms. Collisions with argon atoms show a strong propensity for population transfer with ΔJ = even. Conversely, collisions with potassium atoms do not show this ΔJ = even propensity, but do show a propensity for ΔJ = positive compared to ΔJ = negative, for this particular initial state. The density matrix equations of motion have also been solved numerically in order to test the approximations used in the rate equation model and to calculate fluorescence and polarization spectroscopy line shapes. In addition, we have measured rate coefficients for broadening of NaK 3(1)Π ← 2(A)(1)Σ(+)spectral lines due to collisions with argon and potassium atoms. Additional broadening, due to velocity changes occurring in rotationally inelastic collisions, has also been observed.

Using perturbation facilitated infrared-infrared double resonance excitation of the R85b2 molecule, we have observed spectrally resolved fluorescence to the a Σ3u+ state. We have analyzed the rovibrational energy level structure of the R85b2 a Σ3u+ state and derived a multiparameter Morse Long Range (MLR) potential and molecular constants for this state, which can be used to predict term values without needing to solve the radial Schrodinger equation.

We report a comparison between experimental and theoretical electronic transition dipole moment values for the (7)Li(2) A (1)Sigma(u) (+)-X (1)Sigma(g) (+) system. The experimental results are based on measuring the absolute magnitude of the transition dipole matrix elements from Autler-Townes splitting of rovibrational transitions for different R-centroid values. The ab initio theoretical calculations of the transition dipole moment for the (7)Li(2) A (1)Sigma(u) (+)-X (1)Sigma(g) (+) system were performed using two different quantum-mechanical models: an all-electron valence bond self-consistent-field method and a pseudopotential molecular orbital method. As expected for the smallest molecule with core electrons, the agreement between experiment and theory is very good.

We describe a two-laser experiment using optical-optical double resonance fluorescence and Autler-Townes (AT) splittings to determine the NaK 3 (1)Pi-->1(X)(1)Sigma(+), 2(A)(1)Sigma(+) absolute transition dipole moment functions. Resolved 3 (1)Pi-->A (1)Sigma(+) and 3 (1)Pi-->X (1)Sigma(+) fluorescence was recorded with the frequencies of a titanium-sapphire laser (L1) and a ring dye laser (L2) fixed to excite particular 3 (1)Pi(upsilon = 19,J = 11,f)

The lowest electronically excited states of Na2 are of interest as intermediaries in the excitation of higher states and in the development of methods for producing cold molecules. We have compiled previously obtained spectroscopic data on the AΣu+1 and bΠu3 states of Na2 from about 20 sources, both published and unpublished, together with new sub-Doppler linewidth measurements of about 15 000 A←X transitions using polarization spectroscopy. We also present new ab initio results for the diagonal and off-diagonal spin-orbit functions. The discrete variable representation is used in conjunction with Hund’s case a potentials plus spin-orbit effects to model data extending from v=0 to very close to the 3S2+3P1∕22 limit. Empirical estimates of the spin-orbit functions agree well with the ab initio functions for the accessible values of R. The potential function for the A state includes an exchange potential for S+P atoms, with a fitted coefficient somewhat larger than the predicted value. Observed and calculat...

The hyperfine structure of the 1 3Δg Rydberg state of Na2 has been studied by sub‐Doppler CW perturbation facilitated optical–optical double resonance (PFOODR) spectroscopy via A 1Σu+∼b 3Πu mixed intermediate levels.

We have measured the far wing absorption profiles of the MgH2 collision system leading to both the nonreactive formation of Mg* and into two distinct final rotational states of the reaction product MgH (v‘=0, J‘=6, 23). We have observed qualitatively expected behavior including a pronounced red wing in the reactive absorption profile indicating strong reaction probability on the excited attractive potential surfaces. We have also observed novel aspects of the excited state dynamics including reactive vs nonreactive channel competition effects and a strong far blue wing reactive absorption suggesting significant reaction probability even for trajectories on the repulsive surfaces. We have developed a simple theoretical model to semiquantitatively explain our experimental results. This model uses standard quasistatic theory to estimate the absorption probability as a function of detuning between levels of MgH2 and with assumed nonreactive vs reactive branching ratios, accounts for the subsequent evolution on the excited potential surfaces. This theory correctly predicts the overall shapes of the profiles and in general gives reasonable predictions for the relative magnitudes of the wing intensities.