Elastic Depolarization of OH(A) by He and Ar: A Comparative Study

Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory

The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response. In our previous work, we have found that these two approaches yield different results while a perturbing field is acting on the system. Here, we prove, for the first time, that differences between the two approaches may persist after the perturbing fields have been completely turned off. We have designed a pair of overlapping pulses in order to establish the possibility of lasting differences, in a case with dephasing. Our work goes beyond the analysis presented by Landau and Lifshitz, since they considered only linear response and required that a constant perturbation must remain as t → ∞. First, a "plateau" pulse populates an excited rotational state and produces coherences between the ground and excited states. Then, an infrared pulse acts while the electric field of the first pulse is constant, but after dephasing has occurred. The nonadiabatic perturbation theory permits dephasing, but dephasing of the perturbed part of the wave function cannot occur within Dirac's method. When the frequencies in both pulses are on resonance, the lasting differences in the calculated transition probabilities may exceed 35%. The predicted differences are larger for off-resonant perturbations.

Non-adiabatic quantum dynamics of the electronic quenching OH(A2Σ+) + Kr

The quantum dynamics is investigated in full dimensionality, using three PESs and all the non-adiabatic couplings of a total Hamiltonian.

Experimental and theoretical studies of the Xe-OH(A/X) quenching system

New multi-reference, global ab initio potential energy surfaces (PESs) are reported for the interaction of Xe atoms with OH radicals in their ground X²Π and excited A²Σ⁺ states, together with the non-adiabatic couplings between them. The 2A' excited potential features a very deep well at the collinear Xe-OH configuration whose minimum corresponds to the avoided crossing with the 1A' PES. It is therefore expected that, as with collisions of Kr + OH(A), electronic quenching will play a major role in the dynamics, competing favorably with rotational energy transfer within the 2A' state. The surfaces and couplings are used in full three-state surface-hopping trajectory calculations, including roto-electronic couplings, to calculate integral cross sections for electronic quenching and collisional removal. Experimental cross sections, measured using Zeeman quantum beat spectroscopy, are also presented here for comparison with these calculations. Unlike similar previous work on the collisions of OH(A) with Kr, the surface-hopping calculations are only able to account qualitatively for the experimentally observed electronic quenching cross sections, with those calculated being around a factor of two smaller than the experimental ones. However, the predicted total depopulation of the initial rovibrational state of OH(A) (quenching plus rotational energy transfer) agrees well with the experimental results. Possible reasons for the discrepancies are discussed in detail.

An experimental study of OH(A2Σ+) + H2: Electronic quenching, rotational energy transfer, and collisional depolarization

Zeeman quantum beat spectroscopy has been used to determine the thermal (300 K) rate constants for electronic quenching, rotational energy transfer, and collisional depolarization of OH(A²Σ⁺) by H₂. Cross sections for both the collisional disorientation and collisional disalignment of the angular momentum in the OH(A²Σ⁺) radical are reported. The experimental results for OH(A²Σ⁺) + H₂ are compared to previous work on the OH(A²Σ⁺) + He and Ar systems. Further comparisons are also made to the OH(A²Σ⁺) + Kr system, which has been shown to display significant non-adiabatic dynamics. The OH(A²Σ⁺) + H₂ experimental data reveal that collisions that survive the electronic quenching process are highly depolarizing, reflecting the deep potential energy wells that exist on the excited electronic state surface.

Rotationally inelastic scattering of NO(A(2)Σ(+)) + Ar: Differential cross sections and rotational angular momentum polarization

We present the implementation of a new crossed-molecular beam, velocity-map ion-imaging apparatus, optimized for collisions of electronically excited molecules. We have applied this apparatus to rotational energy transfer in NO(A(2)Σ(+), v = 0, N = 0, j = 0.5) + Ar collisions, at an average energy of 525 cm(-1). We report differential cross sections for scattering into NO(A(2)Σ(+), v = 0, N' = 3, 5, 6, 7, 8, and 9), together with quantum scattering calculations of the differential cross sections and angle dependent rotational alignment. The differential cross sections show dramatic forward scattered peaks, together with oscillatory behavior at larger scattering angles, while the rotational alignment moments are also found to oscillate as a function of scattering angle. In general, the quantum scattering calculations are found to agree well with experiment, reproducing the forward scattering and oscillatory behavior at larger scattering angles. Analysis of the quantum scattering calculations as a function of total rotational angular momentum indicates that the forward scattering peak originates from the attractive minimum in the potential energy surface at the N-end of the NO. Deviations in the quantum scattering predictions from the experimental results, for scattering at angles greater than 10°, are observed to be more significant for scattering to odd final N'. We suggest that this represents inaccuracies in the potential energy surface, and in particular in its representation of the difference between the N- and O-ends of the molecule, as given by the odd-order Legendre moments of the surface.

Parity-dependent oscillations in collisional polarization transfer: CN(A²Π, v = 4) + Ar

We report the first systematic experimental and theoretical study of the state-to-state transfer of rotational angular momentum orientation in a (2)Π-rare gas system. CN(X(2)Σ(+)) was produced by pulsed 266 nm photolysis of ICN in a thermal bath (296 K) of Ar collider gas. A pulsed circularly polarized tunable dye laser prepared CN(A(2)Π, v = 4) in two fully state-selected initial levels, j = 6.5 F1e and j = 10.5 F2f, with a known laboratory-frame orientation. Both the prepared levels and a range of product levels, j' F1e and j' F2f, were monitored using the circular polarized output of a tunable diode laser via cw frequency-modulated (FM) spectroscopy in stimulated emission on the CN(A-X) (4,2) band. The FM Doppler lineshapes for co-rotating and counter-rotating pump-and-probe geometries reveal the time-dependence of the populations and orientations. Kinetic fitting was used to extract the state-to-state population transfer rate constants and orientation multipole transfer efficiencies (MTEs), which quantify the degree of conservation of initially prepared orientation in the product level. Complementary full quantum scattering (QS) calculations were carried out on recently computed ab initio potential energy surfaces. Collision-energy-dependent tensor cross sections for ranks K = 0 and 1 were computed for transitions from both initial levels to all final levels. These quantities were integrated over the thermal collision energy distribution to yield predictions of the experimentally observed state-to-state population transfer rate constants and MTEs. Excellent agreement between experiment and theory is observed for both measured quantities. Dramatic oscillations in the MTEs are observed, up to and including changes in the sign of the orientation, as a function of even/odd Δj within a particular spin-orbit and e/f manifold. These oscillations, along with those also observed in the state-to-state rate constants, reflect the rotational parity of the final level. In general, parity-conserving collisions conserve rotational orientation, while parity-changing collisions result in large changes in the orientation. The QS calculations show that the dynamics of the collisions leading to these different outcomes are fundamentally different. We propose that the origin of this behavior lies in interferences between collisions that sample the even and odd-λ terms in the angular expansions of the PESs.

Rotational alignment of NO (A2Σ+) from collisions with Ne

We report the direct angle-resolved measurement of collision-induced alignment of short-lived electronically excited molecules using crossed atomic and molecular beams. Utilizing velocity-mapped ion imaging, we measure the alignment of NO in its first electronically excited state (A(2)Σ(+)) following single collisions with Ne atoms. We prepare A(2)Σ(+) (v = 0, N = 0, j = 0.5) and by comparing images obtained using orthogonal linear probe laser polarizations, we experimentally determine the degree of alignment induced by collisional rotational excitation for the final rotational states N' = 4, 5, 7, and 9. The experimental results are compared to theoretical predictions using both a simple classical hard-shell model and quantum scattering calculations on an ab initio potential energy surface (PES). The experimental results show overall trends in the scattering-angle dependent polarization sensitivity that are accounted for by the simple classical model, but structure in the scattering-angle dependence that is not. The quantum scattering calculations qualitatively reproduce this structure, and we demonstrate that the experimental measurements have the sensitivity to critique the best available potential surfaces. This sensitivity to the PES is in contrast to that predicted for ground-state NO(X) alignment.

Depolarization of rotational angular momentum in CN(A2Π, v = 4) + Ar collisions

Angular momentum depolarization and population transfer in CN(A(2)Π, v = 4, j, F(1)e) + Ar collisions have been investigated both experimentally and theoretically. Ground-state CN(X(2)Σ(+)) molecules were generated by pulsed 266-nm laser photolysis of ICN in a thermal (nominally 298 K) bath of the Ar collision partner at a range of pressures. The translationally thermalized CN(X) radicals were optically pumped to selected unique CN(A(2)Π, v = 4, j = 2.5, 3.5, 6.5, 11.5, 13.5, and 18.5, F(1)e) levels on the A-X (4,0) band by a pulsed tunable dye laser. The prepared level was monitored in a collinear geometry by cw frequency-modulated (FM) spectroscopy in stimulated emission on the CN(A-X) (4,2) band. The FM lineshapes for co- and counter-rotating circular pump and probe polarizations were analyzed to extract the time dependence of the population and (to a good approximation) orientation (tensor rank K = 1 polarization). The corresponding parallel and perpendicular linear polarizations yielded population and alignment (K = 2). The combined population and polarization measurements at each Ar pressure were fitted to a 3-level kinetic model, the minimum complexity necessary to reproduce the qualitative features of the data. Rate constants were extracted for the total loss of population and of elastic depolarization of ranks K = 1 and 2. Elastic depolarization is concluded to be a relatively minor process in this system. Complementary full quantum scattering (QS) calculations were carried out on the best previous and a new set of ab initio potential energy surfaces for CN(A)-Ar. Collision-energy-dependent elastic tensor and depolarization cross sections for ranks K = 1 and 2 were computed for CN(A(2)Π, v = 4, j = 1.5-10.5, F(1)e) rotational/fine-structure levels. In addition, integral cross sections for rotationally inelastic transitions out of these levels were computed and summed to yield total population transfer cross sections. These quantities were integrated over a thermal collision-energy distribution to yield the corresponding rate constants. A complete master-equation simulation using the QS results for the selected initial level j = 6.5 gave close, but not perfect, agreement with the near-exponential experimental population decays, and successfully reproduced the observed multimodal character of the polarization decays. On average, the QS population removal rate constants were consistently 10%-15% higher than those derived from the 3-level fit to the experimental data. The QS and experimental depolarization rate constants agree within the experimental uncertainties at low j, but the QS predictions decline more rapidly with j than the observations. In addition to providing a sensitive test of the achievable level of agreement between state-of-the art experiment and theory, these results highlight the importance of multiple collisions in contributing to phenomenological depolarization using any method sensitive to both polarized and unpolarized molecules in the observed level.

Rotationally elastic and inelastic dynamics of NO(X2Π, v = 0) in collisions with Ar

A combined theoretical and experimental study of the depolarization of selected NO(X(2)Π, v = 0, j, F, ɛ) levels in collisions with a thermal bath of Ar has been carried out. Rate constants for elastic depolarization of rank K = 1 (orientation) and K = 2 (alignment) were extracted from collision-energy-dependent quantum scattering calculations, along with those for inelastic population transfer to discrete product levels. The rate constants for total loss of polarization of selected initial levels, which are the sum of elastic depolarization and population transfer contributions, were measured using a two-color polarization spectroscopy technique. Theory and experiment agree qualitatively that the rate constants for total loss of polarization decline modestly with j, but the absolute values differ by significantly more than the statistical uncertainties in the measurements. The reasons for this discrepancy are as yet unclear. The lack of a significant K dependence in the experimental data is, however, consistent with the theoretical prediction that elastic depolarization makes only a modest contribution to the total loss of polarization. This supports a previous conclusion that elastic depolarization for NO(X(2)Π) + Ar is significantly less efficient than for the electronically closely related system OH(X(2)Π) + Ar [P. J. Dagdigian and M. H. Alexander, J. Chem. Phys. 130, 204304 (2009)].

Collisional transfer of population and orientation in NaK

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.