Quantum mechanical calculations of collisional quenching cross sections and rate coefficients for... more Quantum mechanical calculations of collisional quenching cross sections and rate coefficients for various internally excited atoms and molecules at cold and ultracold temperatures are presented. The efficiencies of relaxation for vibrationally, rotationally, and electronically excited states are given and in each case the dominant decay mechanisms are discussed. £ R¥ prevents the atoms from reaching short distances where autoionization can
We examine the effect of theoretically varying the collision-system reduced mass in collisions of... more We examine the effect of theoretically varying the collision-system reduced mass in collisions of He with vibrationally excited molecular hydrogen and observe zero-energy resonances for select atomic "hydrogen" masses less than 1 u or a "helium" mass of 1.95 u. Complex scattering lengths, state-to-state vibrational quenching cross sections, and a low-energy elastic scattering resonance are all studied as a function of collision-system reduced mass. Experimental observations of these phenomena in the cold and ultracold regimes for collisions of 3 He and 4 He with H 2 , HD, HT, and DT should be feasible in the near future.
Accurate rate coefficients for molecular vibrational transitions due to collisions with H2, criti... more Accurate rate coefficients for molecular vibrational transitions due to collisions with H2, critical for interpreting infrared astronomical observations, are lacking for most molecules. Quantum calculations are the primary source of such data, but reliable values that consider all internal degrees of freedom of the collision complex have only been reported for H2-H2 due to the difficulty of the computations. Here we present essentially exact, full-dimensional dynamics computations for rovibrational quenching of CO due to H2 impact. Using a high-level six-dimensional potential surface, time-independent scattering calculations, within a full angular momentum coupling formulation, were performed for the de-excitation of vibrationally excited CO. Agreement with experimentally determined results confirms the accuracy of the potential and scattering computations, representing the largest of such calculations performed to date. This investigation advances computational quantum dynamical st...
Along with H 2 , HD has been found to play an important role in the cooling of the primordial gas... more Along with H 2 , HD has been found to play an important role in the cooling of the primordial gas for the formation of the first stars and galaxies. It has also been observed in a variety of cool molecular astrophysical environments. The rate of cooling by HD molecules requires knowledge of collisional rate coefficients with the primary impactors, H, He, and H 2. To improve knowledge of the collisional properties of HD, we present rate coefficients for the He-HD collision system over a range of collision energies from 10 −5 to 5 × 10 3 cm −1. Fully quantum mechanical scattering calculations were performed for initial HD rovibrational states of j = 0 and 1 for v = 0-17 which utilized accurate diatom rovibrational wave functions. Rate coefficients of all Δv = 0, −1, and −2 transitions are reported. Significant discrepancies with previous calculations, which adopted a small basis and harmonic HD wave functions for excited vibrational levels, were found for the highest previously considered vibrational state of v = 3. Applications of the He-HD rate coefficients in various astrophysical environments are briefly discussed.
New quantum scattering calculations for rotational deexcitation transitions of CO induced by H co... more New quantum scattering calculations for rotational deexcitation transitions of CO induced by H collisions using two CO-H potential energy surfaces (PESs) from Shepler et al. (2007) are reported. State-to-state rate coefficients are computed for temperatures ranging from 1 to 3000 K for CO(v = 0, j) deexcitation from j = 1 − 5 to all lower j ′ levels, with j being the rotational quantum number. Different resonance structures in the cross sections are attributed to the differences in the anisotropy and the long-range van der Waals well depths of the two PESs. These differences affect rate coefficients at low temperatures and give an indication of the uncertainty of the results. Significant discrepancies are found between the current rate coefficients and previous results computed using earlier potentials, while the current results satisfy expected propensity rules. Astrophysical applications to modeling far infrared and submillimeter observations are briefly discussed.
Previous calculations of low-temperature cross sections for collisions between spin-polarized met... more Previous calculations of low-temperature cross sections for collisions between spin-polarized metastable hydrogen atoms are improved to include nonadiabatic radial and angular coupling at large interatomic separations. The electrostatic dipole-quadrupole interaction produces nonadiabatic radial coupling between ͑2s , 2p͒ and ͑2p , 2p͒ states, while the Coriolis interaction produces nonadiabatic angular coupling. Both of these long-range contributions are handled in a space-fixed atomic gauge that is particularly convenient for a spinpolarized system. The improved theoretical results are compared with an existing experiment.
The translational and internal level cooling of atoms and molecules in ultracold gases results fr... more The translational and internal level cooling of atoms and molecules in ultracold gases results from a combination of elastic and inelastic collisional processes. While elastic collisions lead to rapid thermalization, exoergic inelastic collisions may lead to heating and trap loss. To date, most collisional studies have targeted low-lying levels of diatomic molecules. Here we investigate inelastic quenching and elastic scattering of rotationally excited linear (H 2 , HD, CO, O 2 , and CO 2) and nonlinear (H 2 O and NH 3) molecules in ultracold collisions with He and report the corresponding complex scattering lengths. It has been found that the ratio of the imaginary component β to the real component α of the scattering length generally increases with decreasing rotational constant for linear molecules. With the exception of CO, β becomes significantly smaller than α as the energy gap for rotational transitions increases. In all cases, β decreases with rotational energy gap for relatively large rotational excitation, allowing for convenient fits to an exponential energy gap formula. Excited rotational levels of H 2 and HD appear to be collisionally stable due to the very low values of β/α. Rotationally excited H 2 O also appears to be a viable candidate for He buffer gas cooling due to relatively small values of β.
Collisions between noble-gas atoms and hydrogen molecules are investigated theoretically by solvi... more Collisions between noble-gas atoms and hydrogen molecules are investigated theoretically by solving the time-independent Schrödinger equation. Various initial states of the molecule are considered and the calculations are performed for each system over a large range of collision energies. Cross sections for quenching of rovibrationally excited states of H 2 are reported for Ar and Kr colliders and comparisons are made with previous calculations involving He. For both Ar and Kr colliders, the effect of vibrational excitation is found to be more pronounced for ortho-H 2. The T → 0 limit of the total quenching rate coefficient, which is presented here as the imaginary part of a complex scattering length, is found to increase by about 7 orders of magnitude as the vibrational quantum number of ortho-H 2 is increased from 1 to 10. Trends in the energy dependence for the heavier systems are very similar, including resonance behavior, which suggest that the dynamics of heavy noble-gas H 2 systems are less sensitive to the fine details of the potential.
between argon atoms and hydrogen molecules are investigated at very low temperatures. Quantum-mec... more between argon atoms and hydrogen molecules are investigated at very low temperatures. Quantum-mechanical ¤ calculations are performed using two different potential-energy surfaces. Rate coefficients ¥ for all possible combinations of initial vibrational and rotational level have been computed in the limit of ¦ zero temperature. Resonant and quasiresonant behavior is found using both potential-energy surfaces. The results § are interpreted and estimates are made of the reliability of the calculations.
Collisional ¤ relaxation of highly rotating hydrogen molecules is investigated as a function of e... more Collisional ¤ relaxation of highly rotating hydrogen molecules is investigated as a function of energy. Calculations ¥ demonstrate that inelastic collisions are dramatically suppressed for specific rotational levels of the molecule as the energy is lowered due to the closing of quasiresonant rotation-vibration channels. It is predicted ¦ that a 3 § He buffer gas may be used to load these highly excited molecules into a trap without a significant loss ¥ of population. It is further predicted that evaporative cooling may be used to cool the ''super rotors'' to even lower temperatures.
Rotational and vibrational distributions of zero-temperature collisional rate coefficients for at... more Rotational and vibrational distributions of zero-temperature collisional rate coefficients for atom-diatom scattering are used together with effective range theory to obtain lifetimes for predissociation. High-order indirect potential coupling in the quantum-mechanical calculation is interpreted using a simple classical picture that describes the quasiresonant dynamics of atom-diatom collisions by the conservation of classical action. The importance of closed channel thresholds in determining the structure of the distributions and the balance between momentum gap and near-resonant effects is discussed.
Building on recent advances in ultrafast lasers and methods to slow molecules, a novel experiment... more Building on recent advances in ultrafast lasers and methods to slow molecules, a novel experiment is proposed to produce translationally cold CO2 super rotors (j ∼ 200) by combining an optical centrifuge with helium buffer-gas cooling. Quantum mechanical calculations of the complex scattering length for He-CO2 collisions demonstrate that the efficiency of rotational quenching decreases rapidly with increasing rotational excitation j in the ultracold regime. Extrapolating to helium cryogenic temperatures, rotational quenching is predicted to remain inefficient up to ∼1 K, allowing for the possibility to create a beam of translationally cold, rotationally hot molecules.
Cross sections for He+ H 2 collisions are reported for rovibrational states near dissociation at ... more Cross sections for He+ H 2 collisions are reported for rovibrational states near dissociation at translational energies less than 1000 cm −1. In contrast to our previously reported cross sections for lower-lying initial rotational states, the excited rotational states near dissociation give rise to shape resonances for energies between 0.001 and 1 cm −1. The emergence of these resonances with increasing rotational level is opposite to the trend found for He+ CO where the shape resonance strength decreases with rotational level for low-lying states. Quasiresonant energy transfer and low energy excitation thresholds are also discussed and it is found that there are 11 rovibrationally excited states that are stable against collision at ultracold temperatures.
We show that weakly bound He-containing van der Waals molecules can be produced and magnetically ... more We show that weakly bound He-containing van der Waals molecules can be produced and magnetically trapped in buffer-gas cooling experiments, and provide a general model for the formation and dynamics of these molecules. Our analysis shows that, at typical experimental parameters, thermodynamics favors the formation of van der Waals complexes composed of a helium atom bound to most open-shell atoms and molecules, and that complex formation occurs quickly enough to ensure chemical equilibrium. For molecular pairs composed of a He atom and an S-state atom, the molecular spin is stable during formation, dissociation, and collisions, and thus these molecules can be magnetically trapped. Collisional spin relaxation is too slow to affect trap lifetimes. However, 3 He-containing complexes can change spin due to adiabatic crossings between trapped and untrapped Zeeman states, mediated by the anisotropic hyperfine interaction, causing trap loss. We provide a detailed model for Ag 3 He molecules, using ab initio calculation of Ag-He interaction potentials and spin interactions, quantum scattering theory, and direct Monte Carlo simulations to describe formation and spin relaxation in this system. The calculated rate of spin-change agrees quantitatively with experimental observations, providing indirect evidence for molecular formation in buffer-gas-cooled magnetic traps. Finally, we discuss the possibilities for spectroscopic detection of these complexes, including a calculation of expected spectra for Ag 3 He, and report on our spectroscopic search for Ag 3 He, which produced a null result. The ability to cool and trap molecules holds great promise for new discoveries in chemistry and physics. 1-4 Cooled and trapped molecules yield long interaction times, allowing for precision measurements of molecular structure and interactions, tests of fundamental physics, 5,6 and applications in quantum information science. 7 Chemistry shows fundamentally different behavior for cold molecules, 8,9 and can be highly controlled based on the kinetic energy, external fields, 10 and quantum states 11 of the reactants.
Quantum mechanical calculations of collisional quenching cross sections and rate coefficients for... more Quantum mechanical calculations of collisional quenching cross sections and rate coefficients for various internally excited atoms and molecules at cold and ultracold temperatures are presented. The efficiencies of relaxation for vibrationally, rotationally, and electronically excited states are given and in each case the dominant decay mechanisms are discussed. £ R¥ prevents the atoms from reaching short distances where autoionization can
We examine the effect of theoretically varying the collision-system reduced mass in collisions of... more We examine the effect of theoretically varying the collision-system reduced mass in collisions of He with vibrationally excited molecular hydrogen and observe zero-energy resonances for select atomic "hydrogen" masses less than 1 u or a "helium" mass of 1.95 u. Complex scattering lengths, state-to-state vibrational quenching cross sections, and a low-energy elastic scattering resonance are all studied as a function of collision-system reduced mass. Experimental observations of these phenomena in the cold and ultracold regimes for collisions of 3 He and 4 He with H 2 , HD, HT, and DT should be feasible in the near future.
Accurate rate coefficients for molecular vibrational transitions due to collisions with H2, criti... more Accurate rate coefficients for molecular vibrational transitions due to collisions with H2, critical for interpreting infrared astronomical observations, are lacking for most molecules. Quantum calculations are the primary source of such data, but reliable values that consider all internal degrees of freedom of the collision complex have only been reported for H2-H2 due to the difficulty of the computations. Here we present essentially exact, full-dimensional dynamics computations for rovibrational quenching of CO due to H2 impact. Using a high-level six-dimensional potential surface, time-independent scattering calculations, within a full angular momentum coupling formulation, were performed for the de-excitation of vibrationally excited CO. Agreement with experimentally determined results confirms the accuracy of the potential and scattering computations, representing the largest of such calculations performed to date. This investigation advances computational quantum dynamical st...
Along with H 2 , HD has been found to play an important role in the cooling of the primordial gas... more Along with H 2 , HD has been found to play an important role in the cooling of the primordial gas for the formation of the first stars and galaxies. It has also been observed in a variety of cool molecular astrophysical environments. The rate of cooling by HD molecules requires knowledge of collisional rate coefficients with the primary impactors, H, He, and H 2. To improve knowledge of the collisional properties of HD, we present rate coefficients for the He-HD collision system over a range of collision energies from 10 −5 to 5 × 10 3 cm −1. Fully quantum mechanical scattering calculations were performed for initial HD rovibrational states of j = 0 and 1 for v = 0-17 which utilized accurate diatom rovibrational wave functions. Rate coefficients of all Δv = 0, −1, and −2 transitions are reported. Significant discrepancies with previous calculations, which adopted a small basis and harmonic HD wave functions for excited vibrational levels, were found for the highest previously considered vibrational state of v = 3. Applications of the He-HD rate coefficients in various astrophysical environments are briefly discussed.
New quantum scattering calculations for rotational deexcitation transitions of CO induced by H co... more New quantum scattering calculations for rotational deexcitation transitions of CO induced by H collisions using two CO-H potential energy surfaces (PESs) from Shepler et al. (2007) are reported. State-to-state rate coefficients are computed for temperatures ranging from 1 to 3000 K for CO(v = 0, j) deexcitation from j = 1 − 5 to all lower j ′ levels, with j being the rotational quantum number. Different resonance structures in the cross sections are attributed to the differences in the anisotropy and the long-range van der Waals well depths of the two PESs. These differences affect rate coefficients at low temperatures and give an indication of the uncertainty of the results. Significant discrepancies are found between the current rate coefficients and previous results computed using earlier potentials, while the current results satisfy expected propensity rules. Astrophysical applications to modeling far infrared and submillimeter observations are briefly discussed.
Previous calculations of low-temperature cross sections for collisions between spin-polarized met... more Previous calculations of low-temperature cross sections for collisions between spin-polarized metastable hydrogen atoms are improved to include nonadiabatic radial and angular coupling at large interatomic separations. The electrostatic dipole-quadrupole interaction produces nonadiabatic radial coupling between ͑2s , 2p͒ and ͑2p , 2p͒ states, while the Coriolis interaction produces nonadiabatic angular coupling. Both of these long-range contributions are handled in a space-fixed atomic gauge that is particularly convenient for a spinpolarized system. The improved theoretical results are compared with an existing experiment.
The translational and internal level cooling of atoms and molecules in ultracold gases results fr... more The translational and internal level cooling of atoms and molecules in ultracold gases results from a combination of elastic and inelastic collisional processes. While elastic collisions lead to rapid thermalization, exoergic inelastic collisions may lead to heating and trap loss. To date, most collisional studies have targeted low-lying levels of diatomic molecules. Here we investigate inelastic quenching and elastic scattering of rotationally excited linear (H 2 , HD, CO, O 2 , and CO 2) and nonlinear (H 2 O and NH 3) molecules in ultracold collisions with He and report the corresponding complex scattering lengths. It has been found that the ratio of the imaginary component β to the real component α of the scattering length generally increases with decreasing rotational constant for linear molecules. With the exception of CO, β becomes significantly smaller than α as the energy gap for rotational transitions increases. In all cases, β decreases with rotational energy gap for relatively large rotational excitation, allowing for convenient fits to an exponential energy gap formula. Excited rotational levels of H 2 and HD appear to be collisionally stable due to the very low values of β/α. Rotationally excited H 2 O also appears to be a viable candidate for He buffer gas cooling due to relatively small values of β.
Collisions between noble-gas atoms and hydrogen molecules are investigated theoretically by solvi... more Collisions between noble-gas atoms and hydrogen molecules are investigated theoretically by solving the time-independent Schrödinger equation. Various initial states of the molecule are considered and the calculations are performed for each system over a large range of collision energies. Cross sections for quenching of rovibrationally excited states of H 2 are reported for Ar and Kr colliders and comparisons are made with previous calculations involving He. For both Ar and Kr colliders, the effect of vibrational excitation is found to be more pronounced for ortho-H 2. The T → 0 limit of the total quenching rate coefficient, which is presented here as the imaginary part of a complex scattering length, is found to increase by about 7 orders of magnitude as the vibrational quantum number of ortho-H 2 is increased from 1 to 10. Trends in the energy dependence for the heavier systems are very similar, including resonance behavior, which suggest that the dynamics of heavy noble-gas H 2 systems are less sensitive to the fine details of the potential.
between argon atoms and hydrogen molecules are investigated at very low temperatures. Quantum-mec... more between argon atoms and hydrogen molecules are investigated at very low temperatures. Quantum-mechanical ¤ calculations are performed using two different potential-energy surfaces. Rate coefficients ¥ for all possible combinations of initial vibrational and rotational level have been computed in the limit of ¦ zero temperature. Resonant and quasiresonant behavior is found using both potential-energy surfaces. The results § are interpreted and estimates are made of the reliability of the calculations.
Collisional ¤ relaxation of highly rotating hydrogen molecules is investigated as a function of e... more Collisional ¤ relaxation of highly rotating hydrogen molecules is investigated as a function of energy. Calculations ¥ demonstrate that inelastic collisions are dramatically suppressed for specific rotational levels of the molecule as the energy is lowered due to the closing of quasiresonant rotation-vibration channels. It is predicted ¦ that a 3 § He buffer gas may be used to load these highly excited molecules into a trap without a significant loss ¥ of population. It is further predicted that evaporative cooling may be used to cool the ''super rotors'' to even lower temperatures.
Rotational and vibrational distributions of zero-temperature collisional rate coefficients for at... more Rotational and vibrational distributions of zero-temperature collisional rate coefficients for atom-diatom scattering are used together with effective range theory to obtain lifetimes for predissociation. High-order indirect potential coupling in the quantum-mechanical calculation is interpreted using a simple classical picture that describes the quasiresonant dynamics of atom-diatom collisions by the conservation of classical action. The importance of closed channel thresholds in determining the structure of the distributions and the balance between momentum gap and near-resonant effects is discussed.
Building on recent advances in ultrafast lasers and methods to slow molecules, a novel experiment... more Building on recent advances in ultrafast lasers and methods to slow molecules, a novel experiment is proposed to produce translationally cold CO2 super rotors (j ∼ 200) by combining an optical centrifuge with helium buffer-gas cooling. Quantum mechanical calculations of the complex scattering length for He-CO2 collisions demonstrate that the efficiency of rotational quenching decreases rapidly with increasing rotational excitation j in the ultracold regime. Extrapolating to helium cryogenic temperatures, rotational quenching is predicted to remain inefficient up to ∼1 K, allowing for the possibility to create a beam of translationally cold, rotationally hot molecules.
Cross sections for He+ H 2 collisions are reported for rovibrational states near dissociation at ... more Cross sections for He+ H 2 collisions are reported for rovibrational states near dissociation at translational energies less than 1000 cm −1. In contrast to our previously reported cross sections for lower-lying initial rotational states, the excited rotational states near dissociation give rise to shape resonances for energies between 0.001 and 1 cm −1. The emergence of these resonances with increasing rotational level is opposite to the trend found for He+ CO where the shape resonance strength decreases with rotational level for low-lying states. Quasiresonant energy transfer and low energy excitation thresholds are also discussed and it is found that there are 11 rovibrationally excited states that are stable against collision at ultracold temperatures.
We show that weakly bound He-containing van der Waals molecules can be produced and magnetically ... more We show that weakly bound He-containing van der Waals molecules can be produced and magnetically trapped in buffer-gas cooling experiments, and provide a general model for the formation and dynamics of these molecules. Our analysis shows that, at typical experimental parameters, thermodynamics favors the formation of van der Waals complexes composed of a helium atom bound to most open-shell atoms and molecules, and that complex formation occurs quickly enough to ensure chemical equilibrium. For molecular pairs composed of a He atom and an S-state atom, the molecular spin is stable during formation, dissociation, and collisions, and thus these molecules can be magnetically trapped. Collisional spin relaxation is too slow to affect trap lifetimes. However, 3 He-containing complexes can change spin due to adiabatic crossings between trapped and untrapped Zeeman states, mediated by the anisotropic hyperfine interaction, causing trap loss. We provide a detailed model for Ag 3 He molecules, using ab initio calculation of Ag-He interaction potentials and spin interactions, quantum scattering theory, and direct Monte Carlo simulations to describe formation and spin relaxation in this system. The calculated rate of spin-change agrees quantitatively with experimental observations, providing indirect evidence for molecular formation in buffer-gas-cooled magnetic traps. Finally, we discuss the possibilities for spectroscopic detection of these complexes, including a calculation of expected spectra for Ag 3 He, and report on our spectroscopic search for Ag 3 He, which produced a null result. The ability to cool and trap molecules holds great promise for new discoveries in chemistry and physics. 1-4 Cooled and trapped molecules yield long interaction times, allowing for precision measurements of molecular structure and interactions, tests of fundamental physics, 5,6 and applications in quantum information science. 7 Chemistry shows fundamentally different behavior for cold molecules, 8,9 and can be highly controlled based on the kinetic energy, external fields, 10 and quantum states 11 of the reactants.
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