Rotational Relaxation Cross Sections Research Articles

Total angular momentum representation for state-to-state quantum scattering of cold molecules in a magnetic field.

We show that the integral cross sections for state-to-state quantum scattering of cold molecules in a magnetic field can be efficiently computed using the total angular momentum representation despite the presence of unphysical Zeeman states in the eigenspectrum of the asymptotic Hamiltonian. We demonstrate that the unphysical states arise due to the incompleteness of the space-fixed total angular momentum basis caused by using a fixed cutoff value Jmax for the total angular momentum of the collision complex J. As a result, certain orbital angular momentum (l) basis states lack the full range of J values required by the angular momentum addition rules, resulting in the appearance of unphysical states. We find that by augmenting the basis with a full range of J-states for every l, it is possible to completely eliminate the unphysical states from quantum scattering calculations on molecular collisions in external magnetic fields. To illustrate the procedure, we use the augmented basis sets to calculate the state-to-state cross sections for rotational and spin relaxation in cold collisions of 40CaH(X2Σ+, v = 0, N = 1, MN = 1, MS = 1/2) molecules with 4He atoms in a magnetic field. We find excellent agreement with benchmark calculations, validating our proposed procedure. We find that N-conserving spin relaxation from the highest-energy to the lowest-energy Zeeman state of the N = 1 manifold, |1112〉→|1-1-12〉 is nearly completely suppressed due to the lack of spin-rotation coupling between the fully spin-stretched Zeeman states. Our results demonstrate the possibility of rigorous, computationally efficient, and unphysical state-free quantum calculations on cold molecular collisions and on near-threshold energy levels of strongly anisotropic atom-molecule collision complexes in an external magnetic field.

He–ThO(1Σ+) interactions at low temperatures: Elastic and inelastic collisions, transport properties, and complex formation in cold 4He gas

We present an ab initio study of cold (4)He + ThO((1)Σ(+)) collisions based on an accurate potential energy surface (PES) evaluated by the coupled cluster method with single, double, and noniterative triple excitations using an extended basis set augmented by bond functions. Variational calculations of rovibrational energy levels show that the (4)He-ThO van der Waals complex has a binding energy of 10.9 cm(-1) in its ground J = 0 rotational state. The calculated energy levels are used to obtain the temperature dependence of the chemical equilibrium constant for the formation of the He-ThO complex. We find that complex formation is thermodynamically favored at temperatures below 1 K and predict the maximum abundance of free ground-state ThO(v = 0, j = 0) molecules between 2 and 3 K. The calculated cross sections for momentum transfer in elastic He + ThO collisions display a rich resonance structure below 5 cm(-1) and decline monotonically above this collision energy. The cross sections for rotational relaxation accompanied by momentum transfer decline abruptly to zero at low collision energies (<0.1 cm(-1)). We find that Stark relaxation in He + ThO collisions can be enhanced by applying an external dc electric field of less than 100 kV∕cm. Finally, we present calculations of thermally averaged diffusion cross sections for ThO in He gas, and find these to be insensitive to small variations of the PES at temperatures above 1 K.

Accurate three-dimensional intermolecular potential of the He–MgH complex

An accurate three-dimensional interaction potential energy surface of the He–MgH(2Σ+) van der Waals complex is developed using the partially spin-restricted open-shell single and double excitation coupled cluster method with perturbative triples [RCCSD(T)] level of theory for a large number of geometries. The calculated single point energies at each of five rMgH values are first fitted by an analytic two-dimensional potential model. The five model potentials are then used to construct the three-dimensional potential energy surface by interpolating along (r−re) by a four-order polynomial. Based on the three-dimensional potential energy surface, the vibrational average potential is obtained. Bound state energy levels of He–MgH complex and cross sections for rotational relaxation are calculated within the spin-free approximation.

Collisions ofNH(Σ3−)with Rb and Cs at ultralow energies: A quantum study of rotational cooling efficiency

Using ab initio calculations for the lowest, spin-stretched, quartet potential energy surfaces for Rb and Cs neutral atoms interacting with the $\text{NH}({^{3}\ensuremath{\Sigma}}^{\ensuremath{-}})$ polar target, the cold collision quantum dynamics is analyzed at ultralow energies to examine possible propensity rules existing for the relaxation of either spin or rotational target states (or both) via sympathetic cooling induced by the partner atoms. The specific coupling of Hund's case (b) is adopted for the dynamical treatment of spin and rotational angular momenta and the coupled channel approach is employed to solve the scattering equations. Both rotational and/or spin relaxation cross sections are obtained down to ${10}^{\ensuremath{-}6}\text{ }{\text{cm}}^{\ensuremath{-}1}$ of energy and corresponding cooling rates are analyzed and compared between the two systems.

Low-Temperature Rotational Relaxation of CO in Self-Collisions and in Collisions with Ne and He

The low-temperature rotational relaxation of CO in self-collisions and in collisions with the rare-gas atoms Ne and He has been investigated in supersonic expansions with a combination of resonance-enhanced multiphoton ionization (REMPI) spectroscopy and time-of-flight techniques. For the REMPI detection of CO, a novel 2 + 1' scheme has been employed through the A(1)Pi state of CO. From the measured data, average cross sections for rotational relaxation have been derived as a function of temperature in the range 5-100 K. For CO-Ne and CO-He, the relaxation cross sections grow, respectively, from values of approximately 20 and 7 A(2) at 100 K to values of approximately 65-70 and approximately 20 A(2) in the 5-20 K temperature range. The cross section for the relaxation of CO-CO grows from a value close to 40 A(2) at 100 K to a maximum of 60 A(2) at 20 K and then decreases again to 40 A(2) at 5 K. These results are qualitatively similar to those obtained previously with the same technique for N(2)-N(2), N(2)-Ne, and N(2)-He collisions, although in the low-temperature range (T < 20 K) the CO relaxation cross sections are significantly larger than those for N(2). Some discrepancies have been found between the present relaxation cross sections for CO-CO and CO-He and the values derived from electron-induced fluorescence experiments.

Determination of multiple excitation parameters by photoacoustic methods in gas mixtures

Using photoacoustic measurements, the relaxation processes have been studied in various gas mixtures. The analysis of rotational parameters shows strong buffer gas pressure dependence and different pressure regimes can be distinguished. In contrast, for vibrational to translational relaxation in the same gas mixture, pressure regimes cannot be distinguished. It was shown that the PA method can be used in investigation of relaxation parameters for detailed description of multiphoton processes in gas mixtures, especially for evaluation of bulk rotational relaxation cross-sections and times.

Peculiarities of atom–quasidiatom collision complex formation: classical trajectory study

General peculiarities in the formation of quasibound complexes (QC) in collisions of an atom with a rigid diatomic or linear polyatomic molecule are studied using the method of classical trajectories. The CO2–Ar system is taken as an example. Statistical distributions of parameters characterizing either the formation of QC or those appropriate to rotational relaxation cross-sections are simulated and analyzed. Various factors are examined as far as their role in the formation of the QC is concerned: (1) the complexity of a trajectory approach (exact classical, planar, coplanar); (2) the selection of intermolecular potential energy surface (ab initio Parker–Snow–Pack potential; empirical Berreby–Dayan potential); (3) the departure of the initial CO2 rotational distribution from equilibrium. The cross-sections and bimolecular thermal rates for QC formation are obtained using the modified Sorbie–Murrell model. The use of derived analytical expressions makes the computations of QC fractions in CO2–Ar collisions easier both in equilibrium and in rotational non-equilibrium conditions.

Gas phase molecular relaxation at very low temperatures. A comparative study of N 2 and its mixtures with He and Ne

The low temperature (<100 K) relaxation of N 2 in self-collisions and in collisions with He and Ne has been experimentally studied with resonance-enhanced-multiphoton-ionization and time-of-flight techniques. The following average values of the rotational relaxation cross sections, σ r, have been derived from the measurements: σ r N 2–N 2 ( T=5–60 K)≈35 Å 2; σ r N 2–He ( T=5–80 K) ≈15 Å 2 and σ r N 2–Ne ( T=5–60 K)≈40 Å 2. The cross section trend σ r N 2–N 2 ≈ σ r N 2–Ne > σ r N 2–He reported in the literature for T=300 K is confirmed below 100 K, but the absolute values are larger in the low temperature range.

Rotational relaxation rates in CO-He mixtures

The rotational level populations of CO molecules were measured in CO(<10%) + He free jets by electron beam fluorescence (in a stationary jet) and resonantly enhanced multiphoton ionization (in a pulsed jet). The measured evolution of the non-equilibrium rotational energy was used to derive the rotational relaxation cross-sections in the temperature range from 6 K to 140 K. To compare and analyse on a common basis all available experimental data (ours and others) on rotational relaxation of CO in He, the infinite order sudden approximation was explored. The following quantities were investigated: integral rotationally inelastic cross-sections, state-to-state rate coefficients, rotational relaxation times, line broadening coefficients, and non-equilibrium rotational energy distributions in a free jet.

State-to-state rate coefficients for rotational relaxation of CO in Ar

The rotational level populations of CO molecules were measured in CO (&amp;lt;10%)+Ar free jets by electron beam fluorescence (in a stationary jet) and resonantly enhanced multiphoton ionization (in a pulsed jet). The measured evolution of the nonequilibrium rotational energy was used to derive the rotational relaxation cross sections in the temperature range from 7 to 150 K. Using the pressure-broadened linewidth data the state-to-state rotational relaxation rate coefficients were found using the most popular fitting law forms: The modified exponential gap, the statistical polynomial-exponential gap, and the energy corrected sudden approximation. The fitted rates were compared with the experimental and theoretical data presently available in the literature. They were checked also by consideration of the rotational kinetics in free jets and by comparison between the computed and experimental rotational level populations both in near and far regions of a flow.

Experimental study of rotational relaxation processes by pulsed photoacoustic technique

The IR pulsed photoacoustic method was used to investigate rotational relaxation processes in MPA. We have examined the bulk rotational relaxation times and the bulk rotational relaxation cross sections , related to R-R and R-T relaxation mechanisms. The saturation intensities for gas molecules have been measured in the gas mixtures with (buffer) molecules, at constant gas pressure (0.47 mbar) and variable gas pressure (1-140 mbar), using the 10P(16) laser line in the fluences range 0.1-0.7 J . It has been found that for proper investigation of the rotational relaxation processes, the buffer gas pressure range must be divided into two parts: the low pressure range (0-20 mbar) and the high pressure range (20-140 mbar), according to the behaviour of the saturation intensities versus buffer gas pressure. Consequently, two different sets of values for rotational relaxation parameters are obtained. The found step-function behaviour for shows that the rotational hole-filling effect during MPA only dominates at low buffer gas pressure ( mbar). At higher buffer gas pressures (between 20-140 mbar) collisional deactivation takes place. We also derive the enhanced absorption cross sections for absorbing gas molecules from the measured saturation intensities data (at zero buffer gas pressure) confirming the expectation that the enhanced absorbing cross sections are not only a function of laser fluence and buffer gas pressure, but are very strongly dependent on laser beam parameters, too.

Classical trajectories on simple model potentials for N2–Kr: Comparison with relaxation and other data

We compare the ability of six N2–Kr potential energy surfaces to predict experimental interaction second virial coefficients, diffusion coefficients, mixture viscosity, thermal conductivity, and nuclear magnetic resonance (NMR) rotational relaxation cross sections. These include a previously published empirical surface derived from fits to molecular beam experiments and various model potentials of the Tang and Toennies (TT) type. The TT type potentials differ in the set of dispersion coefficients employed. Two sets are obtained from published ab initio calculations, another from combining rules and one from empirical considerations. The repulsive parameters have been obtained from published results of a charge overlap combining rule. A variation of the TT model suggested by Aziz is also used to further investigate the effect of the repulsive wall anisotropy on the rotational relaxation cross sections. Forty-five effective cross sections that determine the bulk transport and relaxation phenomena have been calculated by classical trajectories for temperatures ranging from 100 to 800 K. The sensitivity of the NMR-derived cross sections to the various characteristics of the anisotropy of the potential (such as the anisotropy in the well depth, in the high repulsive wall, in the low repulsive wall, and at V=0) are examined. The empirical anisotropic LJ(12,6) surface of Rotzoll provides the best agreement with the diffusion, viscosity, thermal conductivity, and NMR relaxation experimental results.

Photoacoustic study of collisional effects on rotational relaxation processes induced by infrared multiphoton absorption

The novel experimental approach is applied to investigate the cross sections for rotational relaxation σ rot.-rel. in the SF 6 -Ar mixtures irradiated by pulsed CO 2 laser line. The applied method is the pulsed photoacoustic technique, and it is based on proposal for σ rot.-rel. determination by transmission spectroscopy technique. The collisional effects have been investigated for the 0.1-0.8 J/cm 2 laser fluence range. Also, the collisional effects on rotational and translational temperature (T R ) for SF 6 -Ar mixtures have been calculated

Comparison and analysis of rotationally inelastic collision models describing the Q-branch collapse at high density

The fitting laws usually employed to model the relaxation matrix and, therefore, to account for the collisional narrowing of the Q-branch have been tested against the density dependence of the isotropic Raman band width (Λ) for nitrogen. The behavior of Λ has been theoretically studied in a wide density range: from 10 to 1072 amagat at 295 K in gas and liquid phases. The independent binary collision (IBC) approach has been applied to reproduce the density dependence of Λ in this domain. Quite surprisingly, the IBC expression reproduces the density variation of Λ rather well, despite the limited validity of such an approach. Rotational energy relaxation cross sections (σ′ E and σ E) are also employed for comparison. Relaxation models that do not provide the experimental value of σ E cannot be used to describe the Q-branch collapse in the limit of extreme narrowing. We find that at the stage of narrowing the reconstructed dephasing rate is essentially dependent on the accepted model of rotational relaxation.

Cross sections for rotational relaxation in alkali dimer molecular beams

A sudden-freeze model for the extraction of effective rotational relaxation cross sections from nozzle beam expansions is refined by introducing a temperature-dependent cross section σ rot ( T). Since (i)σ rot ∝ exp ( − Δ E j ), (ii) the rotational energy level spacing Δ E J ∝ J and (iii) J* ∝ T 1 2 it is assumed that σ rot ( T) ∝ exp [− α ( T/Θ r) 1 2 ]. Here, J* stands for the most probable value of J and Θ r= B/k, where B is the rotational constant. The value of α was determined from a semi-logarithmic plot of directly measured values of σ rot ( J) versus ( T/Θ r) 1 2 . The resulting sudden-freeze-model expression for σ rot ( T rot) was used to deduce values of σ rot for Li/Li 2 and Na/Na 2 from measurements in nozzle-beam expansions. A combined plot of the directly measured values of σ rot ( J) and the deduced values of σ rot ( T rot) exhibits a common semi-logarithmic dependence on J*. Rotational relaxation cross sections deduced from quasi-classical trajectory calculations for Na/Li 2 ( J = 5, J= 20) collisions at E coll = 100 meV agree quantitatively with the predicted values.

Chattering collisions and their effects on gas phase rotational energy relaxation cross sections

Rotational energy relaxation cross sections, σR , for nitrogen in dilute atomic gases (He, Ne, Ar, and Xe) are calculated by classical trajectory simulations for a variety of simple potentials and from the Boltzmann equation for hard convex bodies in the single impulse collision approximation. The single impulse approximation, which ignores multiple impulse (chattering) collisions, is reasonably adequate to describe linear and angular momentum relaxation, but not rotational energy relaxation. For the light noble gases, the hard body derived results together with the small chattering corrections suffice to fit σR . It is also the case that chattering collisions markedly decrease σR from the single impulse approximation value for Xe–N2 in the hard-body model. However, the value of σR experimentally measured and calculated by Kistemaker and de Vries using a soft potential is considerably less than that obtained from hard-body models including chattering. Addition of a square well attractive potential of the appropriate shape to the hard core potential leads to the desired decrease in σR with well depth in accord with both the trajectory calculations and experiments of Kistemaker and de Vries. The reasons are analyzed.

Cross sections for translational and rotational relaxation in Li/Li 2 and Na/Na 2 molecular beams

Translational and rotational relaxation processes in alkali monomer-dimer free-jet expansions are investigated both theoretically and experimentally. Based on a sudden-freeze model, simple formulas are derived for the extraction of effective translational relaxation cross sections from terminal Mach numbers and effective rotational relaxation cross sections from measured terminal rotational populations. These formulas are verified in a state-resolved laser-molecular beam study. The magnitude of the rotational cross section is found to be strongly state dependent and to be essentially the same for Na 2 and Li 2. The terminal dimer velocity exceeds that for the monomers in Na/Na 2 but not in Li/Li 2. An earlier sudden-freeze analysis for rare gases is used to correlate terminal dimer mole fractions measured for Li/Li 2 beams with dimensionless parameters. From this correlation and applying energy conservation to the measured terminal velocities we found that at least 60% of the binding energy released in dimer formation in Li/Li 2 beams resides terminally in internal degrees of freedom.

Rotational energy transfer in D2CO (v4=1): IR–UV double resonance studies of J-changing collisions

The technique of time-resolved infrared–ultraviolet double resonance (IRUVDR) spectroscopy is used to characterize the rate and mechanism of state-to-state rotational energy transfer (RET) in D2CO/D2CO collisions. The investigations employ CO2-laser irradiation to prepare a D2CO molecule in the v4=1, (J,Ka) =(18,11) rovibrational level of its X̃ 1A1 electronic ground state. Vapor-phase collisions with other D2CO (v=0) molecules then induce RET, with IRUVDR-monitored quantum-number changes ΔJ for the state-selected molecule ranging between +3 and −7. Kinetic modeling of the resulting experimental data shows that the inelastic cross sections for such J-changing rotational relaxation can be described adequately by simple scaling laws based on the rotational energy change ‖ΔE‖ for the state-selected molecule, with a power-gap fitting law proving marginally superior to an exponential-gap fitting law. The range of ‖ΔJ‖ monitored in these experiments is sufficiently extensive to discredit a simple propensity-rule fitting law, comprising consecutive collision-induced processes with individual changes ‖ΔJ‖ confined to values of 1 or 2. The microscopic rate constants derived reflect the dominance of ΔJ=±1 contributions for J-changing RET in D2CO/D2CO collisions, owing to long-range dipole/dipole interactions. These results elucidate RET in collisions between a pair of dipolar polyatomic (D2CO) molecules at a level of detail usually confined to studies of dipolar diatomic molecules, such as HF. Less detailed IRUVDR results, for RET in self-collisions of HDCO and for D2CO colliding with a variety of foreign-gas molecules, are also presented.

Classical trajectory calculations for anisotropy-dependent cross sections for He-N2mixtures

The classical expressions for kinetic theory cross sections which are related to the Senftleben-Beenakker effect on viscosity, diffusion, conductivity and thermal diffusion are evaluated using the HFD1 surface (R. Fuchs et al. (1984)) in the temperature range 77.3-1100K. The depolarised Rayleigh scattering and rotational-relaxation cross sections are also obtained. Comparisons with experiment show that the authors' values for these cross sections are 10-80% larger than the measurements. These consistent discrepancies suggest that this potential surface is too anisotropic.

Quantum calculations of rotational and NMR relaxation, depolarized Rayleigh and rotational Raman line shapes for H 2(HD)−He mixtures

The two ab initio vibrotor potentials of H 2−He previously published by Meyer, Hariharan, and Kutzelnigg have been composed in one potential grid. After using this potential in close coupled scattering calculations we have subsequently obtained rotational relaxation cross sections for para- and ortho-H 2, NMR relaxation times for ortho-H 2, depolarized Rayleigh line broadening cross sections for para-, ortho-, and normal-H 2, and rotational Raman line width and shift cross sections for S 0(0), S 0(2) transitions, at temperatures between 20 and 450 K. The agreement with previous and more recent measurements has been found completely satisfying, with the exception of the rotational relaxation cross sections of para-H 2. Throughout the paper previous results derived from the multiple property fit of Shafer and Gordon have been included for comparison. The new ab initio potential is obviously better, except for the rotational relaxation cross sections. The interaction potential of HD−He transformed from the new H 2−He potential is also presented in this paper. It has been used recently in a very successful application of the Waldmann-Snider kinetic theory describing transport, relaxation, and reorientation phenomena in magnetic fields. Therefore, only the rotational relaxation cross sections, converged up to about 400 K, have been presented in this paper.