Close-coupling calculations of polarization cross sections for (Ar,LiF)

To assist the interpretation of polarized rotational scattering experiments from states (j, m) to (j, m'), differential and total cross sections obtained from close-coupling calculations are given for m values corresponding to j? 3 in collisions between LiF and Ar at 20 cm^?1. The hypothesis ¦m¦-¦m'¦= 0 is proposed for the most likely transition, as an extension of the Δm = 0 rule.     

Classical dependence of polarization on potential energy surface in rotationally inelastic collisions

Quasiclassicol trajectory calculations have been performed for model potential energy surfaces to investigate polarization in (j,m_j) → (j',m_j) integral cross sections For j = 0, it was found that the occurrence of polarization requires an attractive well, and that it be in the collinear configuration Results for j≠ 0 are also presented.     

A study of reorientation effects in CsF—Ar using approximate quantum methods

The EB (exponential Born) and IOS (infinite order sudden) methods are used to calculate a variety of j → j′ and jm → j′m′ integral cross sections and j → j′ differential cross sections for CsF—Ar at E_cm = 87.7 meV. Inelastic rotational cross sections are found to depend primarily on the odd long range parts of the interaction potential. The jm → j′m′ integral cross sections for the quantization axis parallel to the initial relative velocity vector are found to approximately obey the selection rule “Δj + Δm = even” and cross sections for which the orientation of the rotor is left unchanged (i.e. 11 → 11, 11 → 22, and 11 → 33 transitions) are strongly favored over those which are changed for low lying rotational states. Good agreement between the IOS and EB methods is found for most of the scattering quantities calculated.     

Transfer of state multipoles in excited A 1Σ+u7Li2 following rotationally inelastic collisions with He: Experiment and theory

Circularly polarized dye laser radiation is used to prepare rotational levels j = 1 to j = 20 of the A ¹Σ⁺_u excited state of ⁷Li₂ with well defined values of the state multipoles K = 0, 1 and 2. Inelastic collisions with helium atoms populate other j levels and we have measured the circular polarisation ratio of emission, C, from these levels. C is plotted versus final j′ for each value of Δj from +2 to +18 and a family of curves is obtained which may be used as a critical test of current theories. The results are interpreted in terms of cross sections σ^K for transfer of the state multipoles under isotropic collision conditions. The observation of substantial polarisation following inelastic collision indicates that the σ^K are dominated by certain restricted scattering channels. Relative magnitudes of the multipole cross sections are calculated using the “l-dominant”, “restricted Δm_j channels” nd the Born approximation. These cross sections are then used to calculate C.     

Quantal close-coupling calculation of the cross sections for the j 1 m 1 → j 2 m 2 transitions in the 4p 2P and 3d 2D excited states of Ca+ induced by collisions with helium

Cross sections for the j ₁ m ₁ → j ₂ m ₂ transitions in the resonance 4p ²P and metastable 3d ²D states of the singly charged calcium ion induced by collisions with the ground-state He atom have been calculated using the quantal close-coupling method. The calculations are based on the earlier obtained Ca⁺-He pseudopotential SCF potential energy curves. The calculated cross sections are discussed in the energy range from threshold to 1.5 eV. Satisfactory agreement with other theoretical results has been found for the 4p ²P state. However, relatively large discrepancy between theory and available experimental data still exists for both the Ca⁺ states.     

Fully converged sudden rotation total integral cross sections for 4He + H2 (ν = 0, j = 0) → 4He + H2 (ν′ = 1, j′)

Total integral cross sections for ⁴He + H₂ (ν = 0, j = 0) → ⁴He + H₂ (ν′ = 1, j′ = 0, 2) have been calculated in the total energy range 1.2 to 5.5 eV, according to a quantal sudden approximation for the H₂ rotational degrees of freedom and a close coupling expansion of the vibrational degree of freedom. Convergence of the above cross sections is investigated by employing four vibration basis sets in the close coupling calculations, i.e., ν = 0,1, ν = 0,1, 2, ν = 0, 1, 2, 3 and ν = 0, 1, 2, 3, 4. Between 4.2 and 5.5 eV calculations were done with three vibration basis sets; ν = 0.–4, ν = 0–5, and ν = 0–6. It is found that at least four vibrational basis functions are needed to converge (to within 5–10%) these cross sections in the above energy range. Comparison of breathing sphere calculations and summed sudden rotation results shows good agreement for the (weakly anisotropic) Mies-Krauss potential. However, as expected the former results underestimate the vibrational 0 → 1 total integral cross sections.     

Polarization in elastic scattering: close-coupling studies on ArN2

We present the results of close-coupling calculations of m_j-dependent differential and integral cross sections forj₁ = 2 → j₂ = 2 rotationally elastic ArN₂ collisions. Two potential surfaces were used with differing long-and short-range anisotropies. If the anisotropy is long-ranged the scattering of an isotropic beam results in a significant angle dependent polarization of the elastically scattered products. To a certain extent this reflects a selective loss of m_j-state population due to rotationally inelastic transitions. For quantization along the initial relative velocity vector or perpendicular to the scattering plane, the depolarization of an initially m_j-state selected beam vanishes in the forward direction and is significantly less than the statistical limit at all angles, which indicates a dynamical conservation of the direction of the molecular rotational angular momentum. By contrast, in the helicity frame depolarization is much more pronounced. The oscillatory structure present in the rotationally inelastic differential cross section does not appear to be quenched by the interference between various m → m′ transitions.     

Close-coupling elastic and inelastic integral and differential cross sections for Li+ + H2 collisions

The quantum mechanical close-coupling formalism is applied to the study of elastic and rotationally inelastic Li⁺ + H₂ collisions making use of the Kutzelnigg-Staemmler-Hoheisel potential energy surface. Integral and differential cross sections for j = 0 → 0 and j = 0 → 2 are obtained in the collision energy range 0.2 to 0.9 eV and for j = 1 → 1 and j = 1 → 3 at 0.6 eV. A rainbow structure is observed in both the elastic and inelastic angular distributions and a quenching of the fast oscillations is found in the cross sections for j = 1 initially compared to the case j = 0 initially. At 0.6 eV. the calculated quantum mechanical angular distributions are compared to those from a classical trajectory calculation using the same surface and to the experimental ones. The dynamics of rotational excitation in the Li⁺ + H₂ system is contrasted to rotational excitation in systems for which the atom-diatom interaction is predominantly repulsive.     

List of subjects

Elastic and inelastic cross sections for well specified m_j-states have been investigated in exact quantum mechanical calculations for H₂—inert gas systems using realistic potentials. The influence of different approximations like the neglect of closed channels and the distorted wave approximation is investigated, especially also in the orbiting resonances of H₂Ar. Compensations of effects of the repulsive and attractive part of the intermolecular potential are found in many cross sections. The diffraction pattern in the inelastic differential cross sections is shown to depend only on k′_j, the wave number of the final state.     

Distorted-wave calculations for the three dimensional chemical reaction H + H2(v ⩽ 2, j = 0) → H2(v′ ⩽ 2, j′, mj) + H

Calculations of the vibrational—rotational product state population distributions and differential cross sections for the chemical reaction H + H₂(v ? 2, j = 0) → H₂(v′ ? 2, j′, m_j) + H have been carried out on the Porter—Karplus potential energy surface. The vibrationally-adiabatic-distorted-wave (VADW) method has been used. The relative rotational product distributions, differential cross sections and the helicity m_j, dependences of these quantities for the v = 0 reaction agree well with accurate close-coupling results. The absolute integral cross sections are considerably smaller than the accurate quantum values, however. The calculations for the v = 1 reaction agree with the findings of previous sudden quantum, limited close-coupling and quasiclassical theoretical studies and experiments that product H₂(v′ = 1) is more likely to be produced than H₂(v′ = 0). For the reaction with v = 2, it is found that at high translational energies product H₂(v′ = 2) is favoured over H₂(v′ = 1) or H₂(v′ = 0). The VADW differential cross sections for the v = 1 and v = 2 reactions have a similar shape to those of the v = 0 reaction, with backward peaking when summed over all m_j states. The relative rotational distributions for the v = 2, j = 0 → v′ = 2, j and v = 1, j = 0 → v′ = 1, j reactions are also similar to those obtained for the v = 0, j = 0 → v′ = 0, j reaction, with low rotational excitation.     

Theoretical study of the low-temperature vibrational relaxation of o-H2 in collisions with 4He

Cross sections and rate constants for the vibrational relaxation of H₂(υ = 1, j = 1) in collisions with ⁴He were determined using the coupled states method with a fully-converged channel basis. The interaction potential was taken to be that of Gordon and Secrest with the elastic matrix elements modified to include the spherically-symmetric component of the semi-empirical Shafer-Gordon potential. First-order forbidden transitions play a significant role in the overall relaxation process. The cross sections for the de-excitation of the υ = 1, j = 1 level are slightly larger than those for the υ = 1, j = 0 level. The ratio of the corresponding rate constants for vibrational relaxation varies smoothly from a value of 1.25 at 500 K to 1.63 at 60 K.     

Classical rotational and centrifugal sudden approximations for atom—molecule collisional energy transfer

The application of centrifugal and rotational sudden approximations to classical trajectory studies of rotational energy transfer in atom—molecule collisions to examined. Two different types of approximations are considered: a centrifugal sudden (CS) approximation, in which the orbital angular momentum is assumed to be constant during collisions, and a classical infinite order sudden (CIOS) approximation, in which the CS treatment is combined with an energy sudden approximation to totally decouple translational and rotational equations of motion. The treatment of both atom plus linear and nonlinear molecule collisions is described, including the use of rotational action-angle variables for the rotor equations of motion. Applications of both CS and CIOS approaches to rotational energy transfer in He + I₂ collisions are presented. We find the calculated CS and CIOS rotationally inelastic cross sections are in generally good agreement [errors of (typically) 10–50%] with accurate quasiclassical (QC) ones, with the CS results slightly more accurate than CIOS. Both methods are less accurate for small |Δj| transitions than for large |Δj| transitions. Computational savings for the CS and CIOS applications is about a factor of 3 (per trajectory) compared to QC. We also present applications using the CS method to rotational energy transfer in He, Ar, Xe + O₃ collisions, making comparisons with analogous QC results of Stace and Murrell (SM). The agreement between exact and approximate results in these applications is generally excellent, both for the average energy transfer at fixed impact parameters, and for rotationally inelastic cross sections. Results are better for He + O₃ and Ar + O₃ than for Xe + O₃, and better at low temperatures than at high. Since SM's quasiclassical treatment considered only total internal energy transfer without attempting a partitioning between vibration and rotation, while our CS calculation considers only rotational energy transfer, the observed good agreement between our and SM's cross sections indicates that most internal energy transfer in He, Ar, Xe + O₃ is rotational. The relation of this result to models of the activation process in thermal unimolecular rate constant determination is discussed.     

Elastic differential cross sections and intermolecular potentials for Ar + CH4 and Ar + NH3

Differential elastic cross sections are reported for CH₄ + Ar (E = μg²/2 = 8.43 kJ/mole) and NH₃ + Ar (E = 8.31 kJ/mole) in the region of the rainbow angles. Quantum interference undulations are apparently observed as well for CH₄ + Ar and, possibly, NH₃ + Ar. The measurements are fit to spherically symmetric intermolecular potentials yielding well depths and equilibrium intermolecular separations of 1.32 kJ/mole and 3.82 Å for CH₄ + Ar and 1.32 kJ/mole and 3.92 Å for NH₃ + Ar.     

Cross sections and rate constants for the vibrational relaxation of D2 (υ = 1,j = 0) in collisions with 4He

Fully converged quantum cross sections for ⁴He—D² (υ = 1,j = 0) vibrational relaxation were determined using the coupled-states method and a modified version of the Gordon—Secrest surface. First-order forbidden rotational transitions play a significant role, comparable to that observed previously for the He—H₂ system. At 60 K the υ = 1,j = 0 level of D₂ is predicted to relax ≈4 times slower than the corresponding level of H₂. This difference decreases with increasing temperature.     

On m-changes in atom-rigid-rotor collissions: influence of an initial rotation

Reorientation of the angular momentum of a diatomic molecule in collisions with atoms is investigated using classical mechanics. A factorisation formula for cross sections for rotational excitation is given. The factorisation allows the calculation of the state-specific cross section d σ (j′ m′ ← jm)/dΩ once the m-averaged cross sections d σ (j″← 0 )/dΩ for all possible j″ are known. The approach is applied to the Na₂-He system.     

Lifetime measurements on electronically excited Ch(A2Δ) radicals

The radiative lifetime of electronically excited CH(A²Δ, υ' = 0) radicals was measured by laser-induced CH(A²Δ-X²5) fluorescence as t_o(CH^*) = 537.5 ± 5 ns Additionally, the rate constants or cross sections for quenching of CH(A²Δ, υ' = 0) by Ar and He were determined.     

Integral cross sections for electronic excitation in KHg collisions

The energy dependence of the integral cross section for the electronic excitation in collisions of K and Hg is investigated for energies between 50 eV and 1500 eV. By the measurement of the spectra of the emitted light the 4²P_{$\text{3}\text{2}$} and the 4²P_{$\text{1}\text{2}$} states of potassium are found to be dominant. For these the energy dependence of the cross sections is studied in detail. By the measurement of the polarization the contributions to the 4²P_{$\text{3}\text{2}$} state are differentiated with respect to |m_j|.     

Energy dependence of rotational and vibrational distributions of N2(C) for the Ar*(3P0,2) + N2(X) excitation transfer reaction

The Ar* + N₂(X) → N₂(C, v′, N′) + Ar excitation transfer reaction has been investigated experimentally in two different atomic beam experiments. The inelastic cross sections Q_{v′ = 0}(E) and Q_{v′ = 1}(E) to the v′ vibrational level have been measured in the energy range 0.06 ⩽ E(eV) ⩽ 6, using a crossed beam machine. Both cross sections show a behaviour typical for a curve crossing mechanism, with maximum values Q₀ = 8.0 Ų and Q₁ = 1.2 Ų at E = 0.16 eV and E = 0.13 eV, respectively. The oscillatory behaviour of the ratio Q₁(E)/Q₀(E), as first observed by Cutshall and Muschlitz, is also present in our data. Within the model of Gislason et al. the results indicate a decreasing bond stretching with increasing energy. As an alternative we discuss the possibility that the oscillation is due to a different energy dependence of the cross sections for the Ar*(³P₀) and Ar*(³P₂) fine structure states in the mixed beam of metastable Ar*. The vibrational and rotational distributions have also been measured at E = 0.065 eV in a small scale atomic beam-scattering cell experiment, which can be considered as an intermediate between a bulk experiment and a crossed beam experiment. The relative vibrational populations are n_v′ = 100, 16.0, 3.03 and 0.31 for v′ = 0 through 3, with rotational “temperatures” of T_rot,v′ = 1960, 1010, 370 and 130 K. Pronounced deviations (“hump”) of the Boltzmann rotational distributions occur at N′ ≈ 27 for v′ = 0, 1 and 2, with a fractional population of 1, 3 and 11%. For v′ = 0 the “hump” is largely obscured by overlap with the v′ = 1 bandhead. These bimodal distributions are in qualitative agreement with the results of Nguyen and Sadeghi for v′ = 0. The results are discussed within the framework of a curve crossing mechanism with the Ar⁺-N⁻₂ diabatic potential as an intermediate. By assuming equal charges on both N atoms the Coulomb potential of the collinear orientation lies lower (0.45 eV at R = 2.5 Å) than the perpendicular orientation, with the consequence of different transfer probabilities for both orientations. Within a classical model or rotational excitation the final N′ values can be calculated for both orientations, resulting in much higher N′ values for the perpendicular orientation. This mechanism supplies a qualitative explanation for the observed bimodal rotational distributions.     

Model potential calculations for the excited states of the Ar*+He,Ar*+Ne molecular systems. Interpretation of thermal energy collisions involving Ar*(3p 54p) and Ne*(2p 53p)

The method developed by Hennecart and Masnou-Seeuws (1985) for the Ne*+He and Ne*+Ne systems is applied to the calculation of the molecular potential curves of the Ar*+He and Ar*+Ne systems that are correlated to the levels of the 3p ⁵ 4s and 3p ⁵ 4p configurations of the Ar atom. The computed potential curves and dynamical coupling matrix elements are next used in the framework of a two-state quantal calculation to determine the temperature variation of a few population transfer cross sections. A simple interpretation is proposed for Ar*+He and Ne*+He collisions using the Nikitin's exponential model, and it is shown that in many cases the cross sections can be predicted correctly by a two-state model.