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.     

Classical trajectory study of rotationally inelastic scattering of two HF molecules

Classical trajectory calculations of the partial opacities and integral cross sections for rotationally inelastic collisions of HF—HF were carried out for the j₁ = 0,j₂ = 0 → (11), (02), (22) transitions at initial relative translational energies of 500, 1000, and 8000 cm^?1 and for the (11) → (02) transition at 1000 cm^?1. Three different methods of relating the initial and final quantum rotational levels to classical distributions were used. The results were compared to the quantum calculations of DePristo and Alexander. It was found that the classical method using a random distribution of initial rotational energies was in poor agreement with the quantum results, while the other two methods which assigned definite classical energies to the quantum levels were in good agreement with the quantum results.     

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.     

Entropy analysis of product energy distributions in nonreactive inelastic collisions

Final state distributions for inelastic collisions of I^*₂ with rare gas atoms are analyzed with the recently introduced surprisal function. Both experimental data and classical trajectory results are compared. Both vibrational and rotational state distributions follow linear surprisal plots, with fairly large values of λ = dj( ?E)/d(?E, indicating relatively weak coupling between internal and translational degrees of freedom. The λ_u and λ_j values appear to be relatively independent of the initial state of the excited molecule and of the collision partner.     

Measurement of state-to-state rotational transfer rates in collision of I2*(B 0u+, υ = 15, j) with 3He, 4He,Ne, Ar,H2, D2 and I2

The selective laser excitation and induced fluorescence observation technique has been used to study rotationally inelastic collisions of I₂^*(B 0_u⁺, υ = 15,j) with I₂, ³He, ⁴He, Ne, Ar, H₂ and D₂. For each collision partner, several initial rotational levels ranging from j_i = 12 up to j_i = 146 have been excited. For purely rotational transfer within the υ = 15 level, our data are perfectly consistent with energy sudden (eventually corrected) scaling laws. Thus, any thermally averaged rate constant, k(j_i → j_f), can be expressed as a function of the basis rate constants k(l → 0). Furthermore, these k(l → 0) are found to follow simple empirical fitting laws. Consequently any k(j_i → j_f) can be predicted given a set of two or three fitting parameters. Collisions with relatively heavy particles (I₂, Ar and Ne) are well described by using the inverse power fitting law k(l → 0) = b[l(l+1)]^?γ, where b = 1.7, 1.2 and 1.2×10^?10 cm³ s^?1 and γ = 1.08, 1.02 and 1.17 for I₂^*-Ne, I₂^*-Ar and I₂^*-I₂ collisions respectively. For collisions with light particles (³He, ⁴He, H₂ and D₂), k(l → 0) shows a sharp decrease with l which can be accounted for by a hybrid power-exponential fitting law k(l → 0) = b[l(l+1)]^?γ exp[-l(l+1)/l^* (l^*+1)], where b = 0.84, 0.71, 2.77 and 2.78×10^?10 cm³ s^?1l⁺ = 20.6, 23.1, 18.8 and 31.4, and γ = 0.66, 0.66, 0.78 and 0.91 for I₂^*-³He, I₂^*-He, I₂^*-H₂ and I₂^*-D₂ collisions, respectively. We confirm that the rotational transfer dynamics in heavy molecules is mainly governed by angular momentum exchange.     

Experimental determination of the mj distribution in inelastic scattering of Na2 by He

The orientational distribution of Na₂ molecules scatterd by He has been determined in a molecules beam experiment. At large angle scattering where inelastic collisions are dominant, a high degree of alignment has been observed. This alignment depends strongly on the rotational quantum number J after scattering. The J dependence can be explained by assuming that during collisions m_j is conserved when the quantization axis is chosen parallel with the geometric apse.     

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.     

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 and inelastic angular distributions in the jz-conserving coupled states approximation for molecular collisions

An approximation scheme is described which allows the decoupling of molecular rotational j and l angular momenta in molecular collisions. With a particular choice of the interaction potential, the potential matrix couples only the molecular states of the system and in particular those in which the z-axis projection of j is conserved. Test calculations on He + H₂ for the elastic j = O → O and rotationally inelastic j = O → 2 differential cross sections are presented in the energy range 0.1 to 0.9 eV. These results are compared with the full coupled-channel cross sections and are found to be extremely accurate.     

Collisions of metastable Ne*, He* atoms with ground-state He,Ne atoms studied by atomic beam and laser techniques

A crossed nozzle-beam experiment is used to investigate thermal energy collisions: Ne*(2p ⁵3s,³ P _{0, 2})+He(1s ²,¹ S ₀), almost purely elastic, and He*(1s2s,^{1, 3} S)+Ne(2p ⁶,¹ S ₀), in which inelastic excitation transfers occur. State and velocity selection of the scattered Ne* atoms is performed using a tunablecw dye laser frequency locked on a definite Zeeman component of the transition 1s ₅→2p ₆ (λ=614.3 nm) of²⁰Ne or²²Ne. In the purely elastic case, this technique allows the selection of one of the two final velocities, and then an unambiguous LAB-CM transformation. The differential cross section at 62 meV tallies on accords with a calculation using a single effective potential. In He* on Ne collisions, the main inelastic processes are endothermic excitation transfers from He*(2¹ S). Experimental results obtained at different energies (62, 95, 109, 124 meV) show that the transfers essentially result in levels 3s and 4d of Ne.     

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.     

Dynamically based fitting law for thermal rate coefficients in rotational relaxation

An earlier analytical, approximative result for the semi-classical, sudden limit of energy dependent j_o → j cross sections of rotational relaxation of homonuclear, diatomic molecules perturbed by an atom has been integrated to obtain dynamical fitting of temperature dependent rate coefficients. The result can be written by using two parameters, k_jjo = [(2j + 1)/(2j_o + 1)] ^1/2a (lj - 1]^?1 ? b), where the parameters a and b are given from the assumed intermolecular potential, The reduced mass for the collisions and the temperature. A comparison with several experimental results proves the validity of the above expression and gives some statements about the intermolecular potentials for the systems considered.     

Comparison of classical mechanics and the coupled states approximation for Li+-CO scattering on an ab initio calculated CI potential energy surface

The dynamics of rotational excitation on an ab initio calculated CI rigid rotor potential energy surface for Li⁺-CO are investigated using classical mechanics and the quantum mechanical coupled-states (CS) approximation. Transition probabilities out of the j = 0 initial level are calculated for various impact parameters between b = 0 and 40a_o for 1 eV collisions. The classical results agree well with the average of Δj-even and Δj-odd quantum transition probabilities except for a few lower impact parameters where CS seems to underestimate the large Δ transitions. No propensity rule is observed for the preference of the Δj-even versus Δj-odd transitions as might have been expected.     

Energy transfer in classical collinear and perpendicular central collisions of a structureless atom with a morse oscillator

The energy transfer in classical collinear (C_∞) and perpendicular (C_2v) central collisions of an atom with a Morse oscillator is compared. These collision geometries contribute in classical collisions to experimentally observed inelastic backward scattering of alkali ions from H₂ molecules. For both collision geometries the equations of motion reduce to a set of only two coupled differential equations which can be easily solved numerically. The calculations show that the C_2v collisions are much more effective than C_∞ collisions at all but the very lowest energies. The calculated ΔE/E versus E curves for C_2v collisions using a Born-Mayer potential for the atom atom-in-molecule interaction could be fitted to the experimental results for Na⁺-D₂ yielding reasonable potential values.     

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.     

New experimental evidence for the energy corrected sudden scaling law

New measurements of rate constants for the rotationally inelastic process Na₂^*(j_o) + Xe → Na₂^*(j_f) + Xe show the superiority of the energy corrected sudden scaling law of DePristo and Rabitz over other such laws, including the statistical power gap law which we proposed earlier, particularly at high j_o. All rates decrease as an inverse power of the energy transfer.     

Dimensionality control of coupled scattering equations using partitioning techniques

A method of variable reduction of the dimensionality of the coupled equations for inelastic scattering is presented, based upon a projection operator P with a restricted range of orbital angular momentum states. For rotational states in the range O?j ?j^* and total angular momentum large, the coupled equations have dimensionality (j^* + 1) ? N ?(j^* + 1)², where the value of N is controlled by the choice of P. This is in contrast to conventional partitioning techniques which utilize further restrictions on the important molecular rotational states. The equations for the P subspace and its complementary Q subspace are decoupled by an approximation on the equation of motion of Qψ_scat. Information about scattering into the Q subspace is retained, within this degree of approximation, and is reintroduced at the end of the computation with little additional labor. The theory is developed in terms of atom-rigid-rotor scattering, although addition of vibrational modes would not in any way interfere with the basic techniques used.     

Simultaneous vibrational and rotational transitions in hydrogen + argon at high collision velocities: Collisions at nonzero impact parameters

The problem of vibrationally and rotationally inelastic scattering processes in H₂ + Ar for nonzero impact parameter b has been investigated in the collision velocity range of 10⁶–10⁷ cm/sec by use of the sudden approximation. The simultaneous vibrational (0 → 1) and rotational (00 → 00, 20, or 40) transitions were studied. For υ > 3 x 10⁶ cm/sec, the probabilities for b/l = 1.0 are found to be very large compared with those for b = 0, where l is the hard-sphere collision diameter; for b/l > 1.0, the probabilities decrease very rapidly with increasing b. The results show that nonzero-b collisions must be included in the calculation of simultaneous transition processes in H₂ + Ar at higher collision velocities.     

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.