Glory undulations in the total cross section for ArAr, Kr, Xe and KrAr, Kr
Abstract
The glory undulations in the velocity dependence of the total cross section Q have been accurately measured for the scattering of the noble-gas systems ArAr, ArKr, ArXe, KrAr and KrKr. We present a new method to describe quantitatively the results of these measurements. A least-squares analysis of the data is performed, using a seven-parameter function, based on the semiclassical description of small-angle molecular scattering. From this function we calculate the value of the exponent s of the attractive part Va of the potential, generally described by Va = −Csr−s and we calculate the positions of the extrema in the glory undulations. We determine the product of the potential well depth ϵ and the well position rm that in first order determines the phase of the glory undulations. Small deviations from existing potentials are found. The method of analysis also offers a quantitative separation of the glory contribution and the attractive contribution to Q that is essential to find the potential parameter C6 in case absolute values of Q are measured. The description given here offers the possibility to incorporate the total cross section data in a new multiproperty analysis.
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Cited by (5)
Long-range intermolecular potentials for the metastable rare gas-rare gas systems Ar*, Kr*(<sup>3</sup>P<inf>0,2</inf>)+Ar, Kr, Xe
1988, Chemical PhysicsIn a crossed beam experiment with a calibrated supersonic secondary beam the absolute value (rms accuracy 2.5%) and the velocity dependence of the total cross section Q have been measured in a wide range of relative velocities 500<g<5000 m s−1 for the title systems. The data have been analysed with the ion-atom Morse-Morse-spline-van der Waals potential of Gregor and Siska for the Ne*-Xe system as a reference, resulting in accurate values for the well depth ϵ, well position Rm and long-range pure van der Waals constants C6 (without the influence of C8 and C10). These long-range pure C6 values are in excellent agreement with the calculated values of Dalgarno for the corresponding alkali atom-rare gas systems when scaled with the ratio of polarisabilities. The major difference in comparison with the alkali systems is the larger influence of the higher-order dispersion terms C8 and C10 (due to the (np)−1 core hole), as reflected in the velocity dependence of the attractive contribution Qa ∝ (2ϵRm/ħg)2/(s−1) with s=6.5–7 for high velocities and in the large amplitude of the glory contribution Qgl. For all systems the interesting N=1 glory maximum has been observed, with the glory range extending to the N=1.5 minimum for Ar*-Ar and to the N=6 maximum for Kr*-Xe. For the homonuclear systems only the glory oscillations due to the van der Waals-type potentials are observed. The glory damping due to the scattering on multiple potentials is described in terms of a rms spread Δ(ϵRm) in the ϵRm product, e.g., for Ar*-Ar we find Δ(ϵRm)/ϵRm=0.13. These measurements are fully complementary to the high-energy differential cross section measurements of Gillen et al., which only probe the chemical type potential with a deep well. For the heteronuclear Kr*-Xe system a strong velocity-dependent damping of the glory oscillations is observed, which can be described quantitatively by an excitation transfer process to a near-resonant short-lived Xe**((5p)5 (6p)) state. The characteristic velocity dependence is used to calculate the radial coupling matrix element for this transition.
Intermolecular potentials for the metastable Ne*-rare gas and Ne*-molecule systems
1988, Chemical PhysicsThe absolute value and the velocity dependence of the total cross section Q(g) has been measured in a crossed beam machine for the Ne*-Ar, Kr, Xe and Ne*-O2, N2, CH2 and CO2 systems, using a mixed beam containing Ne*(3P(0) and Ne * (3P2) fine structure states in a 1:5 ratio. The range of velocities is typically 1000 ⩽ g ⩽ 8000 m s−1, always including the interesting N = 1 glory oscillation. The results for the Ne* -rare gas systems are in excellent agreement with the predictions of the ion-atom Morse-Morse-spline-van der Waals potentials of Gregor and Siska, both with regard to the absolute value (1.5%), position of the N = 1 glory maximum (2.7%) and the amplitude of the N = 1 glory maximum (4.3%). The predictions of the potentials proposed by Hausamann are less satisfactory, most likely due to the specific switchover function used to connect the well area at R/RM ≈ 1.1 to the van der Waals long-range attractive branch at R/RM ≈ 2 (RM is the well position). By using a semiclassical scaling method the potential parameters ϵ (well depth), RM (well position) and C6 (van der Waals constant) have been determined for the Ne*-molecule systems, using the Gregor and Siska IAMMSV potential for the Ne*-Xe system as a reference. The well parameters are (ϵ (meV), RM (Å)) = (3.21, 5.43), (4.24, 5.17), (13.55, 4.74) and (7.08, 5.44) for the Ne*-N2, O2, CO2 and CH4, systems, respectively. For the C6 values we observe a fair scaling with the polarisibility α of the molecule. For the Ne*-CO2 system we observe a damping of the amplitude of the glory oscillations, which increases rapidly with decreasing velocity. This damping is interpreted in terms of the probability for ionisation along the glory trajectory, providing useful information for determining a complex potential for this system.
The excitation transfer cross section of the Kr*-N2 system has been measured in a crossed-beam experiment in the energy range 0.5 ⩽ E(eV) ⩽ 2.7, using a mixed beam of metastable Kr* atoms. The strongly different threshold energies (0.47 and 1.12 eV for the values J = 0 and J = 2, respectively, of total electronic angular momentum of Kr*) allow for an analysis in terms of fine-structure-dependent cross sections QJ(E), resulting in Q0 (0.94 eV) = 3.38 Å2 and Q2(2.24 eV) = 2.46 Å2 at twice the threshold energy. The slightly larger cross section for J = 0 can be explained qualitatively in terms of diabatic initial- and final-state potentials, coupled by two curve crossings with the ionic Kr+-N−2 Coulomb potential. The large difference with the experiments of Tabayashi and Shobatake, resulting in Q0 ≈ 10−2 Q2, is most likely due to a population ratio 3P0:3P2 = 1:146 in their atmospheric-arc beam source which is far from the assumed ratio 1:5 of statistical weights.
Energy dependence of rotational and vibrational distributions of N<inf>2</inf>(C) for the Ar*(<sup>3</sup>P<inf>0,2</inf>) + N<inf>2</inf>(X) excitation transfer reaction
1987, Chemical PhysicsThe 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 Qv′ = 0(E) and Qv′ = 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 Å2 and Q1 = 1.2 Å2 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 nv′ = 100, 16.0, 3.03 and 0.31 for v′ = 0 through 3, with rotational “temperatures” of Trot,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.
Charge distribution analysis on Ar-H<inf>2</inf> system
1986, Journal of Molecular Structure: THEOCHEMThe van der Waals Ar—H2 system, using the RHF-SCF-LCAO-MO non-empirical method is studied. The change in the charge distribution (populations, multipolar moments and related properties) produced by the van der Waals interactions is analyzed and the influence of the basis set superposition effect is studied.