Vibrational Excitation Of H2 Research Articles

Voyager electron density measurements on Saturn: Analysis with a time dependent ionospheric model

We have used a one‐dimensional chemical diffusive model of the ionosphere, in conjunction with the measured Voyager ultraviolet spectrometer (UVS) upper atmospheric temperature and composition structure, to analyze the Voyager measurements of Saturn's upper ionospheric electron densities. Electron density measurements are available from the analysis of the radio science (RSS) experiments. In addition, if interpreted as an atmospheric phenomenon the Saturn electrostatic discharges (SED), detected by the Voyager planetary radio astronomy instrument, the measurements also yield important information on electron densities at the peak. These latter data suggest a strong day‐to‐night variation in the peak electron densities with a maximum of ∼5 × 105 cm−3 near noon and a minimum of ∼103 cm−3 near midnight. The analysis of RSS data yields a peak of ∼104 cm−3 in the electron density profiles near the local terminators. As with simpler ionospheric models, we find serious difficulties in interpreting these electron density measurements because time constants in the model for the chemical sinks in the ionosphere, of mostly H+ ions, are >106 s much longer than a Saturnian day, suggesting little diurnal variation. We have investigated the effects of H2 vibrational excitation (characterized by a single vibrational temperature) and a gaseous H2O influx from Saturn's rings, as enhancers of plasma recombination, since they result in the conversion of slowly recombining H+ ions to more rapidly recombining molecular ions. This does introduce a larger diurnal variation in the peak electron densities, but not as strong as that deduced from the analysis of SED measurements. Furthermore, it also reduces the magnitude of the electron densities at the peak well below that inferred from the SED data. Based on the model results and extrapolation of calculations by Kim and Fox [1991] from Jupiter, we suggest that SEDs may not be associated with atmospheric storm systems. In our attempt to interpret the RSS measurements of electron density profile at sunrise, we have invoked an upward field‐aligned drift, H2 vibrational excitation and an influx of H2O to explain the results, and, in particular, maintain plasma peak at the measured altitude.

Analyses of Recent Experimental and Theoretical Determinations of e - H2 Vibrational Excitation Cross Sections: Assessing a Long-Standing Controversy

During the last four years, we have undertaken a major effort to resolve a serious, long-standing discrepancy between various experimental and theoretical determinations of the cross section for the v0 = 0 → v = 1 vibrational excitation of H2. This effort has involved crossed electron-beam molecular-beam measurements of relative angular distributions, measurements of transport coefficients in mixtures of H2 and various rare gases, and ab initio theoretical calculations using a vibrational close-coupling formalism with an exact treatment of non-local exchange effects. The discrepancy remains unresolved—a fact with potentially wide-ranging consequences for beam experiments, theory, and the unfolding of inelastic electron–molecule cross sections from swarm data. New analyses of the transport data and the application of a new method of extrapolating angular distributions beyond the range of measurement sheds light on this disagreement and its implications.

Vibrational excitation of H2 by electron impact: An energy-dependent vibrational-frame-transformation approach.

An energy-dependent rovibrational-frame-transformation method, combined with the multichannel quantum-defect theory, has been applied to study the vibrational excitations of ${\mathrm{H}}_{2}$ by electron collision in the energy range below 5 eV. A class of nonadiabatic effects resulting from large collision time delay has been accounted for. Using a special set of short-range Born-Oppenheimer eigenstates, this approach does not explicitly introduce electron-molecule compound states. We show that the body-frame quantum-defect function ${\mathrm{\ensuremath{\mu}}}_{\mathit{l}=1}$(\ensuremath{\varepsilon},R), containing the information about the dynamical coupling of the incident electron and the molecular target, is all one needs to describe the scattering properties of the system.

Effects of the energy distribution of fast electrons on H2 vibrational excitation in a tandem negative ion source

The population distribution of vibrationally excited hydrogen molecules H2(v″), and the H− production are investigated theoretically by solving numerically a set of particle balance equations in a steady-state pure hydrogen plasma. In particular, the enhancement of the H2(v″) distribution is discussed for different energy distributions of fast electrons ef. Whether the energy distribution for ef is a delta function type or a plateau type, collisional excitation of H2(v″) caused by ef is very effective to enhance the H− production and a resultant vibrational distribution becomes the plateau distribution. Besides these, if ef with energies higher than 30–40 eV are present, both H2(v″) excitation and then H− yield hardly depend on the form of the energy distribution of ef.

The effect of reagent excitation on the dynamics of the reaction O(1D2)+H2→OH(X 2Π)+H

The effect of H2 translational, rotational, and vibrational excitation on the dynamics of the O(1D2)/H2 reaction are explored in a semiclassical trajectory study involving both of the energetically accessible potential energy surfaces of the system. Landau–Zener probabilities determine surface hopping. At low reagent excitation, the deep H2O potential minimum dominates the dynamics, causing the reagents to reorient towards a H–O–H (insertion) configuration and form the H2O intermediate, irrespective of the initial approach geometry. High vibrational excitation enhances the probability for transitions onto the excited state potential during the interaction. Reactions which sample the excited state potential have fundamentally different dynamics from those which remain on the lower state. For reactions involving H2(v=4), the OH product has a bimodal vibrational distribution, peaking in OH(v′=2) and OH(v′=9). The lower peak is due to reactions which access the excited state potential; the higher peak results from those which remain on the lower state for the entire interaction. High translational excitation shortens the interaction time and reduces the effect of the potential minimum to reorient the reagents. Rotational excitation also reduces the effect of the potential minimum by causing the system to rotate out of the insertion geometry before entering the potential minimum.

Identification of H2(ν″) vibrational excitation processes in a hydrogen discharge

The enhancement of the H2(ν″) vibrational distribution observed in the medium-density hydrogen discharge of Eenshuistra and co-workers is investigated theoretically as a function of different excitation processes. The observed fivefold enhancement of the ν″=5 population with increasing discharge current is reproduced in the model. Principal excitations generating this enhancement are H3+surface recombination and fast-electron excitation. Atom-surface recombination may be a principal contributor near the ν″=1 portion of the spectrum.

Near-threshold Rotational and Vibrational Excitation of H2 by Electron Impact: Theory and Experiment

A joint experimental-theoretical attack on low-energy e-H2 scattering is described. The cross sections calculated from a highly converged numerical solution of the nonrelativistic Schrodinger equation, using a parameter-free interaction potential, are first compared with results from swarm experiments, and are later used to improve the accuracy of the swarm analysis at energies above the first vibrational threshold. To provide further perspective, the theoretical results are compared with a variety of other experimental data. The theoretical results for the momentum-transfer and rotational-excitation cross sections are in excellent agreement with the results from swarm experiments, but there is an unresolved and significant difference in the threshold behaviour of the vibrational-excitation cross sections. Both the theoretical and experimental approaches are subjected to close scrutiny in an attempt to uncover possible sources of error that could explain this difference. The failure to locate likely sources points to the need for further independent theoretical and experimental work to resolve a problem that has serious implications.

L ? emission from collisional excitation of H Atoms by threshold energy Ar+ ions

In a specially designed collision chamber, H atoms produced by a microwave discharge were excited into the 2p state by impact of Ar+ ions in a beam. A degree of dissociation up toη=94% was measured at the exit of the microwave source, although in the center of the collision cellη is smaller, with a lower limit of 33 %. The effect of vibrational excitation of H2 by the discharge and the resulting difficulties of measuringη are discussed. The cross section forL α emission increases linearly from the threshold, at 10.2 eVCM, to 17.1 eVCM. The absolute cross section at this energy is 1.5·10−17 cm2 forη=33% (with a minimum of 0.6·10−17 cm2, for the maximum possibleη). The absence of an activation barrier rules out some features shown by an earlier ab initio calculation.

Generation of negative ions in tandem high-density hydrogen discharges

An optimized tandem two-chamber negative-ion source system is discussed. In the first chamber high-energy (E>20 eV) electron collisions provide for H2 vibrational excitation, while in the second chamber negative ions are formed by dissociative attachment. The gas density, electron density, and system scale length are varied as independent parameters. The extracted negative ion current density passes through a maximum as electron and gas densities are varied. This maximum scales inversely with system scale length R. The optimum extracted current densities occur for electron densities nR=1013 electrons cm−2 and gas densities N2R in the range 1014–1015 molecules cm−2. The extracted current densities are sensitive to the atomic concentration in the discharge. The atomic concentration is parametrized by the wall recombination coefficient γ and scale length R. As γ ranges from 0.1 to 1.0 and for system scale lengths of 1 cm, extracted current densities range from 8.0 to 80 mA cm−2. The relative negative-ion yields from single-chamber and tandem two-chamber systems are compared. Estimates are made for the rates of polar dissociation of H2 molecules and H+3 ions, and these rates are compared with the dissociative attachment rates.

The quenching of Na(3 2P) by H2: Interactions and dynamics

An eight-configuration diatomics-in-molecules formalism with symmetrically orthogonalized diabatic input is used to calculate the three lowest potential energy surfaces and nonadiabatic couplings for Na+H2 collisions. The singlet diatomic input for NaH and the singlet and triplet diatomic input for H−2 are chosen to reproduce the accurate adiabatic curves for those cases, and the diatomic input for H2 is based on theoretical interpretations of the resonance states. Trajectory calculations are carried out using the calculated 2 2A′ potential surface and nonadiabatic couplings, and the choice of H−2 input is found to sensitively affect the H2 vibrational excitation in the resonance-line quenching process. One H−2 curve, based on the work of Wadehra and Bardsley, yields an amount of vibrational excitation similar to that observed experimentally. The resulting set of potential energy surfaces provides a reasonable microscopic interpretation of the chemical dynamics of the quenching process Na(3p2P)+H2(v = 0, low j) →Na(3s2S)+H2(v′,j′).

A quasiclassical trajectory study of reagent vibrational excitation effects in the OH+H2→H2O+H reaction

Quasiclassical trajectories have been used to determine reaction rate constant enhancements and product state energy partitioning in the OH(v)+H2(v′)→H2O+H reaction for (v,v′)= (0,0), (1,0), (0,1), and (1,1). An analytical fit to the accurate ab initio potential surface of Walch and Dunning was used in the Monte Carlo calculations. Final H2O vibrational states were assigned using the histogram method to bin the good action variables governing H2O vibrational motions. These actions were calculated by using second order classical perturbation theory to solve the vibrational Hamilton–Jacobi equation. The resulting integral reaction cross sections and thermal rate constants, indicate that OH vibrational excitation leads to a very small enhancement (only a factor of 1.28) in the thermal rate constant at 300 K. H2 excitation, on the other hand, causes a large reduction in the reaction activation energy (from 0.18 eV to 0.03 eV) and a large enhancement in the rate constant (a factor of 393 at 300 K). These results, as well as the ground reagent state thermal rate constants are in good agreement with experiment. We also find that simultaneous H2 and OH vibrational excitation gives a result which is just the superposition of the separate excitation results. Reagent rotational excitation causes a decrease in the reaction cross section, with the rate of decrease larger when H2 is excited than OH. An examination of product state energy partitioning indicates that nearly all of the additional energy coming from reagent vibrational excitation ends up as product vibration, with all of it going to the H2O stretch modes when OH is initially excited, and a more random distribution of the three H2O modes when H2 is excited. This mode specificity of energy flow contrasts with the nonspecific vibrational mode distributions obtained for the reaction from the ground state reagents.

Fourier transform method for the classical trajectory problem

By introducing an impluse potential at an external boundary, or by reflecting the scattering potential at such a boundary, collision dynamics is converted into an equivalent bound-state problem. Recent theoretical developments in classical bound-state dynamics. which make use of the geometrical structure in phase space known as an invariant toroid, can then be applied to collision problems. Fast Fourier transform techniques are used to construct the invariant toroid, which is the locus of an indefinitely extended nonperiodic classical trajectory. This approach to collision dynamics is applied to the collinear atom–oscillator problem modelling He–H2 vibrational excitation. Results are compared to previous classical and quantum dynamical studies. The proposed method obtains in a single calculation the complete ensemble of trajectories that correspond to a semiclassical wave function. At given total energy and for given global action integral values all trajectories are parallel straight lines when expressed in the coordinate space of true angle variables obtained by the Fourier transform calculation. These aspects of the formalism reduce the computation of inelastic transition probabilities and action integrals to simple geometric exercises.

Glory oscillations in inelastic forward scattering for H+-H2

In a crossed-beam experiment the vibrational excitation of H2 by proton impact has been measured at a scattering angle of 0 degrees (angular resolution +or-0.5 degrees ) and in the energy range 15 to 120 eV (CM system). The spectra show resolved vibrational transitions nu =0 to nu ' with nu '=1, 2, 3 and 4. The measured energy dependences of the differential cross sections for all four vibrational transitions are characterised by an oscillatory behaviour superimposed on a linearly rising function. The results of first calculations for the nu =0 to 1 transition are in very satisfactory agreement with the experimental data.

Vibrational excitation of H2 in intense ultraviolet fluxes

The vibrational excitation of H2 in intense ultraviolet radiation fields is studied. The radiative cascade through bound levels of the ground electronic state, following absorption of Lyman- and Werner-band photons, is modified to include effects of 'multiple pumping' and direct photodissociation from the high vibrational levels. Although the column densities in the excited vibrational levels produced by UV pumping appear too low to explain the recently observed Orion quadrupole emission lines, it is suggested that the far-red lines in the (3-0) and (4-0) bands, produced by UV pumping from O stars near dense molecular clouds, may be detectable.

Theoretical study of inelastic scattering of H2 by Li+ on SCF and CI potential energy surfaces

Integral and differential cross sections for pure rotational and simultaneous rotational−vibrational excitation of H2 by Li+ impact have been computed following the coupled−channel formalism using two different SCF potential energy hypersurfaces and a CI hypersurface at 0.6 and 1.2 eV. Sensitivity of integral cross sections to (a) choice of ab initio potential energy surface and (b) expansion length of a Legendre polynomial representation of one of the energy surfaces is examined. It is seen that preparation of H2 in the v = 0, j = 2 state leads to four− and fivefold increases in excitation cross sections to the v′ = 1, j′ = i, i = 0,2,4 states relative to excitation of ground state (v = 0, j = 0) H2. Differential cross sections are reported at 1.2 eV for up to five quantum rotational and for vibrational transitions on one of the energy hypersurfaces. All angular distributions required for determining ratios (inelastic : elastic) of differential cross sections needed for comparison with recent time−of−flight experiments at 0.6 eV are computed using both SCF and CI potential energy surfaces and compared. Further comparisons are made with experiment, beyond those that have appeared to date, which indicate that a significant discrepancy at one of the three angles for which measurements are available is due to experiment.

Semiclassical theory for low-energy molecular collisions II. Atomic exchange reactions

A form of semiclassical theory of molecular collisions, previously formulated and applied to H+, H2 vibrational excitation in I, is applied to H, H2 atomic exchange. The formulation involves separation of the potential into two parts, a ``trajectory'' potential along which only elastic scattering can occur and ``coupling'' potential which can produce inelastic or reactive scattering. The first part is chosen such that the classical two-body central force formulas apply. This determines the coupling potential in the parameters, the classical trajectory R (t), and the classical deflection function θ(t). The time-dependent Schrödinger equation is then solved to produce the reactive probabilities. The problem is formulated in a coordinate system in which initial and final scattering coordinates are constrained to remain the same throughout the reaction. This procedure produces asymptotic momentum transfer or ``recoil'' factors of the form exp[(i/ℏ)μν · R] which multiply the vibrational-rotational wavefunctions, but it preserves orthogonality in the scattering wavefunctions and permits the coupled equations in the two-state approximation to be approximately decoupled in the symmetric process. Calculations are carried out to illustrate effect of trajectory on reaction probabilities.

Study of H2++He → HeH++H at low energies

Laboratory-energy distributions of HeH+ were measured for the reaction H2++He → HeH++H (endothermic by 0.81 eV for ground-state reactants and products) with a merging-beams apparatus over a range of interaction energy W from 0.05 to 12 eV. The He was in the ground state; the H2+ was vibrationally excited. Absolute and relative cross sections were determined from these distributions. For W ≥ 5 eV, the distributions show that in the center-of-mass system the HeH+ peaks along both the incident direction of the H2+ and the incident direction of the He. The peak along the direction of the He is largest, and is the only one for W <5 eV. The role played by W and by the vibrational excitation of H2+ in the formation of the peaks is discussed. It is not clear what mechanism controls the reaction. The data cannot be satisfactorily explained with either the spectator-stripping or the Langevin model.

Comment on Enhancement of the Reaction Cross Section of He+H2+→ HeH++H by Vibrational Excitation of H2+ and the Treatment of Nuclear Spin by the Statistical Phase-Space Theory

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Enhancement of the Reaction Cross Section of He+H2+→HeH++H by Vibrational Excitation of H2+ According to the Statistical Phase-Space Theory

The quantum-mechanical statistical phase-space theory of Peuchukas, Light, and Nikitin is used to calculate the cross sections for the endothermic reaction He+H2+→HeH++H as a function of initial vibrational state and relative translational energy. The theory predicts enhancement of the reaction cross section by vibrational energy of the reagent, in qualitative agreement with the experimental results of Chupka. However, the experimental enhancement is much greater than that predicted by this theory. The energy dependence of the reaction cross sections for each initial vibrational state is also in only qualitative agreement with experiment.

Rotational and Vibrational Excitation of H2 by Slow Electron Impact

Abstract In a beam experiment the processes of elastic scattering, pure rotational excitation and deexcitation, pure vibrational excitation, and simultaneous rotational-vibrational excitation have been investigated for e-H2 scattering in the energy range from 0.3 eV to about 15 eV. Differential and integral cross sections have been determined in arbitrary units and calibrated on an absolute scale by normalization to absolute total cross sections. The results are discussed in terms of super-position of direct scattering, shape resonance and Feshbach resonance scattering and are compared with recent theoretical investigations. The cross sections for rotational and vibrational excitation, which are generally small for direct scattering, are greatly enhanced by a broad shape resonance near 3 eV and by Feshbach resonances around 12 eV. Characteristic differences in the excitation mechanisms are discussed.