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In order to provide a database for modeling hypersonic entry in a partially ionized gas under non-equilibrium, the electron-impact excitation cross sections of atoms have been calculated using perturbation theory. The energy levels covered in the calculation are retrieved from the level list in the HyperRad code. The downstream flow-field is determined by solving a set of continuity equations for each component. The individual structure of each energy level is included. These equations are then complemented by the Euler system of equations. Finally, the radiation field is modeled by solving the radiative transfer equation.

It is well recognized that secondary electrons play an important role in radiation damage to humans. Particularly important is the damage of DNA by electrons, potentially leading to mutagenesis. Molecular-level study of electron interaction with DNA provides information on the damage pathways and dominant mechanisms. Our study of electron-impact ionization of DNA fragments uses the improved binary-encounter dipole model and covers DNA bases, sugar phosphate backbone, and nucleotides. An additivity principle is observed. For example, the sum of the ionization cross sections of the separate deoxyribose and phosphate fragments is in close agreement with the C3(sup prime)- and C5 (sup prime)-deoxyribose-phospate cross sections, differing by less than 5%. Investigation of tandem double lesion initiated by electron-impact dissociative ionization of guanine, followed by proton reaction with the cytosine in the Watson-Crick pair, is currently being studied to see if tandem double lesion can be initiated by electron impact. Up to now only OH-induced tandem double lesion has been studied.

Oxidative damages by ionizing radiation are the source of radiation-induced carcinogenesis, damage to the central nervous system, lowering of the immune response, as well as other radiation-induced damages to human health. Monte Carlo track simulations and kinetic modeling of radiation damages to the DNA employ available molecular and cellular data to simulate the biological effect of high and low LET radiation io the DNA. While the simulations predict single and double strand breaks and base damages, so far all complex lesions are the result of stochastic coincidence from independent processes. Tandem double lesions have not yet been taken into account. Unlike the standard double lesions that are produced by two separate attacks by charged particles or radicals, tandem double lesions are produced by one single attack. The standard double lesions dominate at the high dosage regime. On the other hand, tandem double lesions do not depend on stochastic coincidences and become important at the low dosage regime of particular interest to NASA. Tandem double lesions by hydroxyl radical attack of guanine in isolated DNA have been reported at a dosage of radiation as low as 10 Gy. The formation of two tandem base lesions was found to be linear with the applied doses, a characteristic of tandem lesions. However, tandem double lesions from attack by a charged particle have not been reported.

Recent advances in supercomputers and highly scalable quantum chemistry software render computational chemistry methods a viable means of providing chemistry data for aerothermal analysis at a specific level of confidence. Four examples of first principles quantum chemistry calculations will be presented. Study of the highly nonequilibrium rotational distribution of a nitrogen molecule from the exchange reaction N + N2 illustrates how chemical reactions can influence rotational distribution. The reaction C2H + H2 is one example of a radical reaction that occurs during hypersonic entry into an atmosphere containing methane. A study of the etching of a Si surface illustrates our approach to surface reactions. A recently developed web accessible database and software tool (DDD) that provides the radiation profile of diatomic molecules is also described.

The improved binary-encounter dipole (iBED) model [W.M. Huo, Phys. Rev. A64, 042719-1 (2001)l is used to study the total ionization cross sections of the DNA sugar-phosphate backbone by electron impact. Calculations using neutral fragments found that the total ionization cross sections of C3' - and C5', -deoxyribose-phospate, two conformers of the sugar-phosphate backbone, are close to each other. Furthermore, the sum of the ionization cross sections of the separate deoxyribose and phosphate fragments is in close agreement with the C3' - and C5" -deoxyribose-phospate cross sections, differing by less than 10%. The result implies that certain properties of the-DNA, like the total singly ionization cross section, are localized properties and a building-up or additivity principle may apply. This allows us to obtain accurate properties of larger molecular systems built up from the results of smaller subsystem fragments. Calculations are underway using a negatively charged sugar-phosphate backbone with a metal counter-ion.

Free secondary electrons are the most abundant secondary species in ionizing radiation. Their role in DNA damage, both direct and indirect, is an active area of research. While indirect damage by free radicals, particularly by the hydroxyl radical generated by electron collision with water. is relatively well studied, damage by direct electron collision with DNA is less well understood. Only recently Boudaiffa et al. demonstrated that electrons at energies well below ionization thresholds can induce substantial yields of single- and double-strand breaks in DNA by a resonant, dissociative attachment process. This study attracted renewed interest in electron collisions with DNA, especially in the low energy region. At higher energies ionization becomes important. While Monte Carlo track simulations of radiation damage always include ionization, the probability of dissociative ionization, i.e., simultaneous ionization and dissociation, is ignored. Just like dissociative attachment, dissociative ionization may be an important contributor to double-strand breaks since the radicals and ions produced by dissociative ionization, located in the vicinity of the DNA coil, can readily interact with other parts of the DNA. Using the improved binary-encounter dipole (iBED) formulation, we calculated the ionization cross sections of the four DNA bases, adenine, cytosine, guanine, and thymine, by electrons at energies from threshold to 1 KeV. The present calculation gives cross sections approximately 20% lower than the results by Bemhardt and Paretzke using the Deutsch-Mark and Binary-Encounter-Bethe (BEB) formalisms. The difference is most likely due to the lack of a shielding term in the dipole potential used in the Deutsch-Mark and BEB formalisms. The dissociation channels of ionization for the bases are currently being studied.

It has been suggested that the genotoxic effects of ionizing radiation in living cells are not caused by the highly energetic incident radiation, but rather are induced by less energetic secondary species generated, the most abundant of which are free electrons.' The secondary electrons will further react to cause DNA damage via indirect and direct mechanisms. Detailed knowledge of these mechanisms is ultimately important for the development of global models of cellular radiation damage. We are studying one possible mechanism for the formation cf DNA strand breaks involving dissociative ionization of the DNA sugar-phosphate backbone induced by secondary electron co!lisions. We will present ionization cross sections at electron collision energies between threshold and 10 KeV using the improved binary encounter dipole (iBED) formulation' Preliminary results of the possible dissociative ionization pathways will be presented. It is speculated that radical fragments produced from the dissociative ionization can further react, providing a possible mechanism for double strand breaks and base damage.

Amino acids and other organic compounds important to the chemistry of life are thought to have been delivered to early Earth by asteroids and comets. The survivability of such compounds upon high speed entry is not well understood. If molecular processing occurs during entry, the nature of the new molecules produced by such processing is also an open question. To address this question, we have initiated a study of the ablation of glycine, the simplest amino acid, upon the high speed entry of a comet or meteoroid into an atmosphere. The study assumes glycine is distributed on the surface of the comet/meteoroid. The high speed impact creates electrons, ions, and radicals in the atmosphere that react with the surface and either desorb glycine or break it up. The ablation process is studied as a function of entry speed and atmospheric composition. The AURORA code from the commercially available software package CHEMKIN is used in the study.

A three-dimensional time-dependent quantum dynamics approach using a recently developed ab initio potential energy surface is applied to study ro-vibrational excitation in N+N2 exchange scattering for collision energies in the range 2.1- 3.2 eV. State-to-state integral exchange cross sections are examined to determine the distribution of excited rotational states of N(sub 2). The results demonstrate that highly-excited rotational states are produced by exchange scattering and furthermore, that the maximum value of (Delta)j increases rapidly with increasing collision energies. Integral exchange cross sections and exchange rate constants for excitation to the lower (upsilon = 0-3) vibrational energy levels are presented as a function of the collision energy. Excited-vibrational-state distributions for temperatures at 2,000 K and 10,000 K are included.

Space radiation poses a major health hazard to humans in space flight. The high-energy charged particles in space radiation ranging from protons to high atomic number, high-energy (HZE) particles, and the secondary species they produce, attack DNA, cells, and tissues. Of the potential hazards, long-term health effects such as carcinogenesis are likely linked to the DNA lesions caused by secondary electrons in the 1 - 30 eV range. Dissociative ionization (DI) is one of the electron collision processes that can damage the DNA, either directly by causing a DNA lesion, or indirectly by producing radicals and cations that attack the DNA. To understand this process, we have developed a theoretical model for DI. Our model makes use of the fact that electron motion is much faster than nuclear motion and assumes DI proceeds through a two-step process. The first step is electron-impact ionization resulting in a particular state of the molecular ion in the geometry of the neutral molecule. In the second step the ion undergoes unimolecular dissociation. Thus the DI cross section sigma(sup DI)(sub a) for channel a is given by sigma(sup DI)(sub a) = sigma(sup I)(sub a) P(sub D) with sigma(sup I)(sub a) the ionization cross section of channel a and P(sub D) the dissociation probability. This model has been applied to study the DI of H2O, NH3, and CH4, with results in good agreement with experiment. The ionization cross section sigma(sup I)(sub a) was calculated using the improved binary encounter-dipole model and the unimolecular dissociation probability P(sub D) obtained by following the minimum energy path determined by the gradients and Hessians of the electronic energy with respect to the nuclear coordinates of the ion. This model is used to study the DI from the low-lying channels of benzene and pyridine to understand the different product formation in aromatic and heterocyclic molecules. DI study of the DNA base thymine is underway. Solvent effects will also be discussed.

Comets and meteoroids that bombarded the Earth, other planets and moons are considered possible deliverers of prebiotic materials manufactured in space. Simultaneously, chemical processing can be initiated by the large kinetic energy imparted to the planetary atmosphere during comet/meteoroid entry. The efficiency of organic synthesis and the diversity of products by impact shock are known to decrease as the reducing power of the atmosphere decreases. It is generally accepted that rich organic products are produced in a methane atmosphere whereas a carbon dioxide atmosphere is reported to yield a dearth of products In order to understand the details of impact chemistry and how it depends on the atmospheric composition, we carried out simulations of the chemistry initiated by comet/meteoroid impact upon a planetary atmosphere using different atmospheric compositions. The simulations were done by solving the set of coupled equations for mass, momentum, and energy conservations, chemical kinetics, and transport, that describe a high-energy impact shock, subsequent expansion and cooling of the hot shocked gas by mixing with the ambient gas, and the eventual steady state composition.

Rich reactive resonances are found in a 3D quantum dynamics study of the N + N2 exchange reaction using a recently developed ab initio potential energy surface. This surface is characterized by a feature in the interaction region called Lake Eyring , that is, two symmetric transition states with a shallow minimum between them. An L2 analysis of the quasibound states associated with the shallow minimum confirms that the quasibound states associated with oscillations in all three degrees of freedom in Lake Eyring are responsible for the reactive resonances in the state-to-state reaction probabilities. The quasibound states, mostly the bending motions, give rise to strong reasonance peaks, whereas other motions contribute to the bumps and shoulders in the resonance structure. The initial state reaction probability further proves that the bending motions are the dominating factors of the reaction probability and have longer life times than the stretching motions. This is the first observation of reactive resonances from a "Lake Eyring" feature in a potential energy surface.

We report a theoretical study of the dissociative ionization (DI) and product distributions of benzene (C6H6) and pyridine (C5H5N) from their low-lying ionization channels. Our approach makes use of the fact that electronic motion is much faster than nuclear motion allowing DI to be treated as a two-step process. The first step is the electron-impact ionization resulting in an ion with the same nuclear geometry as the neutral molecule. In the second step, the nuclei relax from the initial geometry and undergo unimolecular dissociation. For the ionization process we use the improved binary-encounter dipole (iBED) model [W.M. Huo, Phys. Rev. A64,042719-I (2001)]. For the unimolecular dissociation, we use multiconfigurational self-consistent field (MCSCF) methods to determine the steepest descent pathways to the possible product channels. More accurate methods are then used to obtain better energetics of the paths which are used to determine unimolecular dissociation probabilities and product distributions. Our analysis of the dissociation products and the thresholds of their productions for benzene are compared with the recent dissociative photoionization meausurements of benzene by Feng et al. [R. Feng, G. Cooper, C.E. Brion, J. Electron Spectrosc. Relat. Phenom. 123,211 (2002)] and the dissociative photoionization measurements of pyridine by Tixier et al. [S. Tixier, G. Cooper, R. Feng, C.E. Brion, J. Electron Spectrosc. Relat. Phenom. 123,185 (2002)] using dipole (e,e+ion) coincidence spectroscopy.

Recent observations from the Galileo satellite indicate that three of the Jupiter moons, Europa, Ganymede, and Callisto, may have subsurface oceans. Possible existence of such ocean and the nature of its composition are of great interest to astrobiologists. Data from Galileo's NIMS spectrometer indicate the possibility of hydrated salts on Europa's surface. To aid in the design of future missions, we investigated infrared spectra of MgSO4-nH20, n=1-3 using ab initio calculations. Geometry, energetics, dipole moments, vibrational frequencies and infrared intensities of pure and hydrated MgSO4 salts were determined. Significant differences are found between vibrational spectra of water molecules in complexes with MgSO4 and pure water. Some of the O-H stretching frequencies in the complexes are shifted to the red by up to 1,500 - 2,000 per cm. In addition, the SO2 stretching vibrations are found at lower frequency regions than the water vibrations. The calculated bands of water and SO2 fragments can serve as markers for the existence of the salt-water complexes on the surface of Jupiter's moon.

Harmonic and anharmonic vibrational frequencies, as well as infrared and Raman intensities, are calculated for MgSO4.nH20 (n=1-3). Electronic structure theory at the second order Moller-Plesset perturbation theory (MP2) level with a triple-zeta + polarization (TZP) basis set is used to determine the geometry, properties, and vibrational spectra of pure and hydrated MgSO4 salts. The direct vibrational self-consistent field (VSCF) method and its correlation corrected (CC-VSCF) extension are used to determine anharmonic corrections to vibrational frequencies and intensities for the pure MgSO4 and its complex with one water molecule. Very significant differences are found between vibrational of water molecules in complexes with MgSO4 and pure water. Some of the O-H stretching frequencies are shifted to the red very significantly (by up to 1500-2000/cm) upon complexation with magnesium sulfate. They should be observed between 1700 and 3000/cm in a region very different from the corresponding O-H stretch frequency region of pure water (3700-3800/cm). In addition, the SO2 stretching vibrations are found at lower frequency regions than the water vibrations. They can serve as unique identifiers for the presence of sulfate salts. The predicted infrared and Raman spectra should be of valuable help in the design of future missions and analysis of observed data from the ice surface of Jupiter's moon Europa that possibly contains hydrated MgSO4 salts.

The N + N2 exchange rate is calculated using a time-dependent quantum dynamics method on a newly determined ab initio potential energy surface (PES) for the ground A" state. This ab initio PES shows a double barrier feature in the interaction region with the barrier height at 47.2 kcal/mol, and a shallow well between these two barriers, with the minimum at 43.7 kcal/mol. A quantum dynamics wave packet calculation has been carried out using the fitted PES to compute the cumulative reaction probability for the exchange reaction of N + N2(J=O). The J - K shift method is then employed to obtain the rate constant for this reaction. The calculated rate constant is compared with experimental data and a recent quasi-classical calculation using a LEPS PES. Significant differences are found between the present and quasiclassical results. The present rate calculation is the first accurate 3D quantal dynamics study for N + N2 reaction system and the ab initio PES reported here is the first such surface for N3.

The discrepancy between experimental and theoretical total electron-impact ionization cross sections for a group of fluorides, CFx, and NFx, (x = 1 - 3), is attributed to the inadequacies in previous theoretical models. Cross-sections calculated using a recently developed siBED (simulation Binary-Encounter-Dipole) model that takes into account the shielding of the long-range dipole potential between the scattering electron and target are in agreement with experimentation. The present study also carefully reanalyzed the previously reported experimental data to account for the possibility of incomplete collection of fragment ions and the presence of ion-pair formation channels. For NF3, our experimental and theoretical cross-sections compare well with the total ionization cross-sections recently reported by Haaland et al. in the region below dication formation.

We report a study of the total ionization of CH_4 by electron impact and its dissociative ionization from the ^2T_2 channel. The calculation of the total ionization cross section uses the improved Binary-Encounter-Dipole model (iBED).(W. A Huo, Phys. Rev. A (submitted for publication).) The dipole Born cross section in the model is expressed in terms of a three-term representation and the optical oscillator strengths are taken from Backx and Van der Wiel.(C. Backx and M. J. Van der Wiel, I Phys. B 18) 3020 (1975). The nuclear dynamics for the dissociation of the ^2T_2 channel is studied using the statistical model. A search of the potential energy surface of the ^2T_2 state of CH_4^+ shows two minima, of C_2v and C_3v symmetries, in agreement with earlier calculations. ((a) K. Takeshita, J. Chem. Phys. 86), 329 (1987). (b) R. F. Frey and E. R. Davidson, J. Chem. Phys. 88, 1775 (1988). The dissociation of the CH_4^+ to CH_3^+ + H goes through a saddle point. Comparison with recent experimental data will be presented and the role of Jahn-Teller effect discussed.

Based on the Binary-Encounter-Bethe (BEB) model, the advantage of using relativistic effective core potentials (RECP) in the calculation of total ionization cross sections of heavy atoms or molecules containing heavy atoms is discussed. Numerical examples for Ar, Kr, Xe, and WF6 are presented.

The finite element Z-matrix method has been applied in a multichannel study of e-N2 Collisions for electron energies from threshold to 30 eV. General agreement is obtained comparing with existing experimental and theoretical data. Some discrepancies are also found.

The present study adapts the Z-matrix formulation using a mixed basis of finite elements and Gaussians. This is a energy-independent basis which allows flexible boundary conditions and is amenable to efficient algorithms for evaluating the necessary matrix elements with molecular targets.

We have applied the Z-matrix method, using a mixed basis of finite elements and Gaussians, to study e-H2 elastic and inelastic collisions. Special attention is paid to the quality of the basis set and the treatment of electron correlation. The calculated cross sections are invariant, to machine accuracy, with respect to the choice of parameters a, b, d, e as long as they satisfy Equation (3). However, the log derivative approach, i.e., the choice a = -e = 1, b = d = 0 appears to converge slightly faster than other choices. The cross sections agree well with previous theoretical results. Comparison will be made with available experimental data.

Computational study of electron-molecule collisions not only complements experimental measurements, but can also be used to investigate processes not readily accessible experimentally. A number of ab initio computational methods are available for these types of calculations. Here we describe a recently developed technique, the finite element Z-matrix method, Analogous to the R-matrix, method, it partitions the space into regions and employs real matrix elements. However, unlike the implementation of the R-matrix method commonly used in atomic and molecular physics, the Z-matrix method is fully variational. In the present implementation, a mixed basis of finite elements and Gaussians is used to represent the continuum electron, thus offering full flexibility without imposing fixed boundary conditions. Numerical examples include the electron-impact dissociation of N2 via the metastable A3Su+ state, a process which may be important in the lower thermosphere, and the dissociation of the CF radical, a process of interest to plasma etching. To understand the dissociation pathways, large scale quantum chemical calculations have been carried out for all target states which dissociate to the lowest five limits in the case of N2, and to the lowest two limits in the case of CF. For N2, the structural calculations clearly show the preference for predissociation if the initial state is the ground X1 Sg+ state, but direct dissociation appears to be preferable if the initial state is the A3Su+ state. Multi-configuration SCF target functions are used in the collisional calculation.

Rotational energy transfer between two N2 molecules is a fundamental process of some importance. Exchange is expected to play a role, but its importance is somewhat uncertain. Rotational energy transfer cross sections of N2 also have applications in many other fields including modeling of aerodynamic flows, laser operations, and linewidth analysis in nonintrusive laser diagnostics. A number of N2-N2 rigid rotor potential energy surface (PES) has been reported in the literature.

A new N2-N2 rigid-rotor surface has been determined using extensive Ab Initio quantum chemistry calculations together with recent experimental data for the second virial coefficient. Rotational energy transfer is studied using the new potential energy surface (PES) employing the close coupling method below 200 cm(exp -1) and coupled state approximation above that. Comparing with a previous calculation based on the PES of van der Avoird et al.,3 it is found that the new PES generally gives larger cross sections for large (delta)J transitions, but for small (delta)J transitions the cross sections are either comparable or smaller. Correlation between the differences in the cross sections and the two PES will be attempted. The computed cross sections will also be compared with available experimental data.

Low-energy electron impact excitation of the fundamental modes of CO2 has been extensively studied, both experimentally and theoretically. Much attention has been paid to the virtual state feature in the the (100) mode excitation and the (sup 2)II(sub upsilon) resonance feature around 3.8 eV, which is observable in all three fundamental modes. For the excitation of the (010) mode away from the resonance region, the Born dipole approximation was generally considered adequate. The present study employs the Born dipole approximation to treat the long range interaction and the Schwinger multichannel method for the short range interaction. The roles of the two interaction potentials will be compared.

Electron-H2 Collisions have been studied using the finite-element R-matrix method. Our approach uses a mixed finite-element and Gaussian basis to describe the continuum electron. In the inner region, the multi-centered nature of the Gaussian basis provides an efficient representation in the regions of space near the nuclei, whereas the piecemeal and energy-independent nature of the FEM basis is particular well suited for R-matrix calculations. Fixed nuclei calculations have been carried out at 1.4 a(sub 0), the equilibrium internuclear distance of the ground state. Up to six target states are included: the X(sup 1)E+(sub g), b(sup 3)E+(sub u), a(sup 3)E+(sub g), B(sup 1)E+(sub u), c(sup 3)II(sub u), and C(sup 1)II(sub u) states, and configuration-interaction functions are used to describe the target states. The results will be compared with available theoretical and experimental data.

For the calculation of electron molecule collision cross sections R-matrix methods automatically take advantage of the division of configuration space into an inner region (I) bounded by radius tau b, where the scattered electron is within the molecular charge cloud and the system is described by an correlated Configuration Interaction (CI) treatment in close analogy to bound state calculations, and an outer region (II) where the scattered electron moves in the long-range multipole potential of the target and efficient analytic methods can be used for solving the asymptotic Schroedinger equation plus boundary conditions.

Rotationally inelastic transitions of N2 have been studied in the coupled state (CS) and infinite-order-sudden (IOS) approximations, using the N2-N2 rigidrotor potential of van der Avoird et al. For benchmarking purposes, close coupling (CC) calculations have also been carried out over a limited energy range. The CC and CS cross sections have been obtained both with and without identical molecule exchange symmetry, whereas exchange was neglected in the IOS calculations. The CS results track the CC cross sections rather well; between 113 - 219 cm(exp -1) the average deviation is 14%. Comparison between the CS and IOS cross sections at the high energy end of the CS calculation, 500 - 680 cm(exp -1), shows that IOS is sensitive to the amount of inelasticity and the results for large DELTA J transitions are subject to larger errors. It is found that the state-to-state cross sections with even and odd exchange symmetry agree to better than 2% and are well represented as a sum of direct and exchange cross sections for distinguishable molecules, an indication of the applicability of a classical treatment for this system. This result, however, does not apply to partial cross sections for given total J, but arises from a near cancellation in summing over partial waves. In order to use rigid-rotor results for the calculation of effective rotational excitation rates of N2 in the v=1 vibrational level colliding with bath N2 molecules in the v=0 level, it is assumed that exchange scattering between molecules in different vibrational levels is negligible and direct scattering is independent of Y. Good agreement with room temperature experimental data is obtained. The effective rates determined using the IOS and energy corrected sudden (ECS) approximations are also in reasonable agreement with experiment, with the ECS results being somewhat better. The problem with a degeneracy factor in earlier cross section expressions for collisions between identical molecules is pointed out and corrected.

At high altitudes and velocities equal to or greater than the geosynchronous return velocity (10 kilometers per second), the shock layer of a hypersonic flight will be in thermochemical nonequilibrium and partially ionized. The amount of ionization is determined by the velocity. For a trans atmospheric flight of 10 kilometers per second and at an altitude of 80 kilometers, a maximum of 1% ionization is expected. At a velocity of 12 - 17 kilometer per second, such as a Mars return mission, up to 30% of the atoms and molecules in the flow field will be ionized. Under those circumstances, electrons play an important role in determining the internal states of atoms and molecules in the flow field and hence the amount of radiative heat load and the distance it takes for the flow field to re-establish equilibrium. Electron collisions provide an effective means of transferring energy even when the electron number density is as low as 1%. Because the mass of an electron is 12,760 times smaller than the reduced mass of N2, its average speed, and hence its average collision frequency, is more than 100 times larger. Even in the slightly ionized regime with only 1% electrons, the frequency of electron-molecule collisions is equal to or larger than that of molecule-molecule collisions, an important consideration in the low density part of the atmosphere. Three electron-molecule collision processes relevant to hypersonic flows will be considered: (1) vibrational excitation/de-excitation of a diatomic molecule by electron impact, (2) electronic excitation/de-excitation, and (3) dissociative recombination in electron-diatomic ion collisions. A review of available data, both theory and experiment, will be given. Particular attention will be paid to tailoring the molecular physics to the condition of hypersonic flows. For example, the high rotational temperatures in a hypersonic flow field means that most experimental data carried out under room temperatures are not applicable. Also, the average electron temperature is expected to be between 10,000 and 20,000 K. Thus only data for low energy electrons are relevant to the model.

Variational methods have proven invaluable in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. For collisional problems they can be grouped into two types: those based on the Schroedinger equation and those based on the Lippmann-Schwinger equation. The application of the Schwinger variational (SV) method to e-molecule collisions and photoionization has been reviewed previously. The present chapter discusses the implementation of the SV method as applied to e-molecule collisions.

Rotational inelastic transitions of N2 have been studied in the coupled state (CS, also called centrifugal sudden) and infinite-order-sudden (IOS) approximations, using the N2-N2 rigid-rotor potential of van der Avoird et al. For benchmarking purposes, close coupling (CC) calculations have also been carried out over a limited energy range and for even j - even j collisions only. Both the CC and CS cross sections have been obtained with and without exchange symmetry, whereas exchange is neglected in the IOS calculations. The CS results track the CC cross sections rather well. At total energies between 113 to 219 cm(exp -1) the average deviation is 14%. The deviation decrease with increasing energy, indicating that the CS approximation can be used as a substitute at higher energies when the CC calculations become impractical. Comparison between the CS and IOS cross sections at the high energy end of the CS calculation, 500 - 680 cm(exp-1), shows significant differences between the two. In addition, the IOS results exhibits sensitivity to the amount of inelasticity and the results for large DELTA J transitions are subjected to bigger errors. At total energy 113 cm(exp -1) and above, the average deviation between state-to-state cross sections calculated with even and odd exchange symmetries is 1.5%.

The electronic transition moment functions between the B(sup 3)Pi(sub g) and the A(sup 3)Sigma(sup +, sub u), W(sup 3)Delta(sub u), B'(sup 3)Sigma(sup -, sub u) states of N2 are studied using the internally contracted multireference configuration interaction (ICMRCI) method based upon complete active space SCF (CASSCF) reference wave-functions. The dependence of the moments on both the one and n-particle basis sets has been investigated in detail. The calculated radiative lifetimes for the vibrational levels of B(sup 3)Pi(sub g) are in excellent agreement with the most recent measurement of Euler and Pipkin (1983)

Using the N2-N2 intermolecular potential of van der Avoird et al. rotational energy transfer cross sections have been calculated using both the coupled state (CS) and infinite order sudden (IOS) approximations. The rotational energy transfer rate constants at 300 K, calculated in the CS approximation, are in reasonable agreement with the measurements of Sitz and Farrow. The IOS approximation qualitatively reproduces the dependence of the rate constants on the rotational quantum numbers, but consistently overestimates their magnitudes. The treatment of exchange symmetry will be discussed.

Current interest in clusters stems from their role as novel materials as well as a possible extension of cluster results to bulk systems. Experimental investigations on clusters have been carried out using laser spectroscopy, microwave spectroscopy, heavy-particle collisions, as well as electron collisions with earlier experimental work on electron attachment and ionization having been reviewed previously. Recently, Mark and coworkers studied the decay channels of cluster ions following electron impact ionization. Rauth et al. reported the formation of the superhalogen ion SF7(-) and other nonstoichiometric cluster ions in their study of electron attachment to SF6 clusters. Kresin et al. measured the absolute electron-impact depletion cross section of metal clusters Na8, Na(20), and Na(40). They found that the inelastic scattering cross section increased with cluster size and was considerably greater than the hard sphere collision cross sections. They hypothesized that electron attachment and collision-induced fragmentation were the dominant physical processes responsible for this effect. For the two smaller clusters, they also found a sharp increase in the cross section near threshold. Most theoretical studies of clusters have been devoted to their electronic structures, vibrational relaxation, and predissociation while investigations of electron scattering from clusters has been lacking. In view of this, we recently undertook an ab initio study of electron scattering from small Be clusters and BeCO. Beryllium was chosen because it is readily amenable to ab t'nitio calculations. Moreover, the electronic structure of Be clusters has been studied extensively, showing that the Be-Be bond is relatively weak in comparison with a normal chemical bond. Our investigation focuses on how the cross sections change with cluster size and geometry. The range of energy studied, 0.05 - 5.0 eV, is chosen because of the ubiquitous resonance in the low-energy scattering of Be. Hence it can be determined if it is possible, as a consequence of the weaker bonds in the Be clusters, to identify the atomic origin of the cluster resonance.

Results are presented of an experimental study of (2+1) resonance-enhanced multiphoton ionization (REMPI) detection of H2, HD, and D2 via the E,F two-photon transition, in which the relationship between ion signals and quantum-state populations was determined by calibration against a thermal effusive source. Vibrational and rotational correction factors were obtained for 102 rovibrational levels for v-double-prime = 0, 1, and 2 and for J-double-prime ranging from 0 to 17. These correction factors make it possible to convert ion signals into relative quantum-state populations without relying on a theoretical description of the (2+1) REMPI process.

This paper reports a theoretical study of the dependence of the E 1Sigma(+)g v(E) = 0, J-X 1Sigma(+)g, v(X),J transitions in H2, HD, and D2 on the initial vibrational and rotational quantum numbers v(X) and J. The results demonstrate the concerted nature of two-photon transitions. The magnitude of the two-photon transition moment increases with v(X) between 0 and 2, then decreases rapidly at higher v(X). The J dependence of the two-photon transition moment is most strongly affected by the changes in vibrational wave functions caused by centrifugal distortion of the vibrational potential. It is shown that the J variation can be used as a probe of resonant tunneling in the double-well potential of the E,F state.

The vibrational excitation/deexcitation of vibrationally and rotationally hot N2 by electron impact, pertinent to the reactions in the flow field around a hypersonic space vehicle entering the planetary atmosphere, is calculatively investigated. It is found that the resonance position shifts to a lower energy when N2 is rotationally hot. Electron impact excitations between electronic excited states of N2 are studied using a multichannel treatment. The results show that the assumption that excited-excited cross sections are the same as ground-excited ones, and result in the same final state, is invalid. A more reliable set of data on N2 is provided.

The Chi 1Sigma - b 3Sigma(+) transition of CO is described using the Schwinger multichannel method in the two-state approximation, in an energy range from threshold to 20 eV. The resonance structure is analyzed by performing a partial-wave decomposition and the resonance positions are established based on the typical discontinuous behavior in the K-matrix elements as well as the pi radian change in the partial-wave eigenphases. The resonance behavior is related to the concept of core-excited resonances and the 'grandparent' model of resonances. The results are related to the formation of the negative ion by carrying out bound-state calculations on the (5 sigma)(3 s sigma)-squared core-excited Rydberg state of CO(-), and the position is found to agree well with the low-energy resonance positions.