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Volume 90, Issue 5, 01 March 1989

Interatomic potentials for van der Waals complexes of group 13 metal atoms: InAr, InKr, and InXe
View Description Hide DescriptionFluorescence excitation and emission spectra of the van der Waals molecules InAr, InKr, and InXe, formed by laser vaporization of a metal target followed by supersonic expansion, have been recorded. Observed vibrational progressions indicate that the interatomic potentials for the X ^{2}Π_{1/2,3/2} and B ^{2}Σ^{+} states can be approximated by Morse functions. Isotopic splittings are observed in the excitation spectra and allow the vibrational numbering in the excited B ^{2}Σ^{+} state to be assigned. The dissociation energies of the three states are estimated for each molecule and are found to correlate well with the rare gas polarizabilities.

The benzene ground state potential surface. III. Analysis of b _{2u } vibrational mode anharmonicity through two‐photon intensity
View Description Hide DescriptionThe 15^{0} _{1}/14^{0} _{1} vibronic two‐photon cross section ratios are reported for a series of isotopically labeled benzenes in the Ã(^{1} B _{2u })←X̃(^{1} A _{1g }) electronic transition. Predictions derived from the B _{2u } force field are found to be in close agreement with the measured ratios. These ratios are shown to provide an excellent test of the B _{2u } force field and mode forms as evidenced by the large variation over D _{6h } labeled benzenes. In C_{6}H_{6} the 15^{0} _{1}/14^{0} _{1} cross section ratio is measured as 0.249±0.008 (equivalent to 0.180 for the theoretically testable ratio: 15^{0} _{1}/14^{0} _{1}[〈1‖Q _{1} _{4}‖0〉/〈1‖ Q _{1} _{5}‖0〉]^{2}). The corresponding ratio in ^{1} ^{3} C_{6}H_{6} is 0.44±0.04 (equivalent to 0.36). The 13% disparity found between the measured and predicted C_{6}H_{6} ratio (i.e., 0.206) is attributed to anharmonic coupling between the b _{2u } modes: 2χ_{15,15}=−9, χ_{14,15}=4, and 2χ_{14,14}=−4 cm^{−} ^{1}. Two‐photon intensities are proven to be useful in determining anharmonic interactions. The relatively small effects of the hydrogen motion provide an approach for solving the bifurcated B _{2u } force constant problem in ground state benzene. The approach utilizes the contribution of harmonic C–C–H bending motions to the two‐photon tensor controlling the 15^{0} _{1} and 14^{0} _{1} vibronic cross sections. This requires knowledge of the sign of the hydrogen motion term in the tensor. However, large anharmonic effects coupling the two b _{2u } modes mask the small harmonic hydrogen contribution.

Time dependent calculations of the absorption spectrum of a photodissociating system with two interacting excited electronic states
View Description Hide DescriptionWe use a time dependent method for solving the Schrödinger equation to calculate the photon absorption cross section for the photodissociation of a model H^{+} _{3} system. The coupling V between the excited states is found to alter the absorption cross section if the time scale ℏ/V is less than the dissociation time. The influence of the relative orientation of the transition dipoles, on the absorptionspectrum, is also investigated.

Rotational branching ratios at low photoelectron energies in resonant enhanced multiphoton ionization of NO
View Description Hide DescriptionWe report calculated rotational branching ratios for very low energy (50 meV) photoelectrons resulting from (1+1’) resonant enhanced multiphoton ionization (REMPI) via the J _{ i } =1/2, 3/2, 5/2, and 7/2 levels of the P _{11} branch of the A ^{2}Σ^{+} (3sσ) state of NO. Even angular momentum transfer (ΔN≡N _{+}−N _{ i }) peaks are dominant in these rotational distributions, in agreement with the selection rule ΔN+l=odd. Angular momentum coupling in the photoelectron wave function arising from the molecular ion potential leads to smaller but appreciable ΔN=odd peaks. The calculated ΔN=0 to ΔN=+2 peak ratios show the same strong decrease when J _{ i } increases from 1/2 to 3/2 as seen in the experimental zero‐kinetic‐energy (ZEKE) photoelectron spectra [Sander e t a l., Phys. Rev. A 3 6, 4543 (1987)], but do not show the rapid die‐off of the ΔN≠0 peaks for higher J _{ i } observed experimentally. The calculated trend in the ΔN=+2 vs ΔN=0 peaks could be understood on the basis of simple angular momentum transfer arguments. These same arguments indicate that this trend in the ΔN=0 and +2 peaks with increasing angular momentum is not generally expected in other branches. Spectra via the R _{21} ( J) branch are presented to support this assertion. We also present photoelectron angular distributions which show a strong dependence on ΔN reflecting the changing composition of the photoelectron wave function.

Shape resonance behavior in 1π_{ g } photoionization of O_{2}
View Description Hide DescriptionWe report calculations of vibrationally resolved cross sections and photoelectron angular distributions for photoionization of O_{2} leading to the X ^{2} Π_{ g } (ν^{+} =0–4) states of O^{+} _{2} using Hartree–Fock continuum photoelectron orbitals. These studies were motivated by recent results which show that a σ_{ u } shape resonance plays a dominant role in producing non‐Franck–Condon vibrational distributions in resonantmultiphoton ionization of O_{2} via the C ^{3}Π_{ g } (1π_{ g }3sσ_{ g }) Rydberg state. In the present study, we investigate how this shape resonance influences photoionization dynamics in single‐photon ionization. Below 21 eV photon energy, we find significant non‐Franck–Condon effects in the vibrational branching ratios as well as in the vibrationally resolved photoelectron angular distributions. Substantial autoionization hinders a direct comparison between theory and experiment.

Observation of l‐dependent rate constants for ion production in Rydberg electron transfer reactions
View Description Hide DescriptionRelative rate constants for negative ion production have been measured for the Rydbergelectron transferreactions Cs**(n s,n p,n d) +SF_{6}→Cs^{+}+SF^{−} _{6} and Cs**(n s,n p,n d) +CCl_{4}→Cs^{+}+Cl^{−}+CCl_{3}. We find that rate constant for production of Cl^{−} from CCl_{4} are dependent upon the angular momentum of the Rydberg electron, with k _{ n d }>k _{ n s } for values of n as large as 40. Preliminary measurements for potassium (n s,n d) Rydberg atoms show that the l dependence for K is much smaller than that for Cs. These results are inconsistent with the ‘‘free electron model’’ used to describe these reactions. It is suggested that the observed l dependence is related to postattachment interactions with the Rydberg atom core which affect the survival of the Cl^{−} ions.

Ionization and temperature dependent attachment cross section measurements in C_{3}F_{8} and C_{2}H_{3}Cl
View Description Hide DescriptionTotal ionization and attachment cross sections have been measured in C_{3}F_{8} at 330 K using an electron beam and a total ion collection technique, calibrated by similar measurements on N_{2}O and Xe. Our total ionization cross section is similar in general shape to a previous measurement of this type, but with typically half the magnitude. The ionization threshold cannot be accurately derived from these measurements, due to severe upward curvature immediately above threshold. The positive‐ion signal rises above the background at 13.0±0.1 eV, to be regarded as a lower limit to the true threshold. An overall ionization cross section with a threshold at 13.3 eV is recommended, based on threshold data from photoelectron spectroscopy and the present data between 14 and 80 eV. The room temperature total attachment cross section peaks at 2.8 eV with a value of 1.75×10^{−} ^{1} ^{7} cm^{2}. This is 14 times smaller than the only other measurement of this type we are aware of. There is much better agreement with two more recently reported values unfolded from swarm experiments. The temperature dependence of the predominant dissociative attachment process, involving F^{−} production, was studied in a different apparatus using a mass filter and ion pulse counting. At 730 K the peak cross section has increased by ∼60% and the threshold is lower by 1.1 eV. This second type of measurement was used to study the predominant dissociative attachment process in C_{2}H_{3}Cl, involving Cl^{−} production. At 290 K this has a threshold at 0.85 eV and a peak at 1.35 eV of 3.2×10^{−} ^{1} ^{7} cm^{2}, in good agreement with recent work elsewhere. At 850 K the cross section at the peak is 2.6 larger, and lower in energy by 0.33 eV, while at 0 eV it has reached 6×10^{−} ^{1} ^{8} cm^{2}. At higher temperatures effects ascribed to thermal dissociation of the C_{2}H_{3}Cl were observed. The implications of the present results regarding the use of these gases in diffuse discharge switches are discussed.

Use of the discrete variable representation in the quantum dynamics by a wave packet propagation: Predissociation of NaI(^{1}Σ^{+} _{0}) →NaI(0^{+})→Na(^{2} S)+I(^{2} P)
View Description Hide DescriptionUsing the Gauss–Chebyshev discrete variable representation (DVR), the dissociative quantum dynamics for a wave packet evolving under the influence of the Hamiltonian for two interacting diabatic states of a diatomic molecule is calculated. The split time evolution operator method is used to obtain the solutions to the time‐dependent Schrödinger equation. A specific example of the numerical calculation is shown for the predissociation process of NaI→Na(^{2} S)+I(^{2} P) from its first excited electronic state (0^{+}). The numerical results are compared with the experimental observations from the femtosecond laser photofragmentation, recently reported by Zewail and co‐workers.

Product state distributions for the vibrational predissociation of NeCl_{2}
View Description Hide DescriptionProduct state distributions are reported for the vibrational predissociation of the NeCl_{2}, B state, v’=6 through v’=13 levels. For the lower vibrational levels, Δv=−1 dissociation produces a bimodal Cl_{2} product rotational state distribution with the first maximum at j=4 and a secondary maximum at j=20. Surprisingly, the positions of these maxima are the same for v’=6, 7, 8, 9, and 10. For higher vibrational levels the limited available phase space constricts the observed rotational distribution allowing the Ne–Cl_{2} bond energy D _{0} to be determined. D _{0} is 54±2 cm^{−} ^{1} for the B electronic state, and 60±2 cm^{−} ^{1} for the ground electronic state. Δv=−2 dissociation produces a rotational distribution which, although not bimodal, is otherwise quite similar to that of the Δv=−1 channel, even though significantly more energy is released to product translation for Δv=−2. This behavior is quite different from what would be predicted by an impulsive half‐collision model for the dynamics. Three dimensional quantum calculations on a simple atom–atom potential energy surface were able to reproduce most of the essential features of the experimental results. We conclude that the anisotropy of the initial wave function and that of the coupling between the covalent and van der Waals modes is more important in determining the product rotational distribution than is the kinematics of the dissociation trajectory. Since the rotational distribution produced by the Δv=−2 channel is similar to that of the Δv=−1 channel, the Δv=−2 dynamics probably occurs by a direct coupling between the quasibound state and the continuum rather than by a sequential mechanism with two Δv=−1 steps.

State resolved cross sections for rotationally inelastic collisions of NH_{2}(X̃ ^{2} B _{1}) with helium
View Description Hide DescriptionIntegral cross sections for rotational transitions from the lowest orthorotational level (0_{0,0}) of NH_{2} induced by collisions with helium have been measured in a crossed beam experiment. A pulsed supersonic beam of rotationally cold NH_{2} was produced by 193 nm photolysis of a dilute mixture of ammonia in argon seed gas at the tip of a nozzle; the helium target was also prepared as a pulsed beam. The final rotational state populations (without spin‐state resolution) in the K _{ a }=0 and 1 manifolds of NH_{2} were interrogated in the collision zone by dye laserfluorescence excitation in the Ã ^{2} A _{1}←X̃ ^{2} B _{1} band system. Because of the rotational selection rules in this band system, it was not possible to put the cross sections for the two K _{ a }manifolds on the same scale. Within a given K _{ a }manifold, there is a marked preference for collisional transitions with the smallest ΔN change. These experimental results are compared to calculated close‐coupling rotationally inelastic cross sections for H_{2}O(0_{0,0})–He collisions.

Variation with temperature of the electron attachment to SO_{2}F_{2}
View Description Hide DescriptionThe total electron attachment rate constant k _{ a }(〈ε〉,T) for SO_{2}F_{2} has been measured, in a buffer gas of N_{2}, as a function of the mean electron energy 〈ε〉 (0.046–0.911 eV) and temperature T (300–700 K) using an electron swarm technique. From the measured k _{ a }(〈ε〉,T), the total electron attachment cross sections σ_{ a }(ε,T) were determined. At 300 K the σ_{ a }(ε,T) exhibits a maximum at ∼0.22 eV which is due to dissociative electron attachment and an increase below ∼0.1 eV which is due to the formation of parent negative ions SO_{2}F^{−} _{2} at near zero energy. At T=400 K, σ_{ a }(ε,T) has only one main peak at ∼0.13 eV which is due only to dissociative electron attachment reflecting the depletion of the parent anions and the prevalence of the fragment negative ions as T increases. The main peak of σ_{ a }(ε,T) shifts to lower electron energies with increasing T so that at 700 K the peak is located at ∼0.03 eV. The value, σ_{ d a }(ε_{max}), of the total electron attachment cross section at the peak energy ε_{max} increases by a factor of ∼32 as T increases from 300 to 700 K. The analysis of these results—and similar earlier work—leads to the conclusion that the increase in σ_{ d a }(ε,T) for the dissociative electron attachment processes in molecules, with increasing T results mainly from an increase with T of the internal energy (principally vibrational) of the molecule.

Photofragment angular distributions for HF dimer: Scalar J–J correlations in state‐to‐state photodissociation
View Description Hide DescriptionPhotofragment angular distributions have been measured for HF dimer which show resolved structure that can be assigned to individual fragment rotational channels. This data is used to establish intermolecular scalar correlations between the rotational states of the two HF fragments. The observed angular distributions are strongly dependent upon whether the ‘‘free’’ or ‘‘hydrogen bonded’’ HF stretch is initially excited. Since the infrared spectrum of the parent molecule is highly resolved, these results can be used to determine the relative state‐to‐state photodissociation cross sections. In addition, the zero point dissociation energy (D _{0} ) of the HF dimer is accurately determined.

A test of recently proposed He–N_{2} interactions: Angular distributions and rotationally inelastic collisions
View Description Hide DescriptionThree recently proposed anisotropicpotential energy surfaces (PES) for the He+N_{2} (^{1}Σ_{ g }) system are employed to compute differential scattering cross sections, total and state‐to‐state rotationally inelastic, at two collision energies for which accurate molecular beam experiments are already available. The experiments have provided scatteringangular distributions which resolved, in one case, rotational energy losses (at 27.7 meV) and which, in the other case, were able to yield only total differential cross sections (at 70.4 meV). Rigorous close‐coupling (CC) calculations at both energies are compared with IOSA (infinite order sudden approximation) results and with the experimental data. The ensuing discussion shows that only one PES, the recently proposed M3SV form, appears to have the correct anisotropic behavior in agreement with all experimental data.

Dissociative photoionization of N_{2}O: Analytical photoion spectroscopy
View Description Hide DescriptionBranching ratios of ions produced from the dissociativephotoionization of N_{2}O have been measured by using a time‐of‐flight mass spectrometer and synchrotron radiation in the 15–36 eV region. The branching ratios in the Franck–Condon gap (15.0–16.4 eV) indicate that the autoionizing Rydberg states in this region predissociate to NO^{+} and O^{+} through various dissociative states. The results obtained by the analytical photoion spectroscopy above the gap show dissociation pathways of the N_{2}O^{+} ions. These pathways are discussed by comparing with the reported electronic states of ions and super excited neutrals.

Adiabatic time evolution of atoms and molecules in intense radiation fields
View Description Hide DescriptionWe derive the condition for a time dependent quantum system to exhibit an exact or higher order adiabatic time evolution. To this end, the concept of adiabaticity is first analyzed in terms of the transformation properties of the time‐dependent Schrödinger equation under a general unitary transformation Û(t). The system will follow an adiabatic time evolution, if the transformed Hamiltonian, K̂(t)=Û^{°} ĤÛ−iℏÛ^{°} Û, is divisible into an effective Hamiltonian ĥ(t), defining adiabatic quasistationary states, and an interaction term Ω̂(t), whose effect on the adiabatic states exactly cancels the nonadiabatic couplings arising from the adiabatic states’ parametric dependence on the time. This decoupling condition, which ensures adiabaticity in the system’s dynamics, can be expressed in a state independent manner, and governs the choice of the unitary operator Û(t), as well as the construction of the effective Hamiltonian ĥ(t). Using a restricted class of unitary transformations, the formalism is applied to the time evolution of an atomic or molecular system in interaction with a spatially uniform electromagnetic field, and gives an adiabatic approximation of higher order to the solutions of the semiclassical Schrödinger equation for this system. The adiabatic approximation so obtained exhibits two properties that make it suitable for the studies of intense field molecular dynamics: It is valid for any temporal profile of the field, and improves further as the field intensity increases, as reflected in the weakening of the associated residual nonadiabatic couplings with increasing field strength.

Recombination of electron–ion pairs for arbitrary mean free path
View Description Hide DescriptionA theory is developed of the dependence of the steady‐state electron–ion pair recombination rate constant on the electron mean free path. The problem, in classical mechanics, is reduced to the stochastic dynamics of the electron in the one‐dimensional effective potential Ṽ(R)=−k T R _{ c }/R −2k T ln R. R _{ c } is the Onsager length Z e ^{2}/4πεk T. For a large mean free path λ, the recombination rate is determined by energy relaxation of electrons which cross the transition state of Ṽ(R) at R _{ T }=R _{ c }/2, whereas for small λ the Debye result for spatial diffusion‐controlled recombination is obtained. The theory gives the dependence of the rate in the crossover regime where λ is comparable to R _{ c }. The results are in good agreement with experiment and Monte Carlo simulations.

Rotationally induced vibrational mixing in formaldehyde
View Description Hide DescriptionAlmost‐degenerate perturbation theory is used to derive an effective Hamiltonian describing the vibrational states of H_{2}CO. Eigenvalues have been determined for energies up to 8600 cm^{−} ^{1} above the zero‐point energy. Both curvilinear and rectilinear representations of the vibrational dynamics are presented and explored. Although differences are observed between the two effective Hamiltonian matrix elements, their eigenvalues generally agree to better than a wave number for the energies studied. Using the Watson Hamiltonian, the mechanism of rotationally induced vibrationally mixing is investigated as a function of K, the projection of the total angular momentum onto the body‐fixed a axis. The combination of a‐axis Coriolis coupling and Fermi couplings leads to extensive vibrational mixing between the rotational–vibrational states in this energy regime.

Vibrational predissociation of He–I_{2}*(v)–Ne: An approximate quantal study
View Description Hide DescriptionThe vibrational predissociation (VP) of the He–I_{2}(B ^{3}Π_{0} ^{+} _{ u },v)–Ne complex is studied in the range of initial vibrational excitations 25≤v≤35. The rare gas atoms are restricted to move on a perpendicular plane to the I_{2} axis. A simple addition of pairwise Morse atom–atom interactions is used to describe the potential energy surface. The breaking up of the I_{2}–Ne bond is found to be the dominant dissociation channel for v≤29. However, due to the anharmonicity of the I_{2} stretch, the situation for v>29 is just the opposite and the He atom escapes first.

Velocity‐aligned Doppler spectroscopy
View Description Hide DescriptionThe technique of velocity‐aligned Doppler spectrosocopy (VADS) is presented and discussed. For photolysis/probe experiments with pulsed initiation, VADS can yield Doppler profiles for nascent photofragments that allow detailed center‐of‐mass (c.m.) kinetic energy distributions to be extracted. When compared with traditional forms of Doppler spectroscopy, the improvement in kinetic energy resolution is dramatic. Changes in the measured profiles are a consequence of spatial discrimination (i.e., focused and overlapping photolysis and probe beams) and delayed observation. These factors result in the selective detection of species whose velocities are aligned with the wave vector of the probe radiation k _{pr}, thus revealing the speed distribution along k _{pr} rather than the distribution of nascent velocity components projected upon this direction. Mathematical details of the procedure used to model VADS are given, and experimental illustrations for HI, H_{2}S, and NH_{3}photodissociation are presented. In these examples, pulsed photodissociation produces H atoms that are detected by sequential two‐photon, two‐frequency ionization via Lyman‐α with a pulsed laser (121.6+364.7 nm), and measuring the Lyman‐α Doppler profile as a function of probe delay reveals both internal and c.m. kinetic energy distributions for the photofragments. Strengths and weaknesses of VADS as a tool for investigating photofragmentation phenomena are also discussed.

Renormalization‐group approach to the metal–insulator transition in doped semiconductors
View Description Hide DescriptionIn order to calculate the critical concentration for the metal–insulator transition in dopedsemiconductors, we study a model of randomly positioned interacting hydrogenic atoms within the one‐electron approximation. We calculate approximate eigenfunctions for the system with the standard linear combination of atomic orbital variation method, considering explicitly the nonorthogonality of hydrogenic 1s orbitals. We then compute the correlation length using the concept of quantum connectivity, which we developed to study the localization transition in other disordered quantum‐mechanical models. Finally, we employ a finite‐size scaling analysis to determine the critical impurity concentrationn _{ c }. If the isolated impurities have a Bohr radius a, then we find that R _{ c }≡n ^{1/3} _{ c } a=0.250±0.011, which is in good agreement with experiment (R _{ c }=0.26±0.05).