David A. Micha

A self‐consistent eikonal treatment of electronic transitions in molecular collisions

We develop an eikonal treatment of electronic transitions in many‐atom collisions, in which classical nuclear trajectories are self‐consistently coupled to quantal electronic transitions. The treatment starts with a discussion of the electronic representations required to assure that Hamiltonian matrices are Hermitian. The amplitudes of wave functions are found to satisfy coupled equations which are expanded in powers of a local de Broglie wavelength. Time‐dependent equations are transformed to derive a Hamiltonian formalism that couples nuclear positions and momenta with electronic amplitudes. Cross sections are obtained from flux conservation and also from T‐matrix elements.

Long‐Range Casimir Forces: Theory and Recent Experiments on Atomic Systems

An Overview of LongRange Casimir Interactions L. Spruch. Experimental Studies of High-L Rydberg States in Helium S.R. Lundeen. High Precision Calculations for the Rydberg States of Helium G.W.F. Drake. High Rydberg States of Two-Electron Atoms in Perturbation Theory R.J. Drachman. Long-Range Electromagnetic Forces in Quantum Theory J. Sucher, G. Feinberg. Index.

The linearly driven parametric oscillator: Application to collisional energy transfer

The time‐evolution operator is explicitly constructed for a general linearly driven parametric quantum oscillator, equivalent to a harmonic oscillator driven by linear plus quadratic potentials. The method is based on an algebra of operators which are bilinear in the position and momentum operators, and form a closed set with respect to commutation. The obtained result requires only integrals over time and the solution of two coupled first order linear differential equations related to the classical equations of motion. The model is used to obtain vibration‐translation probabilities in a collinear collision of an atom with a diatomic molecule. Numerical calculations have been performed for systems with several mass combinations and potential parameters. Approximation methods are compared, and criteria are established to determine when it is necessary to go beyond the popular linearly driven harmonic oscillator.

Erratum: Variational Methods in the Wave Operator Formalism. A Unified Treatment for Bound and Quasibound Electronic and Molecular States

The wave operator formalism of Lowdin, heretofore used to describe states belonging to the discrete energy spectrum, has been extended to unify the treatment of bound and quasibound (or decaying) states. The approach makes use of an arbitrary reference function that may be chosen to approximate the physical state at short distances. Real and complex eigenvalues are obtained, respectively, for bound and quasibound states from an implicit equation, valid for all coupling strengths. Resonance positions and linewidths are explicitly independent of energy. Variational principles of the Lippmann—Schwinger type are presented which apply to states with either bound‐state or decay boundary conditions. Particular cases leading to minimization or maximization principles for real energies are discussed. The formalism is considered in connection with decaying electronic states of atoms and decaying molecular states.

Quantum Dynamics of Complex Molecular Systems

I. Complex Molecular Phenomena.- I.1 Condensed Matter and Surface Phenomena.- Photoexcitation Dynamics on the Nanoscale: O. Prezhdo, W.R. Duncan, C.F. Craig, S.V. Kilina, and B.F. Habenicht.- Ultrafast Exciton Dynamics in Molecular Systems: B. Bruggemann, D. Tsivlin, and V. May.- Exciton and Charge Transfer Dynamics in Polymer Semiconductors: E.R. Bittner and J.G.S. Ramon.- Dynamics of Resonant Electron Transfer in the Interaction Between an Atom and a Metallic Surface: J.P. Gauyacq and A.G. Borisov.- I.2 From Multidimensional Dynamics to Dissipative Phenomena.- Nonadiabatic Quantum Dynamics at Symmetry-Allowed Conical Intersections: H. Koeppel.- Non-Markovian Dynamics at a Conical Intersection: Ultrafast Excited-State Processes in the Presence of an Environment: I. Burghardt.- Density Matrix Treatment of Electronically Excited Molecular Systems: D.A. Micha, A. Leathers, and B. Thorndyke.- Quantum Dynamics of Ultrafast Molecular Processes in a Condensed Phase Enviroment.- M. Thoss, I. Kondov, and H. Wang.- II. New Methods for Quantum Molecular Dynmaics in Large Systems.- II.1 Semiclassical Methods.- Decoherence in Combined Quantum Mechanical and Classical Mechanical Methods for Dynamics as Illustrated for Non-Born-Oppenheimer Trajectories: D. Truhlar.- Time-Dependent, Direct, Nonadiabatic, Molecular Reaction Dynamics: Y. Ohrn and E. Deumens.- The Semiclassical Initial Value Series Representation of the Quantum Propagator: E. Pollak.- II.2 Mixed Quantum-Classical Statistical Mechanics Methods.- Quantum Statistical Dynamics With Trajectories: G. Ciccotti, D.F. Coker, and R. Kapral.- Quantum-Classical Reaction Rate Theory: G. Hanna, H. Kim, and R. Kapral.- Linearized Non-Adiabatic Dynmaics in the Adiabatic Representation: D.F. Coker and S. Bonella.- II.3 Quantum Trajectory Methods.- Atom-Surface Diffraction : A Quantum Trajectory Description: A.S. Sanz and S. Miret-Artes.- Hybrid Quantum /Classical Dynamics Using Bohmian Trajectories: C. Meier and J.A. Beswick.- Quantum Hydrodynamics And a New Approach to Mixed Quantum-Classical Theory: I. Burghardt, K.B. Moller and K.H. Hughes

Atom–polyatomic collisions: A many‐body approach

We present an approach to atom–polyatomic collisions that takes into account the quantum nature of the polyatomic motion, but avoids expansions in target states by instead describing the target as a many‐atom system. Following a discussion of interaction potentials, kinematics, and the general scattering formalism, we introduce two basic assumptions that lead to useful expressions for differential cross sections. The treatment is specialized to quasielastic scattering, of interest in the interpretation of experiments. This study shows that the atomic‐pair correlation functions of the target play a central role in determining collisional energy and momentum transfer.

Interaction of atoms with solid surfaces: Energy transfer in hyperthermal collisions of Li+ with W(110)

A recently developed many‐body approach to atom–polyatomic collisions at hyperthermal energies is applied to scattering of light ions by metal surfaces. Following a brief description of the scattering model, which can in principle describe surface diffraction, surface rainbows, and phonon excitation, we concentrate on energy transfer processes. Cross sections are related to atom–pair correlation functions of the target surface, which are expressed in terms of the normal vibrational modes of a solid slab. The correlation functions are calculated within a short‐time expansion which gives Gaussian distributions for energy transfer probabilities. A simple surface model of Einstein anisotropic oscillators is worked out in detail. Results of calculations for scattering of Li+ by W(110) at kinetic energies of several eV show good agreement with experimental values of most probable final energies and of distribution widths for several angles and initial ion energies.

Transition operators for atom–atom potentials: The Hilbert–Schmidt expansion

Transition operators 〈p‖t (e) ‖p′〉 with p≠p′≠√2me, required in collisions of atoms with bound atoms, are investigated and calculated within the Hilbert–Schmidt expansion. We have expanded in the eigenvalues and eigenfunctions of the kernel of the Lippmann–Schwinger equation, to obtain t operators for a Morse potential describing the ground 1Σ potential of H2, and for a repulsive Hulthen potential representing the lowest 3Σ potential of H2. Studies made at negative energies e, required for inelastic and reactive processes below the dissociation threshold of the target, show that the expansion for the Morse potential is rapidly convergent, and that the relative magnitude of the + operator for the Hulthen potential is at least 1 order of magnitude smaller. Results are presented for momenta and energies appropriate to reactive collisions at energies just above the saddle‐point energy of the H3 potential surface.

Collision dynamics of three interacting atoms: Stripping reactions of Ar++H2 and of K+I2

Equations for stripping reaction cross sections, obtained from a multiple‐collision expansion for triatomic systems, are applied to Ar++H2 → ArH++H and its isotopic substitutions, and to K+I2 → KI+I. The equations involve the momentum distributions of reactant and product molecules, and are considered for mechanisms where stripping begins either before or after electron transfer, for both systems. Calculations of forward velocity distributions, product angular and energy distributions, isotope ratios, and total cross sections for Ar++H2 are in over‐all agreement with experiments and indicate that stripping begins after electron transfer in these systems. Comparison with experiment of calculated product angular and energy distributions and forward velocity distrubutions for K+I2 favors a mechanism where a vertical electron transfer occurs first, with simultaneous partial vibrational relaxation of I−2, followed then by stripping. Discrepancies remain however for K+I2, suggesting some contribution from other...

Coulomb interactions in nuclear and atomic few-body collisions

Collision Theory for Two and Threeparticle Systems Interacting via Shortrange and Coulomb Forces E. Alt, W. Sandhas. Proton-Deuteron Scattering and Reactions J. Friar, J. Payne. Timedependent Scattering in Coulombic Fewbody Systems and the Strong Operator Approximation Method H. Kroeger. H Spectroscopy H. Bryant, M. Halka. Coulomb Forces in Threeparticle Atomic and Molecular Systems J. Briggs. Index.