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Full-Text Articles in Physics
Theory Of Near-Adiabatic Collisions. Ii. Scattering Coordinate Method, W. R. Thorson, John B. Delos
Theory Of Near-Adiabatic Collisions. Ii. Scattering Coordinate Method, W. R. Thorson, John B. Delos
Arts & Sciences Articles
A rigorously correct and fully quantum-mechanical theory of slow atomic collisions is presented, which removes the formal defects and spurious nonadiabatic couplings of perturbed-stationary-states theory, and arrives at coupled equations for the heavy-particle motion which are the same as those obtained in the preceding paper by the electron translation factor formulation. Here, however, the theory is formulated in terms of suitably defined scattering coordinates, and electron translation factors do not appear. A unified physical interpretation of both approaches can thereby be made, and smaller terms in the coupled equations, describing corrections of order mμ to electronic binding energies and to …
Theory Of Near-Adiabatic Collisions. I. Electron-Translation-Factor Method, W. R. Thorson, John B. Delos
Theory Of Near-Adiabatic Collisions. I. Electron-Translation-Factor Method, W. R. Thorson, John B. Delos
Arts & Sciences Articles
The theory of near-adiabatic collisions is formulated in a fully quantum-mechanical form, correctly taking into account the role of electron translation factors (ETF's). A general form for the ETF, using switching functions, is given for systems which are electrically either asymmetric or symmetric (with or without mass asymmetry). The main result is that the close-coupled scattering equations obtained in the perturbed-stationary-states theory must be replaced by equations of identical form, but having modified nonadiabatic coupling matrices. In general, the corrections involved are substantial; their nature, and effect on coupling matrices, is discussed, and conditions when they are likely to …
Generalization Of The Rosen-Zener Model Of Noncrossing Interactions. I. Total Cross Sections, T. R. Dinterman, John B. Delos
Generalization Of The Rosen-Zener Model Of Noncrossing Interactions. I. Total Cross Sections, T. R. Dinterman, John B. Delos
Arts & Sciences Articles
The formalism developed previously to study electronic transitions by the curve-crossing mechanism is used to obtain a general model for transitions which take place due to the strong coupling of curves which do not cross. This exactly solvable model is a generalization of a model developed by Rosen and Zener. The model is shown to give respectable agreement with exact calculations at low velocities, and to go to the correct resonant-charge-exchange limit at high velocities. Predictions of the model are shown to give good agreement with the measured total cross sections for charge exchange in the sytem Li+ + Na⇄Li+Na+.
Generalization Of The Rosen-Zener Model Of Noncrossing Interactions. Ii. Differential Cross Sections., T. R. Dinterman, John B. Delos
Generalization Of The Rosen-Zener Model Of Noncrossing Interactions. Ii. Differential Cross Sections., T. R. Dinterman, John B. Delos
Arts & Sciences Articles
The generalized Rosen-Zener model developed in the accompanying paper is used to calculate differential cross sections for a model noncrossing system, and the structure of the cross sections is explained in terms of the deflection functions. It is found that the angular threshold effects that are typical of potential-curve crossings do not appear in this noncrossing system.
Semiclassical Calculation Of Regge Poles, John B. Delos, C. E. Carlson
Semiclassical Calculation Of Regge Poles, John B. Delos, C. E. Carlson
Arts & Sciences Articles
We have calculated the locations of the Regge poles for an actual interatomic potential by following the semiclassical formulation. For negative energies, this formulation is equivalent to the Bohr-Sommerfeld quantization condition. For positive energies there are three complex turning points; use of linear and parabolic connection formulas yields a semiclassical quantization condition for the poles. The poles are found to lie symmetrically along lines in the first and third quadrants of the angular-momentum plane. The locations of the poles at a given energy and the motion of these poles as the energy changes are presented. Remler has shown that Regge …
Electron Detachment In Low-Energy Collisions Of H- And D- With He, S. K. Lam, John B. Delos, L. Champion, L. D. Doverspike
Electron Detachment In Low-Energy Collisions Of H- And D- With He, S. K. Lam, John B. Delos, L. Champion, L. D. Doverspike
Arts & Sciences Articles
Measurements and calculations have been made of elastic scattering and electron detachment in collisions of H− and D− with He at energies of 5-120 eV. The measurements show no other inelastic processes occurring in this energy range. The mechanism responsible for electron detachment is assumed to be the crossing of the H− bound state with the continuum of free states; the bound state is then assigned a complex energy. The measured elastic scattering differential cross section shows no structure except at Eθ∼200 eV deg, where there is a region of downward curvature in the graph of logσ vs θ. This …
Studies Of The Potential Curve Crossing Problem. Iii. Collisional Spectroscopy Of Close Crossings, John B. Delos
Studies Of The Potential Curve Crossing Problem. Iii. Collisional Spectroscopy Of Close Crossings, John B. Delos
Arts & Sciences Articles
Using a previously developed semiclassical theory of electronic excitations, the cross sections that result from potential-curve crossings are calculated for a model system. The phenomena appearing in the differential cross sections are displayed and discussed.
On The Reactions Of N2 With O, John B. Delos
On The Reactions Of N2 With O, John B. Delos
Arts & Sciences Articles
Unimolecular decomposition of N2O, quenching of O(1D) by N2, and vibrational relaxation of N2 in the presence of O(3P) are all believed to occur by the same curve crossing mechanism. This mechanism is examined making use of a complete theory of curve crossings that we have developed earlier. Good agreement with experiment is found for the unimolecular decomposition rate. The simple curve crossing mechanism does not explain the observed O(1D) quenching rate; this rate must be due to complex formation and/or additional crossings. At high temperatures, the calculated vibrational relaxation time …
Semiclassical Theory Of Inelastic Collisions Ii. Momentum Space Formulation, John B. Delos, Walter R. Thorson
Semiclassical Theory Of Inelastic Collisions Ii. Momentum Space Formulation, John B. Delos, Walter R. Thorson
Arts & Sciences Articles
The time-dependent equations of the classical picture of inelastic collisions (classical-trajectory equations) are derived using the momentum-space semiclassical approximation. Thereby it is shown that the classical-trajectory equations remain valid in the vicinity of classical turning points provided that (a) the momentum-space semiclassical approximation is valid, (b) the trajectories for elastic scattering in the various internal states differ only slightly, and (c) the slopes of the elastic scattering potentials have the same sign. A brief review of the existing derivations of the classical-trajectory equations is given, and the general conditions for their validity are discussed.
Studies Of The Potential Curve Crossing Problem Ii. General Theory And A Model For Close Crossings, John B. Delos, W. R. Thorson
Studies Of The Potential Curve Crossing Problem Ii. General Theory And A Model For Close Crossings, John B. Delos, W. R. Thorson
Arts & Sciences Articles
A unified formal treatment of the two-state potential-curve-crossing problem in atomic collision theory is presented, and the case of close crossings analyzed in detail. A complete solution for this case, including necessary computations, is given using a suitable generalization of the linear model originally suggested by Landau, Zener, and Stueckelberg. Our solution is based upon a hierarchy of approximations concerned with (i) choice of a discrete basis set for electronic coordinates, (ii) semiclassical treatment of the nuclear motion, (iii) an appropriate model for the two-state electronic Hamiltonian, and (iv) a complete solution to that model.
Semiclassical Theory Of Inelastic Collisions I. Classical Picture And Semiclassical, John B. Delos, W. R. Thorson, Stephen Knudson
Semiclassical Theory Of Inelastic Collisions I. Classical Picture And Semiclassical, John B. Delos, W. R. Thorson, Stephen Knudson
Arts & Sciences Articles
This series of papers is concerned with the derivation of the equations of the classical picture of atomic collisions, iℏddtdi(t)=Σjhij(t)dj(t), which describe the "time" dependence of electronic-quantum-state amplitudes as the nuclei move along a classical trajectory. These equations are derived in two ways. In the first formulation, which coincides with the intuitive classical picture of the collision, the nuclear part of the wave function is treated as a superposition of narrow wave packets, each traveling along a classical trajectory. In the second formulation, a semiclassical approach is used. The validity and meaning of the two formulations are discussed and compared.
Solutions Of The Two-State Potential-Curve-Crossing Problem, John B. Delos, W. R. Thorson
Solutions Of The Two-State Potential-Curve-Crossing Problem, John B. Delos, W. R. Thorson
Arts & Sciences Articles
A general theory of the two-state curve-crossing problem has been developed, with a complete solution of an accurate model for "close" crossings (including numerical computations for strong coupling). Results clarify the position of the Landau-Zener approximation and its improvements by Nikitin and others, provide a general way of extending these approximations into regions often treated incorrectly (including the high-energy limit), and can be readily adapted to simple, rapid calculations.
Studies Of The Potential Curve Crossing Problem I. Analysis Of Stueckelberg's Method, W. R. Thorson, John B. Delos, Seth A. Boorstein
Studies Of The Potential Curve Crossing Problem I. Analysis Of Stueckelberg's Method, W. R. Thorson, John B. Delos, Seth A. Boorstein
Arts & Sciences Articles
A detailed critical analysis is made of Stueckelberg's treatment of inelastic transitions at a crossing of two potential curves. Using an asymptotic method analogous to the WKB approximation, Stueckelberg obtained the well-known Landau-Zener-Stueckelberg (LZS) formula for the inelastic transition probability. His method involved the determination of "connection formulas" linking amplitudes associated with his asymptotic approximants on either side of the crossing-point region. Here we show that (a) Stueckelberg's asymptotic approximants are just the WKB approximants for elastic scattering on the adiabatic (noncrossing) potential curves; (b) Stueckelberg's method for obtaining the connection formulas can be put on a rigorous footing, including …