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Full-Text Articles in Physics
Photodetachment Cross Section Of H- In Crossed Electric And Magnetic Fields. I. Closed-Orbit Theory, Aaron D. Peters, John B. Delos
Photodetachment Cross Section Of H- In Crossed Electric And Magnetic Fields. I. Closed-Orbit Theory, Aaron D. Peters, John B. Delos
Arts & Sciences Articles
In this, the first of two papers, we obtain a simple analytic formula for the photodetachment cross section of H− in crossed electric and magnetic fields. The three-dimensional semiclassical approximation predicts oscillations in the spectrum and these oscillations are correlated with closed classical orbits. In the following paper [A. D. Peters and J. B. Delos, Phys. Rev. A 47, 3036 (1993)] we derive fully-quantum-mechanical formulas for the cross section in perpendicular electric and magnetic fields and show how these results can be reduced to the semiclassical results of this paper.
Closed-Orbit Theory Of Oscillations In Atomic Photoabsorption Cross Sections In A Strong Electric Field. Ii. Derivation Of Formulas, J. Gao, John B. Delos
Closed-Orbit Theory Of Oscillations In Atomic Photoabsorption Cross Sections In A Strong Electric Field. Ii. Derivation Of Formulas, J. Gao, John B. Delos
Arts & Sciences Articles
A formula for photoabsorption cross sections of hydrogen and alkali-metal atoms in a static electric field is derived, based on the closed-orbit theory previously used to study hydrogen in a magnetic field. Electric fields are simpler than magnetic fields, because the classical motion is regular and closed orbits can be enumerated. In alkali metals the core modifies the relevant dipole matrix elements, and it produces additional phase shifts.
Closed-Orbit Theory Of Oscillations In Atomic Photoabsorption Cross Sections In A Strongelectric Field. I. Comparison Between Theory And Experiments On Hydrogen And Sodium Above Threshold, J. Gao, John B. Delos, M. Baruch
Closed-Orbit Theory Of Oscillations In Atomic Photoabsorption Cross Sections In A Strongelectric Field. I. Comparison Between Theory And Experiments On Hydrogen And Sodium Above Threshold, J. Gao, John B. Delos, M. Baruch
Arts & Sciences Articles
Using a simple analytic formula from closed-orbit theory, we calculate photoabsorption cross sections of hydrogen and sodium in a strong electric field. The theoretical spectra show good agreement with experimental results. A scaled variable measurement is also suggested.
Hamiltonian Bifurcation Theory Of Closed Orbits In The Diamagnetic Kepler Problem, J. M. Mao, John B. Delos
Hamiltonian Bifurcation Theory Of Closed Orbits In The Diamagnetic Kepler Problem, J. M. Mao, John B. Delos
Arts & Sciences Articles
Classically chaotic systems possess a proliferation of periodic orbits. This phenomenon was observed in a quantum system through measurements of the absorption spectrum of a hydrogen atom in a magnetic field. This paper gives a theoretical interpretation of the bifurcations of periodic or closed orbits of electrons in atoms in magnetic fields. We ask how new periodic orbits can be created out of existing ones or ‘‘out of nowhere’’ as the energy changes. Hamiltonian bifurcation theory provides the answer: it asserts the existence of just five typical types of bifurcation in conservative systems with two degrees of freedom. We show …
Mechanism Of Collisionally-Induced Transitions Among Fine-Structure Levels: Semiclassical Calculations Of Alignment Effects In The Na-He System, Laurie J. Kovalenko, Stephen R. Leone, John B. Delos
Mechanism Of Collisionally-Induced Transitions Among Fine-Structure Levels: Semiclassical Calculations Of Alignment Effects In The Na-He System, Laurie J. Kovalenko, Stephen R. Leone, John B. Delos
Arts & Sciences Articles
To gain insight into the mechanism of Na(3p)2P3/2→2P1/2 fine‐structure transitions induced by collision with He, we monitor the expectation values of the orbital‐ and spin‐angular momentum vectors, l and s, as a function of time along the trajectory, using a semiclassical formalism. In a typical collision, 〈s〉 remains nearly space‐fixed while 〈l〉 precesses about the rotating internuclear axis. Thus, in the interaction region, the projection of 〈l〉 onto the internuclear axis, 〈λ〉, remains nearly constant, and the molecular alignment of the orbital is preserved. We show how equations of motion for …
Effect Of Closed Classical Orbits On Quantum Spectra: Ionization Of Atoms In A Magnetic Field. I. Physical Picture And Calculations, M. L. Du, John B. Delos
Effect Of Closed Classical Orbits On Quantum Spectra: Ionization Of Atoms In A Magnetic Field. I. Physical Picture And Calculations, M. L. Du, John B. Delos
Arts & Sciences Articles
This is the first of two papers that develop the theory of oscillatory spectra. When an atom is placed in a magnetic field, and the absorption spectrum into states close to the ionization threshold is measured at finite resolution, so that individual energy levels are not resolved, it is found that the absorption as a function of energy is a superposition of sinusoidal oscillations. These papers present a quantitative theory of this phenomenon. In this first paper, we describe the physical ideas underlying the theory in the simplest possible way, and we present our first calculations based upon the theory. …
Effect Of Closed Classical Orbits On Quantum Spectra: Ionization Of Atoms In A Magnetic Field. Ii. Derivation Of Formulas, M. L. Du, John B. Delos
Effect Of Closed Classical Orbits On Quantum Spectra: Ionization Of Atoms In A Magnetic Field. Ii. Derivation Of Formulas, M. L. Du, John B. Delos
Arts & Sciences Articles
A formula is derived for oscillations in the near-threshold absorption spectrum of an atom in a magnetic field. Three approximations are used. (1) Near the atomic nucleus, the diamagnetic field is negligible. (2) Far from the nucleus, the waves propagate semiclassically. (3) Returning waves are similar to (cylindrically modified) Coulomb-scattering waves. With use of these approximations, together with the physical picture described in the accompanying paper, an algorithm is specified for calculation of the spectrum.
Atomic Electrons In Strong Magnetic Fields: Transition From Elliptical To Helical Behavior., John B. Delos, Stephen Knudson, Shena Sikora, Robert Leonard Waterland, S. Whitworth
Atomic Electrons In Strong Magnetic Fields: Transition From Elliptical To Helical Behavior., John B. Delos, Stephen Knudson, Shena Sikora, Robert Leonard Waterland, S. Whitworth
Arts & Sciences Articles
The behavior of an atomic electron in a static magnetic field strong enough to correspond to the transition regime is examined. The field strength is characterized by the parameter L^, the effective component of angular momentum. A Floquet-Mathieu analysis shows that the bifurcation of classical trajectories into elliptical and helical families is related to the 2:1 resonance which occurs at L^=L^T. Quantum mechanics gives an avoided crossing at L^T; we examine the nature of the wave functions as L^ passes through the resonance. Semiclassical calculations accurately reproduce the quantum eigenvalues and produce trajectories which underlie the quantum wave functions. …
Laser-Induced Collisional Detachment, D. Luo, John B. Delos, S. Geltman
Laser-Induced Collisional Detachment, D. Luo, John B. Delos, S. Geltman
Arts & Sciences Articles
A theoretical study is presented of the process of photodetachment of a negative ion by sub-threshold-frequency radiation in the presence of a simultaneous collision. Calculations are carried out for the H−-He case and the resulting cross section is compared with other competing processes, such as two-photon photodetachment and nonradiative collisional detachment.
Semiclassical Interpretation Of Eigenvectors For Excited Atoms In External Fields, Robert Leonard Waterland, M. L. Du, John B. Delos
Semiclassical Interpretation Of Eigenvectors For Excited Atoms In External Fields, Robert Leonard Waterland, M. L. Du, John B. Delos
Arts & Sciences Articles
Eigenvectors for an electron in an atom in parallel electric and magnetic fields are calculated, and a semiclassical interpretation of their behavior is obtained. Eigenvectors can in this case be regarded as ‘‘wave functions in angular momentum space.’’ The matrix equation defining the eigenvectors is written as a difference equation, and then converted to a pseudodifferential equation; a systematic procedure is then used to construct a semiclassical approximation. It is found that the same classical Hamiltonian that has been previously used to calculate semiclassical eigenvalues provides a WKB-type representation of the eigenvectors. The development sheds new light on action-angle formulations …
High Rydberg States Of An Atom In Parallel Electric And Magnetic Fields, Robert L. Waterland, John B. Delos, M. L. Du
High Rydberg States Of An Atom In Parallel Electric And Magnetic Fields, Robert L. Waterland, John B. Delos, M. L. Du
Arts & Sciences Articles
We have calculated the energy spectrum of a highly excited atom in parallel electric and magnetic fields. The eigenvalues were obtained by semiclassical quantization of action variables calculated from first-order classical perturbation theory. For the field strengths studied, the electron moves on a Kepler ellipse whose orbital parameters evolve slowly in time, and first-order perturbation theory reduces the problem to just one degree of freedom. Action variables were calculated from perturbation theory and the eigenvalues were obtained by semiclassical quantization of the action. The semiclassical analysis leads directly to a correlation diagram which connects the eigenstates of the Stark effect …
Collisions Of F+ With Ne, M. Hottoka, B. Roos, John B. Delos, R. Srivastava, R. B. Sharma, W. Koshi
Collisions Of F+ With Ne, M. Hottoka, B. Roos, John B. Delos, R. Srivastava, R. B. Sharma, W. Koshi
Arts & Sciences Articles
Measurements of inelastic collisions of F+ with Ne have been made. Transitions between 3P and 1D terms of F+ are seen, with the inelastically scattered ions sharply focused in the forward direction. Potential energy curves of (FNe)+ have been calculated. The 3Σ and 3Π curves correlating to F+(3P) are repulsive, while the 1Σ correlating to F+(1D) is attractive. Several curve crossings are identified, where transitions occur through spin-orbit coupling. Scattering angles and differential cross sections have been calculated, and they show the presence of a ‘‘glory’’ (or halo) effect, which accounts for the forward scattering of ions.
Catastrophes And Stable Caustics In Bound States Of Hamiltonian Systems, John B. Delos
Catastrophes And Stable Caustics In Bound States Of Hamiltonian Systems, John B. Delos
Arts & Sciences Articles
Caustics—envelopes of families of classical trajectories, or boundaries between classically allowed and forbidden regions—correspond to singular points of a phase‐space surface called a Lagrangian manifold. According to catastrophe theory, only a limited number of types of caustics are stable under general perturbations of the manifold. Most of the caustics that are found in calculations correspond to members of the canonical list of elementary catastrophes. However, there are some exceptions—examination of trajectories of typical Hamiltonian systems shows that stable structures exist which are not in accord with the stability theorem of catastrophe theory. These exceptional cases are discussed in this paper. …
Bound State Semiclassical Wave Functions, Stephen Knudson, John B. Delos, D. W. Noid
Bound State Semiclassical Wave Functions, Stephen Knudson, John B. Delos, D. W. Noid
Arts & Sciences Articles
The semiclassical theory developed by Maslov and Fedoriuk is used to calculate the wave function for a two‐dimensional bound state system. We investigate in detail an eigenstate of a coupled anharmonic oscillator system. The primitive semiclassical wave function is obtained from the characteristic function S and the density function J. Each of these functions consists of four branches corresponding to the four possible directions of motion of the classical trajectory through any point. The interference from the four branches determines the basic structure of the wave function. A uniform approximation gives a wave function which is well behaved along …
Electron Detachment In Negative-Ion Collisions. Iii. Model Calculations., T. S. Wang, John B. Delos
Electron Detachment In Negative-Ion Collisions. Iii. Model Calculations., T. S. Wang, John B. Delos
Arts & Sciences Articles
With the use of a previously developed close-coupling theory, and simple models for the energy gap and propagator that arise in that theory, calculations are made of the properties of the survival probability for the negative ions and of the energy spectrum of detached electrons. Special attention is given to interference effects that might be seen under favorable circumstances.
Probability Conservation In Theories Of Collisional Ionization And Detachment, M. L. Du, John B. Delos
Probability Conservation In Theories Of Collisional Ionization And Detachment, M. L. Du, John B. Delos
Arts & Sciences Articles
The semiclassical local-complex-potential theory has been widely used to describe detachment and ionization in atom-atom and ion-atom collisions. However, it has been shown that the resulting formulas do not conserve probability. In this paper, we show that the problem arises from the inconsistent treatment of the effects of interference, tunneling, and diffraction. A more complete theory is based upon the close-coupling expansion, which leads to an infinite set of coupled equations. A method for solving such sets of equations was developed in earlier work. Here we implement that method using a new iterative numerical scheme, and we show that the …
Semiclassical Calculation Of Quantum-Mechanical Wave Functions For A Two-Dimensional Scattering System, Stephen Knudson, John B. Delos, B. Bloom
Semiclassical Calculation Of Quantum-Mechanical Wave Functions For A Two-Dimensional Scattering System, Stephen Knudson, John B. Delos, B. Bloom
Arts & Sciences Articles
The semiclassical theory developed by Maslov and Fedoriuk is used to calculate the wave function for two‐dimensional scattering from a Morse potential. The characteristic function S and the density Jacobian J are computed in order to obtain the primitive wave function. The incident part shows distorted plane‐wave behavior and the scattered part shows radially outgoing behavior. A uniform approximation gives a wave function that is well‐behaved near the caustic.
Trajectories Of An Atomic Electron In A Magnetic Field, John B. Delos, Stephen Knudson, D. W. Noid
Trajectories Of An Atomic Electron In A Magnetic Field, John B. Delos, Stephen Knudson, D. W. Noid
Arts & Sciences Articles
Classical trajectories of an atomic electron in a magnetic field are calculated for various values of the field strength B. Qualitative properties of these trajectories are examined. With use of a scaling law, it is shown that the equations of motion can be written in a form such that they depend upon only one parameter, which may be regarded as a reduced angular momentum (proportional to LzB13). For small values of this parameter there is an "elliptical regime" in which the trajectory may be regarded as a Kepler ellipse with orbital parameters that evolve slowly in time. For large values …
Construction Of A Multidimensional Potential Energy Surface From An Energy Spectrum, Robert Leonard Waterland, John B. Delos
Construction Of A Multidimensional Potential Energy Surface From An Energy Spectrum, Robert Leonard Waterland, John B. Delos
Arts & Sciences Articles
A method for the systematic construction of a multidimensional potential energy surface from an energy spectrum is presented. We show that if the Hamiltonian and the energy spectrum satisfy certain conditions then there is an inversion technique which gives a potential energy function from the spectrum. The method proceeds via a sequence of canonical transformations and leads to a potential energy which is symmetric in all its variables. We test the procedure for one‐ and two‐dimensional examples and show that it gives reasonable results. However, the method does not give a unique result and we discuss two types of nonuniqueness …
Electron Detachment In Negative-Ion Collisions. I. Time-Dependent Theory And Models For A Propagator, T. S. Wang, John B. Delos
Electron Detachment In Negative-Ion Collisions. I. Time-Dependent Theory And Models For A Propagator, T. S. Wang, John B. Delos
Arts & Sciences Articles
A theory of electron detachment in slow collisions of negative ions with atoms is developed. The theory is based on assumptions that are similar to, but more general than, the assumptions made in earlier papers: The motion of the nuclei is described semiclassically, the electronic wave function is expanded in a partially diabatic basis that includes a discrete state and a continuum, and certain couplings are assumed to be small. With such assumptions the Schrödinger equation is reduced to a nondenumerably infinite set of coupled differential equations, and then to a single integro-differential equation (an equation with "memory"). It is …
Electron Detachment In Negative-Ion Collisions. Ii. The Dynamical Complex Potential, T. S. Wang, John B. Delos
Electron Detachment In Negative-Ion Collisions. Ii. The Dynamical Complex Potential, T. S. Wang, John B. Delos
Arts & Sciences Articles
No abstract provided.
Atlas Of High Resolution Infrared Spectra Of Carbon Dioxide: February 1984 Edition, D. Chris Benner
Atlas Of High Resolution Infrared Spectra Of Carbon Dioxide: February 1984 Edition, D. Chris Benner
Arts & Sciences Articles
Long-path, low-pressure laboratory absorption spectra of carbon dioxide i are presented in an atlas format for the spectral regions 1830 to 2100 cm" , 2395 to 2680 cm-I i , and 3140 to 3235 cm- . The data were recorded at 0.01 cm"I resolution and room temperature with the Fourier transform spectrometer in the McMath solar telescope complex of the National Solar Observatory at Kitt Peak. A list of positions and assignments is given for the 3336 lines observed. A total of 52 bands of 12C1602, 13C1602, 12C160180, 12C160170, and 13C160180 have been identified.
Electron Detachment For H-(D-) In Collisions With Ne, T. S. Wang, John B. Delos
Electron Detachment For H-(D-) In Collisions With Ne, T. S. Wang, John B. Delos
Arts & Sciences Articles
Total cross sections for electron detachment in collisions of H− and D− with Ne are calculated, using a model based on a first‐order solution to close‐coupled equations. Quantities needed for the calculation are the energy gap and the coupling between bound and free states. The energy gap is taken from previous calculations and the coupling is assumed to be of exponential form, with parameters adjusted to fit experimental data. Special examination is made of isotope effects in the cross sections.
Highly Excited States Of A Hydrogen Atom In A Strong Magnetic Field, John B. Delos, Stephen Knudson, D. W. Knudson
Highly Excited States Of A Hydrogen Atom In A Strong Magnetic Field, John B. Delos, Stephen Knudson, D. W. Knudson
Arts & Sciences Articles
Classical trajectories and semiclassical energy eigenvalues are calculated for an atomic electron in a high Rydberg state in an external magnetic field. With the use of perturbation theory, a classical trajectory is described as a Kepler ellipse with orbital parameters evolving slowly with time. As they evolve, the ellipse rocks, tilts, and flips in space, but the length of its major axis remains approximately constant. Exact numerical calculations verify that perturbation theory is quite accurate for the cases considered (principal quantum number ≃ 30, magnetic field ≲ 6 T). Action variables are calculated from perturbation theory and from exact trajectories, …
Quantum Theory Of Slow Atomic Collisions, John B. Delos
Quantum Theory Of Slow Atomic Collisions, John B. Delos
Arts & Sciences Articles
Quantum-mechanical and semiclassical theories of slow atomic collisions are reviewed, with attention to electron-translation factors and their effects.
Atlas Of High Resolution Infrared Spectra Of Carbon Dioxide: February 1983 Edition, D. Chris Benner
Atlas Of High Resolution Infrared Spectra Of Carbon Dioxide: February 1983 Edition, D. Chris Benner
Arts & Sciences Articles
No abstract provided.
Theory Of Near-Adiabatic Collisions. Iii. Coupled Equations Arising From Expansions Involving Single-Center States, John B. Delos
Theory Of Near-Adiabatic Collisions. Iii. Coupled Equations Arising From Expansions Involving Single-Center States, John B. Delos
Arts & Sciences Articles
The conventional quantum-mechanical formulation of near-adiabatic collision theory is known to have a number of defects. These defects arise because the usual description does not account for the displacement of electronic states with moving nuclei, or for the change of momentum of the electron as it jumps from one moving nucleus to the other. The purpose of this series of papers is to develop an improved theory, in which such effects are taken into account. In this paper, we show that displacement and momentum-transfer effects can be incorporated into the theory in a very simple way, provided that the wave …
Theory Of Electronic Excitations In Slow Atomic Collisions, John B. Delos
Theory Of Electronic Excitations In Slow Atomic Collisions, John B. Delos
Arts & Sciences Articles
This review deals with quantitative descriptions of electronic transitions in atom-atom and ion-atom collisions. In one type of description, the nuclear motion is treated classically or semiclassically, and a wave function for the electrons satisfies a time-dependent Schrödinger equation. Expansion of this wave function in a suitable basis leads to time-dependent coupled equations. The role played by electron-translation factors in this expansion is noted, and their effects upon transition amplitudes are discussed. In a fully quantum-mechanical framework there is a wave function describing the motion of electrons and nuclei. Expansion of this wave function in a basis which spans the …
Diabatic And Adiabatic Representations For Atomic Collision Processes, John B. Delos, W. R. Thorson
Diabatic And Adiabatic Representations For Atomic Collision Processes, John B. Delos, W. R. Thorson
Arts & Sciences Articles
ABSTRACT A consistent general definition of diabatic representations has not previously been given, even though many practical examples of such representations have been constructed for specific problems. Such a definition is provided in this paper. Beginning with a classical trajectory formulation, we describe the form and behavior of velocity‐dependent couplings in slow collisions, including the effects of electron‐translation factors (ETF’s). We compare the couplings arising from atomic representations and atomic ETF’s with those arising from molecular representations and ’’switching function’’ ETF’s. We show that a unique set of switching functions makes the two descriptions identical in their effects. We then …
Semiclassical Calculations Of Vibrational Energy Levels For Non-Separable Systems Using The Birkhoff-Gustavson Normal Form, Randall T. Swimm, John B. Delos
Semiclassical Calculations Of Vibrational Energy Levels For Non-Separable Systems Using The Birkhoff-Gustavson Normal Form, Randall T. Swimm, John B. Delos
Arts & Sciences Articles
We present a semiclassical method of calculating vibrational energy levels for a system of nonseparable coupled oscillators. For a Hamiltonian written as a power series in which the leading terms are given by a sum of one‐dimensional harmonic oscillator Hamiltonians, the method involves transforming the original classical Hamiltonian via a succession of canonical transformations into a normal form which is a power series originally defined by Birkhoff and later generalized by Gustavson. Two cases are distinguished. If the harmonic oscillator frequencies in the unperturbed Hamiltonian are incommensurable, then the normal form is a power series whose terms are products of …