Theory of Near-Adiabatic Collisions. III. Coupled Equations Arising from Expansions Involving Single-Center States

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 function is expanded in terms of electronic states that have single-center character. (Linear combinations of single-center states are also permitted.) A particular form of such an expansion is proposed, and it is shown that this expansion leads to equations in which fictitious displacement couplings are eliminated and momentum-transfer terms are included. The work of this paper and of others on this subject leads to revised notions about the definition and meaning of nonadiabatic couplings

Theory of Electronic Excitations in Slow Atomic Collisions

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 space of electron variables leads to quantum-mechanical close-coupled equations. In the conventional formulation, known as perturbed-stationary-states theory, certain difficulties arise because scattering boundary conditions cannot be exactly satisfied within a finite basis. These difficulties are examined, and a theory is developed which surmounts them. This theory is based upon an intersecting-curved-wave picture. The use of rotating or space-fixed electronic basis sets is discussed. Various bases are classified by Hund\u27s cases (a)-(e). For rotating basis sets, the angular motion of the nuclei is best described using symmetric-top eigenfunctions, and an example of partial-wave analysis in such functions is developed. Definitions of adiabatic and diabatic representations are given, and rules for choosing a good representation are presented. Finally, representations and excitation mechanisms for specific systems are reviewed. Processes discussed include spin-flip transitions, rotational coupling transitions, inner-shell excitations, covalent-ionic transitions, resonant and near-resonant charge exchange, fine-structure transitions, and collisional autoionization and electron detachment

Catastrophes and Stable Caustics in Bound States of Hamiltonian Systems

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. They arise because of the special form of the typical Hamiltonian of physical systems

On the Reactions of N2 with O

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 is in good agreement with experiment, but at low temperatures there is a serious, unexplained discrepancy

Quantum Theory of Slow Atomic Collisions

Quantum-mechanical and semiclassical theories of slow atomic collisions are reviewed, with attention to electron-translation factors and their effects

Studies of the Potential Curve Crossing Problem. III. Collisional Spectroscopy of Close Crossings

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

Scaled-Energy Floquet Spectroscopy in a Strong Electric Field: A Semiquantal Calculation of the Recurrence Spectrum

We consider a hydrogen atom in a strong static electric field with a weak parallel radio-frequency (rf) field. We compute the photoabsorption spectrum by calculating the spectrum of Floquet states, including their quasienergies and their oscillator strengths. Our calculation is based upon “semiquantal” formulas: we calculate the discrete spectrum of quasienergy states by using a quantum adiabatic approximation combined with semiclassical (Bohr-Sommerfeld) quantization rules. We express this spectrum in a manner consistent with the method of scaled-variable spectroscopy, and then calculate the Fourier transform. These calculated absorption spectra and recurrence spectra are in good agreement with experiments on Li atoms. Additional approximations show that the recurrence spectrum is approximately equal to the product of the recurrence spectrum in a static field times an envelope function. That envelope function is the Fourier transform of a cluster of sidebands surrounding a progenitor level in the rf field. The resulting formula agrees with the low-frequency limit of a formula obtained from a semiclassical treatment

Dynamics of Electron Wave Propagation in Photoionization Microscopy: I. Semiclassical Open-Orbit Theory

This is the first of two papers that develop theories and numerical methods for photoionization microscopy of hydrogen atoms in strong electric fields, in semiclassical and quantum-mechanical frameworks, respectively. In this paper, semiclassical open-orbit theory is presented to describe the propagation of outgoing electron waves to macroscopic distances. Spatial distributions of electron probability densities and current densities are predicted. The open-orbit theory, based on an assumption that electron waves propagate along classical paths from a pointlike source to a detector, provides a clear and intuitive physical picture to interpret structures of observed geometrical interference patterns in photoionization microscopy. We calculate photoelectron ejection of hydrogen atoms in electric fields, and comparison is made with quantum-mechanical results, which will be detailed in the second paper [Zhao and Delos, Phys. Rev. A 81, 053418 (2010)]. A strong quantum tunneling effect has been found. Such a tunneling effect should be visible in the experiment

Motion of an Electron from a Point Source in Parallel Electric and Magnetic Fields

Negative ions undergoing near-threshold photodetachment in a weak laser field provide an almost pointlike, isotropic source of low-energy electrons. External fields exert forces on the emitted coherent electron wave and direct its motion. Here, we examine the spatial distribution of photodetached electrons in uniform, parallel electric and magnetic fields. The interplay of the electric and magnetic forces leads to a surprising intricate shape of the refracted electron wave, and mutiple interfering trajectories generate complex fringe patterns in the matter wave. The exact quantum solution is best understood in terms of the classical electron motion

Resonances and Recurrences in the Absorption Spectrum of an Atom in an Electric Field

We use closed-orbit theory to study the absorption spectrum of an atom in an electric field. In previous work we examined absorption spectra above the zero-field ionization threshold. Only one closed orbit exists there, and it is unstable. Now we examine the situation below threshold. Here, the orbit parallel to the electric field is stable and, as the energy decreases, many other closed orbits bifurcate out of it. These closed orbits have simple patterns, and the associated recurrences are most clear if the absorption spectrum is measured using a scaled-variables method. The relation between the semiclassical Einstein-Brillouin-Keller-Marcus (EBKM) theory and periodic-orbit or closed-orbit theory is examined: they are complementary methods in the same sense that energy and time are complementary variables in quantum mechanics. Our numerical calculations show that sinusoidal fluctuations contributed by the closed orbits combine into peaks, and these peaks are in the locations predicted by EBKM theory