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NASA NTRS2023

Experimental and Semiclassical Stark Widths and Shifts for Spectral Lines of Neutral and Ionized Atoms (A Critical Review of Experimental and Semiclassical Data for the Period 2008 through 2020)

This Review Article compares new experimental and corresponding semiclassical Stark broadened data for non-hydrogenic spectral lines of neutral atoms and positive ions. This Review covers the period 2008 until the end of 2020 and presents the continuation of previous critical reviews from 1976 (two), 1984 (two), 1990, 2002, and one from 2009. This Review reports the Stark broadening parameters of 1665 spectral lines belonging to 35 elements with 61 different atomic and ion species. The data are taken from 60 papers. Experimental data are arranged by elements and spectra, and these are reported in tables in alphabetical and numerical order, respectively. Each experimental Stark broadening parameter is followed with estimated accuracy. The experimental Stark broadening and shift data presented in the tables are compared with the corresponding semiclassical results available in the literature. In addition, for comparison experiments versus semiclassical theoretical Stark broadening parameters, a numerically improved theoretical approach developed based on Griem and co-workers’ theory is used to evaluate Stark widths and shifts of all studied lines whenever required atomic energy levels data and transition probabilities are available. At the end of the text report, for each analyzed neutral or ion species, the information about the location of the same species data in preceding reviews is given.

Plasma line broadening↗
NASA NTRS1980

Excitation of the b 3 Sigma u + state of H2 by electron impact - Semiclassical exchange potentials at intermediate energies

Integrated and differential cross sections for the excitation of the b 3 Sigma u + state of H2, from the ground state, by electron impact, are presented. The energy range of interest is 10.5 to 40.0 eV. The close-coupling equations for this process are solved in five different exchange approximations: exact two-electron exchange terms, no orthogonality; exact two-electron exchange terms, orthogonality; semiclassical exchange terms, no orthogonality, with barrier term; semiclassical exchange terms, no orthogonality, no barrier term; and semiclassical exchange terms, orthogonality, with barrier term. The purpose is to judge the reliability of the semiclassical exchange approximation for electronic excitation of molecules by electron impact at intermediate energies. The results are compared with recent theoretical estimates for the same process.

Weatherford, C. A.↗
NASA NTRS1974

Vibration-translation energy transfer in anharmonic diatomic molecules. 1: A critical evaluation of the semiclassical approximation

The semiclassical approximation is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Mckenzie, R. L.↗
NASA NTRS1975

Vibration-translation energy transfer in anharmonic diatomic molecules. I - A comparative evaluation of the semiclassical approximation

The semiclassical approximation (quantum oscillator, classical path) is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Mckenzie, R. L.↗
NASA NTRS1993

Semiclassical approximation for electron impact excitation of hydrogenic ions

The threshold behavior of the electron impact excitation cross sections for hydrogenic ions is investigated using the semiclassical approximation with the hyperbolic orbit for the projectile path, rather than the straight line path. The symmetric approximation is applied to modify the ordinary hyperbolic orbit. The modification factor due to the hyperbolic orbit approximation produces the correct energy dependence of the cross section near the excitation threshold. This result is very similar to that of the quantum mechanical case. The semiclassical enhancement factor due to this simple modification corresponds to the Coulomb focusing factor in the Born-Bethe approximation. In the high-energy limit, the semiclassical cross sections approach the Born-Bethe cross sections, with a finite cutoff in the momentum transfer for dipole transitions.

Jung, Young-Dae↗
NASA NTRS1972

Semiclassical theory of inelastic collisions. II - Momentum-space formulation.

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.

Delos, J. B.↗
NASA NTRS1978

Semiclassical theory of unimolecular dissociation induced by a laser field

A semiclassical nonperturbative theory of direct photodissociation in a laser field is developed in which photon absorption and dissociation are treated in a unified fashion. This is achieved by visualizing nuclear dynamics as a representative particle moving on electronic-field surfaces. Methods are described for calculating dissociation rates and probabilities by Monte Carlo selection of initial conditions and integration of classical trajectories on these surfaces. This unified theory reduces to the golden rule expression in the weak-field and short-time limits, and predicts nonlinear behavior, i.e., breakdown of the golden rule expression in intense fields. Field strengths above which lowest-order perturbation theory fails to work have been estimated for some systems. Useful physical insights provided by the electronic-field representation have been illustrated. Intense field effects are discussed which are amenable to experimental observation. The semiclassical methods used here are also applicable to multiple-surface dynamics in fieldfree unimolecular and bimolecular reactions.

Yuan, J.-M.↗
NASA NTRS1979

Semiclassical theory of electronically nonadiabatic transitions in molecular collision processes

An introductory account of the semiclassical theory of the S-matrix for molecular collision processes is presented, with special emphasis on electronically nonadiabatic transitions. This theory is based on the incorporation of classical mechanics with quantum superposition, and in practice makes use of the analytic continuation of classical mechanics into the complex space of time domain. The relevant concepts of molecular scattering theory and related dynamical models are described and the formalism is developed and illustrated with simple examples - collinear collision of the A+BC type. The theory is then extended to include the effects of laser-induced nonadiabatic transitions. Two bound continuum processes collisional ionization and collision-induced emission also amenable to the same general semiclassical treatment are discussed.

Lam, K. S.↗
NASA NTRS1982

Uniform semiclassical quantization of regular and chaotic classical dynamics on the Henon-Heiles surface

Qualitative arguments are adduced which indicate that the apparently chaotic dynamics on the Henon-Heiles (1964) surface display sufficient regularity on a short to intermediate (but not long) time scale to allow the use of standard EBK quantization techniques. This takes advantage of the remnants of manifold structure implied. A complete uniform semiclassical quantization is performed using the time independent technique of the Birkhoff-Gustavson normal form, which was recently introduced in the context of semiclassical quantization by Swimm and Delos (1977, 1979).

Jaffe, C.↗
NASA NTRS1989

Semiclassical approximations in the coherent-state representation

The semiclassical limit of the stationary Schroedinger equation in the coherent-state representation is analyzed simultaneously for the groups W1, SU(2), and SU(1,1). A simple expression for the first two orders for the wave function and the associated semiclassical quantization rule is obtained if a definite choice for the classical Hamiltonian and expansion parameter is made. The behavior of the modulus of the wave function, which is a distribution function in a curved phase space, is studied for the three groups. The results are applied to the quantum triaxial rotor.

Kurchan, J.↗
NASA NTRS1992

Semiclassical matrix elements from periodic orbits

An extension of Gutzwiller's (1967, 1969, 1970, 1971, 1990) semiclassical theory for chaotic systems that allows a determination of matrix elements in terms of classical periodic orbits. Associated zeta functions are derived. The semiclassical predictions are found to be in good agreement with Fourier transforms of quantum spectra of hydrogen in a magnetic field. Expressions for off-diagonal matrix elements are derived that are extensions of the Bohr correspondence relations for integrable systems.

Eckhardt, B.↗
NASA NTRS2001

Semiclassical Models for Virtual Antiparticle Pairs, the Unit of Charge e, and the QCD Coupling alpha(sub s)

New semiclassical models of virtual antiparticle pairs are used to compute the pair lifetimes, and good agreement with the Heisenberg lifetimes from quantum field theory (QFT) is found. The modeling method applies to both the electromagnetic and color forces. Evaluation of the action integral of potential field fluctuation for each interaction potential yields approximately Planck's constant/2 for both electromagnetic and color fluctuations, in agreement with QFT. Thus each model is a quantized semiclassical representation for such virtual antiparticle pairs, to good approximation. When the results of the new models and QFT are combined, formulae for e and alpha(sub s)(q) are derived in terms of only Planck's constant and c.

Batchelor, David↗