Adiabatic theory of Wannier threshold laws and ionization cross sections

Journal Article · Fri Jul 01 04:00:00 EDT 1994 · Physical Review A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.50.468· OSTI ID:7295952

Macek, J H; Ovchinnikov, S Y ^[1]

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1. Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996-1501 and Oak Ridge National Laboratory, P.O. Box 2009, Oak Ridge, Tennessee 37831 (United States)

Adiabatic energy eigenvalues of H[sub 2][sup +] are computed for complex values of the internuclear distance [ital R]. The infinite number of bound-state eigenenergies are represented by a function [epsilon]([ital R]) that is single valued on a multisheeted Riemann surface. A region is found where [epsilon]([ital R]) and the corresponding eigenfunctions exhibit harmonic-oscillator structure characteristic of electron motion on a potential saddle. The Schroedinger equation is solved in the adiabatic approximation along a path in the complex [ital R] plane to compute ionization cross sections. The cross section thus obtained joins the Wannier threshold region with the keV energy region, but the exponent near the ionization threshold disagrees with well-accepted values. Accepted values are obtained when a lowest-order diabatic correction is employed, indicating that adiabatic approximations do not give the correct zero velocity limit for ionization cross sections. Semiclassical eigenvalues for general top-of-barrier motion are given and the theory is applied to the ionization of atomic hydrogen by electron impact. The theory with a first diabatic correction gives the Wannier threshold law even for this case.

• DOE Contract Number: AC05-84OR21400
• OSTI ID: 7295952
• Journal Information: Physical Review A; (United States), Journal Name: Physical Review A; (United States) Vol. 50:1; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

664100* -- Theory of Electronic Structure of Atoms & Molecules-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
ADIABATIC APPROXIMATION
CHARGED PARTICLES
CORRECTIONS
CROSS SECTIONS
DIABATIC APPROXIMATION
DIFFERENTIAL EQUATIONS
DISTANCE
EIGENVALUES
ELECTRONIC EQUIPMENT
ENERGY
ENERGY LEVELS
EQUATIONS
EQUIPMENT
HARMONIC OSCILLATORS
HYDROGEN IONS
INTERATOMIC DISTANCES
IONIZATION
IONS
MATHEMATICAL SPACE
MOLECULAR IONS
OSCILLATORS
PARTIAL DIFFERENTIAL EQUATIONS
RIEMANN SPACE
SCATTERING
SCHROEDINGER EQUATION
SPACE
THRESHOLD ENERGY
WAVE EQUATIONS