Computational studies of first-Born scattering cross sections II. Moment-theory approach

Journal Article · Sat Jan 01 04:00:00 EST 1983 · J. Comput. Phys.; (United States)

DOI:https://doi.org/10.1016/0021-9991(83)90115-8· OSTI ID:6301003

Margoliash, D J; Langhoff, P W

Moment-theory methods are described for calculations of the high-energy electron impact-excitation and -ionization cross sections and closely related Van Hove correlation functions of atomic and molecular targets. The conventional Bethe--Born expressions are evaluated employing moment-theory techniques that avoid explicit construction of discrete and continuum target eigenspectra. Appropriately defined generalized oscillator-strength spectral moments and corresponding polynomial recurrence coefficients are seen to furnish necessary and sufficient information for Born calculations. The convergence of partial-wave variational calculations of such moments and coefficients is investigated for hydrogenic targets using complete basis sets of square-integrable functions. Calculated spectral moments and recurrence coefficients, and previously devised Stieltjes--Tschebyscheff techniques, are employed in constructing Gaussian and Radau quadratures that provide convergent approximations to the corresponding Bethe surface of discrete and continuum generalized oscillator strengths, and to the associated cross sections and correlation functions. Square-integrable principal pseudostates obtained from variational calculations of multipole spectral moments are shown to provide correctly normalized convergent approximations to the discrete and continuum transition densities appropriate for the target considered, clarifying the underlying basis of reliability and numerical stability of the moment-theory approach to Bethe-Born cross sections. The development should prove particularly useful in investigations of the Bethe surfaces, related scattering cross sections, and Van Hove correlation functions of molecular targets.

• Research Organization: Department of Chemistry, Indiana University, Bloomington, Indiana 47405
• OSTI ID: 6301003
• Journal Information: J. Comput. Phys.; (United States), Journal Name: J. Comput. Phys.; (United States) Vol. 49:1; ISSN JCTPA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ATOM COLLISIONS
BORN APPROXIMATION
COLLISIONS
CORRELATION FUNCTIONS
CROSS SECTIONS
ELECTRON COLLISIONS
ELECTRON-ATOM COLLISIONS
ELECTRON-MOLECULE COLLISIONS
ELEMENTS
ENERGY-LEVEL TRANSITIONS
EXCITATION
FUNCTIONS
HYDROGEN
IONIZATION
MOLECULE COLLISIONS
MOMENTS METHOD
NONMETALS
PARTIAL WAVES