Closed-form expression for 1 s r arrow 1 s electron-capture amplitude in a second-order Faddeev approximation

Journal Article · Wed Nov 01 04:00:00 EST 1989 · Physical Review (Section) A: General Physics; (USA)

DOI:https://doi.org/10.1103/PhysRevA.40.4907· OSTI ID:5354449

Alston, S ^[1]

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1. Department of Physics, Pennsylvania State University, Wilkes-Barre Campus, Lehman, Pennsylvania 18627 (US)

Within a second-order approximation to the Faddeev treatment of the exact transition operator for 1{ital s}{r arrow}1{ital s} electron capture in ion-atom collisions, expressions are derived in terms of {ital F}{sub 4} generalized hypergeometric functions for that part of the full amplitude involving electronic-nuclear potentials only. For totally symmetric collisions, the amplitude is evaluated in terms of {sub 3}F{sub 2} functions. When near-the-energy-shell anomalies of the Coulomb scattering are neglected, the amplitude is seen to reduce to a symmetric impulse-approximation form, and, when the explicit Coulomb nature of the problem is neglected, to a second-order Born approximation form. As a special case, the amplitude is evaluated at the momentum transfer value where the differential cross section exhibits a local maximum---the Thomas peak. The values of the various amplitude norms at the Thomas peak are compared.

• OSTI ID: 5354449
• Journal Information: Physical Review (Section) A: General Physics; (USA), Journal Name: Physical Review (Section) A: General Physics; (USA) Vol. 40:9; ISSN PLRAA; ISSN 0556-2791
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
AMPLITUDES
ATOM COLLISIONS
CAPTURE
COLLISIONS
COULOMB FIELD
ELECTRIC FIELDS
ELECTRON CAPTURE
EQUATIONS
FADDEEV EQUATIONS
ION COLLISIONS
ION-ATOM COLLISIONS
SCATTERING
SCATTERING AMPLITUDES
SMALL ANGLE SCATTERING