NONADIABATIC THEORY OF ELECTRON-HYDROGEN SCATTERING

Journal Article · Sun Apr 01 04:00:00 EST 1962 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.126.130· OSTI ID:4831687

Temkin, A

A rigorous theory of the s-wave elastic scattering of electrons by hydrogen is presented, The Schrodinger equation is reduced to an infinite set of coupled, twodimensional, partial differential equations. A zeroth order scattering problem is defined by neglecting the coupling terms oi the first equation. An exact relation is derived between the phase shift of this zeroth order problem and the true phase shift. The difference between these is contained in a rapidly convergent series whose terms correspond adiabatically to multipole distortions of the hydrogen by the incoming electron. The physical significance of the zeroth order problem is discussed. The ex;hange approximation for s-wave scattering is shown to be a variational approximation of the zeroth order problem. A perturbation theory is introduced to calculate the higher order corrections, The dipole correction has an increasingly important quantitative effect in the limit of zero energy. The effect of the long-range part of this correction on the scattering length can be expressed by a formula in terms of inverse powers of a long-range parameter R. Phase shifts for both singlet and triplet scattering are calculated, including up to quadrupole terms. The convergence is such that this number of terms should yield better than four- place accuracy. Uncertainties in calculated values decrease the accuracy to approximately three significant figures. (auth)

• Research Organization: Goddard Space Flight Center, Greenbelt, Md.
• NSA Number: NSA-16-018254
• OSTI ID: 4831687
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 126; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

DIFFERENTIAL EQUATIONS
DIPOLES
ELASTIC SCATTERING
ELECTRON BEAMS
ENERGY
ERRORS
HYDROGEN
MATHEMATICS
MULTIPOLES
NUMERICALS
PERTURBATION THEORY
PHASE SHIFT
PHYSICS
QUANTUM MECHANICS
S-WAVE
SCATTERING
SCATTERING LENGTH
SCHROEDINGER EQUATION
SERIES EXPANSION