NONADIABATIC THEORY OF ELECTRON-HYDROGEN SCATTERING

Technical Report · Sun Jul 01 04:00:00 EDT 1962

OSTI ID:4797626

Temkin, A

A rigorous theory of the s-wave elastic scattering of electrons from hydrogen is presented. The Schrodinger equation was reduced to an infinite set of coupled twodimensional partial differential equations. A zeroth order scattering problem was deftned by neglecting the coupling terms of the ftrst equation. An exact relation was derived between the phase shift of this zeroth order problem and the true phase shift. The difference between these was given by a rapidly convergent series whose terms correspond adiabatically to multipole distontions of the hydrogen by the incoming electron. Recognition of the physical significance of the zeroth order problem is considered basic to the understanding of the scattering problem. The exchange approximation for s-wave scattering is shown to be a variational approximation of the zeroth order problem. A penturbation theory was introduced to calculate the higher order corrections. The dipole correction had 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 were calculated for both singlet and triplet scattering, including up to quadrupole terms. The convergence was such that this number of terms should yield better than four place accuracy. Uncertainties in the calculated values decreased the accuracy to approximately three significant figures. (auth)

• Research Organization: National Aeronautics and Space Administration. Goddard Space Flight Center, Greenbelt, Md.
• NSA Number: NSA-16-027906
• OSTI ID: 4797626
• Report Number(s): NASA-TN-D-1343
• Country of Publication: United States
• Language: English

Related Subjects

DIFFERENTIAL EQUATIONS
ELECTRONS
ERRORS
FIELD THEORY
HYDROGEN
NUMERICALS
PERTURBATION THEORY
PHASE SHIFT
PHYSICS
QUANTUM MECHANICS
S-WAVE
SCATTERING
SCATTERING LENGTH
SCHROEDINGER EQUATION