Analytic properties of the amplitude for elastic forward scattering of electrons by atoms

Journal Article · Wed Mar 01 04:00:00 EST 1978 · Sov. Phys. - JETP (Engl. Transl.); (United States)

OSTI ID:6473278

Amus'ya, M Y; Kuchiev, M Y

It is shown that the exchange amplitude for forward scattering has an Additional cut at the left semi-axis of the complex energy plane. The branch point is located at the binding energy of the electron in the atom. For scattering by hydrogen atoms, the amplitude diverges logarithmically at E=-1 Ry and hence this branch point is logarithmic. On the left-hand axis of the physical sheet, no singularities have been observed besides the poles corresponding to bound states of the negative ion. Although branch points exist at energies equal to the ionization potentials of the atomic excited states, they lie in the unphysical sheets and hence do not affect the dispersion relation. The position and nature of the singularity is completely determined by the shape of the interaction potential. The singularity also exists for shortrange potentials, but it is considerably separated from the physical region, whereas, in the case of Coulomb forces, it is close to it and plays an essential role in the dispersion relation.

• Research Organization: A. F. Ioffe Physico-technical Institute, USSR Academy of Sciences
• OSTI ID: 6473278
• Journal Information: Sov. Phys. - JETP (Engl. Transl.); (United States), Journal Name: Sov. Phys. - JETP (Engl. Transl.); (United States) Vol. 47:3; ISSN SPHJA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
AMPLITUDES
ATOM COLLISIONS
COLLISIONS
CRYOGENIC FLUIDS
DISPERSION RELATIONS
ELASTIC SCATTERING
ELECTRON COLLISIONS
ELECTRON-ATOM COLLISIONS
ELEMENTS
FLUIDS
HYDROGEN
NONMETALS
SCATTERING
SCATTERING AMPLITUDES
SINGULARITY