Limiting behaviors of off-shell scattering wave functions and T matrices for centrally modified Coulomb potentials

Journal Article · Fri Jul 15 04:00:00 EDT 1988 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.38.636· OSTI ID:7058377

Alston, S

In the formal theory of scattering, the limiting behavior of off-energy-shell scattering wave functions and T matrices as the energy shell is approached is of considerable importance in deriving an impulse approximation to the full scattering amplitudes. On-shell limits do not exist for the pure Coulomb potential, but sufficiently near the shell the off-shell wave function and T matrix are approximated by the continuum eigenstate and scattering amplitude, respectively, multiplied by certain ''off-shell'' factors. For central potentials which are Coulomb-like at large distances, but modified at smaller radii, it is shown that the on-shell limits again do not exist and the near-shell approximations mimic the pure Coulomb case with the asymptotic charge appearing in the off-shell factors. Numerical results for a realistic atomic potential covering a broad range of defects from the energy shell give a picture of the approximations involved and show that the errors arising from the use of near-shell forms are comparable in magnitude to the energy defects divided by the energy.

• Research Organization: Joint Institute for Laboratory Astrophysics, National Bureau of Standards and University of Colorado, Campus Box 440, Boulder, Colorado 80309-0440
• OSTI ID: 7058377
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 38:2; ISSN PLRAA
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
74 ATOMIC AND MOLECULAR PHYSICS
CENTRAL POTENTIAL
COULOMB FIELD
ELECTRIC FIELDS
ERRORS
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IMPULSE APPROXIMATION
MATRICES
POTENTIALS
S MATRIX
SCATTERING
WAVE FUNCTIONS