Fock-Tani representation for positron-hydrogen scattering
A new second-quantization representation for low-energy positron-hydrogen scattering is derived by starting with the standard Fock representation and carrying out two canonical transformations, one to introduce the field operator for bound positronium and the other to introduce one for the bound atomic electron. The transformed ''Fock-Tani representation'' Hamiltonian is obtained in closed form. Its various terms have simple physical interpretations and manifest the various scattering and reaction channels. The interaction-matrix elements obtained are automatically renormalized through inclusion of bound-state--continuum orthogonality corrections. The definition of the S-matrix elements is simpler in the new representation since bound states are exactly redescribed therein as elementary particles. Certain constraints necessary and sufficient for the one-one property of the mapping from Fock- to Fock-Tani-state space are shown to be automatically satisfied when the asymptotic initial and final states for scattering processes are defined by the standard wave-packet method. This representation is expected to be useful for inclusion of the intermediate-state positronium channel in the standard many-body Green's-function approach to evaluation of S-matrix elements.
- Research Organization:
- Department of Physics and Institutes of Chemical Physics and Theoretical Science, University of Oregon, Eugene, Oregon 97403
- OSTI ID:
- 6864439
- Journal Information:
- Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 26:1; ISSN PLRAA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ATOM COLLISIONS
COLLISIONS
ELASTIC SCATTERING
ELEMENTS
FUNCTIONS
GREEN FUNCTION
HYDROGEN
MATRICES
MATRIX ELEMENTS
NONMETALS
POSITRON COLLISIONS
POSITRON-ATOM COLLISIONS
POSITRONIUM
S MATRIX
SCATTERING