Quasipotential Equation Corresponding to the Relativistic Eikonal Approximation
- 15 May 1971
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 3 (10), 2351-2356
- https://doi.org/10.1103/physrevd.3.2351
Abstract
A three-dimensional Lippmann-Schwinger-type equation for the elastic scattering amplitude and the corresponding homogeneous Schrödinger equation for the two-particle bound states are studied. The potential is defined as an infinite power series in the coupling constant which fits the perturbative expansion of the on-energy-shell scattering amplitude. The approximate equation obtained by keeping only the lowest-order term in the potential is local and has the following properties: (i) The scattering amplitude yields the relativistic eikonal approximation for large energies or small exchanged mass and momentum transfer; (ii) for the Coulomb problem the approximate equation is exactly soluble and leads to a relativistic Balmer formula including the fine-structure splitting.Keywords
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