Exact Solution of the One-Photon-ExchangeNDEquations
- 29 July 1966
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 147 (4), 984-992
- https://doi.org/10.1103/PhysRev.147.984
Abstract
The exact solution of the single-Yukawa-meson-exchange equations is obtained in the zero-meson-mass (Coulomb) limit. The solution sums an infinite series of infrared-divergent ladder-graph fragments into finite, unitary partial-wave amplitudes. As with the Schrödinger equation for the hydrogen atom, one finds an infinite number of bound states (zeros of the function) with an accumulation point at threshold. These bound-state poles of the scattering amplitude arise from the long-range force in much the same way as dynamical bound states arise generally in dispersion theory, thus allowing a discussion of the long-range force rather naturally in the usual dispersion-theoretic terms. The bound-state poles are neither so deeply bound nor so dense as those of the hydrogen atom, thus providing some understanding of the role of the one-photon-exchange force relative to the (long-range) multiple-photon-exchange forces. The possibilities for extending the technique to the relativistic one-photon case and the question of electromagnetic corrections to the strong interactions are briefly discussed. Finally, some possible approaches to including higher order photon exchanges are considered.
Keywords
This publication has 9 references indexed in Scilit:
- Solution of very Singular N/D Equations—An Approach to Nonrenormalizable Field TheoryJournal of Mathematical Physics, 1966
- Perturbed Bound-State Poles in Potential Scattering. IPhysical Review B, 1966
- -Matrix Theory and Higher Order Corrections to the Weak InteractionsPhysical Review B, 1965
- -Matrix Method for Calculation of Electromagnetic Corrections to Strong InteractionsPhysical Review B, 1964
- Bound on Screening Corrections in Beta DecayPhysical Review B, 1964
- Propriétés analytiques de l’amplitude de diffusion de deux particules chargées interagissant par un potentiel du type de yukawaIl Nuovo Cimento (1869-1876), 1962
- Analyticity in the Complex Angular Momentum Plane of the Coulomb Scattering AmplitudePhysical Review B, 1962
- The infrared divergence phenomena and high-energy processesAnnals of Physics, 1961
- On higher Born approximations in potential scatteringProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1951