Treatment of the two-body Coulomb problem as a short-range potential (original) (raw)
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We obtain the exact solution to the Dirac equation with the Pöschl-Teller double ringshaped Coulomb (PTDRSC) potential for any spin-orbit quantum number . The relativistic scattering amplitude for spin 12 particles in the field of this potential has been studied. The wave functions are expressed in terms of the hyper-geometric series of the continuous states on the 2 k scale. A formula for the phase shifts has also been found. In the nonrelativistic limits, our solution to the Dirac system converges to that of the Schrödinger one. At the high temperature, the partition function is calculated in order to study the behavior of some thermodynamic properties.
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The fundamental quantities of potential scattering theory are generalized to accommodate longrange interactions. New definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.