Relativistic Coulomb scattering of spinless bosons

Abstract

The relativistic scattering of spin-0 bosons by spherically symmetric Coulomb fields is analyzed in detail with an arbitrary mixing of vector and scalar couplings. It is shown that the partial wave series reduces the scattering amplitude to the closed Rutherford formula exactly when the vector and scalar potentials have the same magnitude, and as an approximation for weak fields. The behavior of the scattering amplitude near the conditions that furnish its closed form is also discussed. Strong suppressions of the scattering amplitude when the vector and scalar potentials have the same magnitude are observed either for particles or antiparticles with low incident momentum. We point out that such strong suppressions might be relevant in the analysis of the scattering of fermions near the conditions for the spin and pseudospin symmetries. From the complex poles of the partial scattering amplitude the exact closed form of bound-state solutions for both particles and antiparticles with different scenarios for the coupling constants are obtained. Perturbative breaking of the accidental degeneracy appearing in a pair of special cases is related to the nonconservation of the Runge-Lenz vector.

References in corpus (11)

• Spin symmetry in the anti-nucleon spectrum
• Relativistic Symmetry Suppresses Quark Spin-Orbit Splitting
• Pseudospin symmetry in single particle resonant states
• Pseudospin symmetry in single particle resonances in spherical square wells
• Spin and pseudospin symmetries in the antinucleon spectrum of nuclei
• Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles
• The Resurrection of a Symmetry in Nucleon - Nucleus Scattering
• Spin and pseudospin symmetries of the Dirac equation with confining central potentials
• Violation of pseudospin symmetry in nucleon-nucleus scattering: exact relations
• Relevance of pseudospin symmetry in proton-nucleus scattering
• On the partial wave amplitude of Coulomb scattering in three dimensions

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