Relativistic Coulomb problem for Z larger than 137

Abstract

We propose a relativistic one-parameter Hermitian theory for the Coulomb problem with an electric charge greater than 137. In the non-relativistic limit, the theory becomes identical to the Schrödinger-Coulomb problem for all Z. Moreover, it agrees with the Dirac-Coulomb problem to order (\alph Z)^2, where αis the fine structure constant. The vacuum in the theory is stable and does not suffer from the "charged vacuum" problem for all Z. Moreover, transition between positive and negative energy states could be eliminated. The relativistic bound states energy spectrum and corresponding spinor wavefunctions are obtained.

12 pages, 4 figures

References in corpus (4)

• Dirac and Klein-Gordon equations with equal scalar and vector potentials
• Calculation of electron-positron production in supercritical uranium-uranium collisions near the Coulomb barrier
• Supercritical Dirac resonance parameters from extrapolated analytic continuation methods
• Pseudospin, Spin, and Coulomb Dirac-Symmetries: Doublet Structure and Supersymmetric Patterns

Cited by in corpus (1)

• Solution of Effective-Mass Dirac Equation with Scalar-Vector and Pseudoscalar Terms for Generalized Hulthén Potential