Fine-structure constant for gravitational and scalar interactions

U. D. Jentschura
Phys. Rev. A 90, 022112 – Published 15 August 2014

Abstract

Starting from the coupling of a relativistic quantum particle to the curved Schwarzschild space time, we show that the Dirac-Schwarzschild problem has bound states and calculate their energies including relativistic corrections. Relativistic effects are shown to be suppressed by the gravitational fine-structure constant αG=Gm1m2/(c), where G is Newton's gravitational constant, c is the speed of light, and m1 and m2m1 are the masses of the two particles. The kinetic corrections due to space-time curvature are shown to lift the familiar (n,j) degeneracy of the energy levels of the hydrogen atom. We supplement the discussion by a consideration of an attractive scalar potential, which, in the fully relativistic Dirac formalism, modifies the mass of the particle according to the replacement mm(1λ/r), where r is the radial coordinate. We conclude with a few comments regarding the (n,j) degeneracy of the energy levels, where n is the principal quantum number, and j is the total angular momentum, and illustrate the calculations by way of a numerical example.

  • Figure
  • Received 5 March 2014

DOI:https://doi.org/10.1103/PhysRevA.90.022112

©2014 American Physical Society

Authors & Affiliations

U. D. Jentschura

  • Department of Physics, Missouri University of Science and Technology, Rolla, Missouri, MO 65409-0640, USA and MTA-DE Particle Physics Research Group, P.O. Box 51, H-4001 Debrecen, Hungary

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Issue

Vol. 90, Iss. 2 — August 2014

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