Hyperfine splitting in muonium, positronium, and hydrogen, deduced from a solution of Dirac's equation in Kerr-Newman geometry

Journal Article · Sun Jan 15 04:00:00 EST 1989 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.39.518· OSTI ID:6554991

Pekeris, C L; Frankowski, K

The nucleus is represented as a Kerr-Newman source, under the assumption that the angular momentum of the source is equal to the intrinsic spin angular momentum of the nucleus. The theoretical values of the hyperfine splitting obtained from a solution of Dirac's equation for this model of the muon, the positron, and the proton agree with the observed values in muonium, positronium, and hydrogen, to within the uncertainty in the respective QED corrections: except for an unaccounted factor of 2. In hydrogen one also has to introduce the observed value of the magnetic moment of the proton. The singularity in Dirac's radial differential equations is shifted from the origin, where it is located in the case of flat space, to a pair of conjugate points on the imaginary axis of the radial coordinate. Consequently, the energy eigenvalues have a trace of an imaginary part, making the bound states of our model unstable.

• Research Organization: Department of Applied Mathematics, The Weizmann Institute, Rehovot, Israel
• OSTI ID: 6554991
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 39:2; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
640303 -- Atomic
Molecular & Chemical Physics-- Positronium
Muonium
& Muonic & Mesic Atoms & Molecules
74 ATOMIC AND MOLECULAR PHYSICS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELECTRONIC STRUCTURE
ELEMENTS
EQUATIONS
EVALUATION
HYDROGEN
HYPERFINE STRUCTURE
KERR METRIC
METRICS
MUONIUM
NONMETALS
PARTIAL DIFFERENTIAL EQUATIONS
POSITRONIUM
WAVE EQUATIONS