Two fermion relativistic bound states: hyperfine shifts

Abstract

We discuss the hyperfine shifts of the Positronium levels in a relativistic framework, starting from a two fermion wave equation where, in addition to the Coulomb potential, the magnetic interaction between spins is described by a Breit term. We write the system of four first order differential equations describing this model. We discuss its mathematical features, mainly in relation to possible singularities that may appear at finite values of the radial coordinate. We solve the boundary value problems both in the singular and non singular cases and we develop a perturbation scheme, well suited for numerical computations, that allows to calculate the hyperfine shifts for any level, according to well established physical arguments that the Breit term must be treated at the first perturbative order. We discuss our results, comparing them with the corresponding values obtained from semi-classical expansions.

16 pages

References in corpus (8)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Precision physics of simple atoms: QED tests, nuclear structure and fundamental constants
• Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments
• Two-Body Dirac Equations for Nucleon-Nucleon Scattering
• How to obtain a covariant Breit type equation from relativistic Constraint Theory
• Variational Derivation of Relativistic Fermion-Antifermion Wave Equations in QED
• Singularity-Free Breit Equation from Constraint Two-Body Dirac Equations
• Two fermion relativistic bound states

Cited by in corpus (5)

• Two body relativistic wave equations
• Unified covariant treatment of hyperfine splitting for heavy and light mesons
• Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction
• Relativistic two fermion treatment of hyperfine transitions
• Relativistic two-body calculation of $b\bar{b}$-mesons radiative decays