Hyperfine Wave Functions and Force Densities for the Hydrogen Atom

TL;DR

This paper investigates how magnetic hyperfine interactions influence the relativistic wave functions and force densities of the hydrogen atom's electron, revealing shifts in electron density and detailed force balance analysis.

Contribution

It provides a numerical analysis of hyperfine effects on relativistic hydrogen wave functions, including force density calculations and virtual positron effects.

Findings

Hyperfine interaction shifts electron density toward the proton in the singlet state

Force densities are balanced and analyzed across different hyperfine states

Wave function behavior is studied at distances smaller than the proton radius

Abstract

This study addresses the effect of the magnetic hyperfine interaction on the relativistic H1s wave functions. These are used to calculate the electric, magnetic, and confinement force densities acting on the 1s electron. The magnetic field couples Dirac equations for different angular momenta. These are solved numerically for the hyperfine singlet and triplet, as well as for a classical magnetic dipole. In the singlet ground state the hyperfine interaction shifts the electron density toward the proton. A similar shift is found for the classical dipole, and an opposite shift for the triplet. The cross-over between charge accumulation and depletion occurs at 1.325 times the Bohr radius. The behavior of the wave functions is investigated down to distances smaller than the proton radius, including the incorporation of virtual positrons. The force densities are determined and balanced against each other.