Quantized magnetic flux through the orbits of hydrogen-like atoms within the atomic model of Sommerfeld

TL;DR

This paper explores how magnetic flux quantization in hydrogen-like atoms, within Sommerfeld's model, is affected by various magnetic sources, leading to energy shifts and a reinterpretation of electron spin.

Contribution

It demonstrates that magnetic flux quantization and resulting energy shifts can be explained without intrinsic electron spin, using classical orbital motion and magnetic moments.

Findings

External magnetic fields cause predictable energy shifts.

Hyperfine splitting and spin-orbit coupling are well-reproduced.

Electron 'spin' is reinterpreted as orbital motion and magnetic moment effects.

Abstract

Within the Sommerfeld atomic model the quantization of magnetic flux through the electronic orbits is investigated together with its dependency on additional sources of magnetic fields. These sources alter the magnetic flux through the atomic orbits and in consequence are causing energy shifts. This effect is investigated for the cases, where the source is an external magnetic field, the magnetic moment of the nucleus or the magnetic moment of the electron. The energy shifts due to external magnetic fields, the magnetic dipole contribution of the hyperfine splitting and the spin-orbit coupling can be reproduced very well. The meaning of 'spin', however, changes within this approach drastically. The unusual Land\'e g-factor of 2 for the electron is a result of the orbital motion and the magnetic moment of the electron rather than it is an intrinsic property of the electron.