Spin-Dependent Quantized Magnetic Flux Through The Electronic Orbits of Dirac Hydrogen Atom

TL;DR

This paper explores the quantized magnetic flux in Dirac hydrogen atom orbits caused by intrinsic magnetic moments, revealing flux quantization formulas and implications for optical transition selection rules and spin relaxation phenomena.

Contribution

It introduces a novel quantization formula for magnetic flux in Dirac hydrogen atom orbits considering intrinsic magnetic moments, linking it to optical transitions and spin relaxation.

Findings

Magnetic flux quantization: (n,l,m_{j})=[ n-l-m_{j}] _{0}

Application to optical transition selection rules

Insights into spin relaxation in nanostructures

Abstract

We investigate the quantized magnetic flux through the electronic orbits of Dirac hydrogen atom in the absence of an external magnetic field. The sources of the magnetic fields are taken to be that of proton's magnetic moment $\mu _{p}$ and electron's magnetic moment $\mu_{e}$ (or $\mu_{j}$) which has two components namely the orbital part $\mu_{l}$ and the spinning part $\mu_{s}$ >.We show that the quantized magnetic fluxes through the electronic orbits corresponding to the ($n,l=n-1,m_{j}$) eigenstates of Dirac hydrogen atom take the forms: $\Phi (n,l,m_{j})=[ n-l-m_{j}] \Phi_{0}$, where $\Phi _{0}=\frac{h}{| e|}$ is the flux quanta. The application of the present result to the selection rules for the optical transitions of hydrogen atom gives access to the spin flip-floppings. The present result is believed to serve a significant help for understanding the recent observations of spin relaxation in excitonic transitions (such as 1s -> 2p or 2p -> 3d) in nanostructures.