Spin-Dependent Quantized Magnetic Flux Through The Electronic Orbits of   Dirac Hydrogen Atom
  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. 
M. Saglam, B. Boyacioglu, Z. Saglam, O. Yilmaz and K. K. Wan