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Journal of Modern Physics

Spin Dependent Selection Rules for Photonic Transitions in Hydrogen-Like Atoms

Ziya Saglam, M. Sağlam

Published Jan 1, 2011• 0 citations
Publisher

Abstract

Spin dependent selection rules for photonic transitions in hydrogen-like atoms is derived by using the solution of Dirac equation for hydrogen-like atoms. It is shown that photonic transitions occur when [ Δj=0,±1,±2, while Δmj=0,±1,±2 ]. By applying the spin dependent selection rules, we can explain the observed (6s→7s) transition in Cesium (Cs) atom.

DOI
10.4236/jmp.2011.28092

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arXiv:1411.1591•Nov 6, 2014•0 citations
Spin dependent selection rules for photonic transitions in hydrogen-like atoms is derived by using the solution of Dirac equation for hydrogen-like atoms. It is shown that photonic transitions occur when [ Δj=0,±1,±2, while Δmj=0,±1,±2 ]. By applying the spin dependent selection rules, we can explain the observed (6s→7s) transition in Cesium (Cs) atom.
We have investigated the spin dependent selection rules for dipole transitions in the hydrogen atom by using the solution of Dirac equation. We showed that some transitions allow spin flip which is not possible according to the conventional selec-tion rules. As an example we look at 1s-2p dipole transitions. The percentage of the spin flip rate in (1s-2p) is found to be 56 % which is larger that the non-flip rate. The present result is believed to serve a significant help for understanding the recent observation of the spin flip in the excitonic transitions in nanostructures.
We have calculated the changes in the quantized magnetic fluxes corresponding to the electronic orbits of Dirac hydrogen atom within the framework of Dirac theory and found that the flux change between the final state and the initial state is equal to (±Φ 0 or zero).We have also calculated the non-zero matrix elements for dipole transitions (such as 1s↔2p and 2p↔3d) for the solutions of Dirac hydrogen atom. We find a complete agreement among all the above results. The combined result is that photon should carry an intrinsic flux quantum of (Φ 0 =hc/e).
We have observed the direct single-photon electric dipole excitation of the 7 2S1/2 state of cesium, by exciting the 6 2S1/2 ground state in an external d. c. electric field of 10 to 1 000 V/cm with a single-mode, c. w., tunable dye laser. The resonance was detected by monitoring the decay fluorescence from the excited state. We verified the selection rules obeyed by the hyperfine transitions which depend on the relative orientation of the linear polarization of the beam with respect to the field. When they are orthogonal, the line pattern reflects the existence of a spin-dependent part of the polarizability induced by spin-orbit effects, the size of which was measured with respect to that of the scalar part. Results in very weak fields show that the oscillator strength of the 6S-7S transition is smaller than 2 x 10-13.
We establish the existence of spin-statistic selection rules (SSSR) for multi-equal-photon transitions in atomic systems. These selection rules are similar to those for systems of many equivalent electrons in atomic theory. The latter ones are the direct consequence of Pauli exclusion principle. In this sense the SSSR play the role of the exclusion principle for photons: they forbid some particular states for the photon systems. We established several SSSR for few-photon systems. 1) First rule (SSSR-1): two-equivalent photons involved in any atomic transition can have only even values of the total angular momentum J. This selection rule is an extension of the Landau-Yang theorem to the photons involved in atomic transitions. 2) second rule (SSSR-2): three equivalent dipole photons involved in any atomic transition can have only odd values of the total angular momentum J=1,3. 3) third rule (SSSR-3): four equivalent dipole photons involved in any atomic transition can have only even values of the total angular momentum J=0,2,4. We also suggest a method for a possible experimental test of these SSSR by means of laser experiments.