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SPIN-DEPENDENT SELECTION RULES FOR DIPOLE TRANSITIONS

M. Sağlam, Bahadır Boyacıoğlu, Ziya Saglam

Published Jan 1, 2006• 0 citations
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Abstract

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.

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Comment on SPIN-DEPENDENT SELECTION RULES FOR DIPOLE TRANSITIONS

A.S. Shumovsky

Despite the fact that properties of atomic transitions are well known since the early days of quantum mechanics, the theoretical analysis of peculiarities of the spectroscopic data still attracts a great deal of interest (e.g., see recent monograph [1]). It is well known that some nanostructures like quantum dots and quantum wells behave like twoor multi-level atoms. For example, an exciton-polariton confined in a quantum well represents an ideal two-level atom, manifesting a number of specific phenomena such as collaps and revival of Rabi oscillations [2, 3, 4]. Similar effects can also be observed in quantum dots [5, 6]. Let us stress that those “artificial atoms” are considered nowadays in the context of design of a hardware for realization of quantum computing. It has been observed that the dipole transitions in excitons and some nanostructures can manifest spin-flip effects [7, 8]. In the article by M. Saglam et al, it is shown that even the conventional Dirac model of hydrogen atom surprisingly allows spin-flip effects. The corresponding rate seems to be quite high (more than 50%).

•Jan 1, 2006•0 citations

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

Ziya Saglam, M. Sağlam

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.

Journal of Modern Physics•Jan 1, 2011•0 citations

Spin dependent selection rules for photonic transitions in hydrogen-like atoms

M. Sağlam, Ziya Saglam

We calculate the spin dependent selection rules for photonic transitions in hydrogen-like atoms by taking the eigenfunctions of Dirac hydrogen-like atoms. It is shown that photonic transitions occur when [Δ j = 0,±l,±2 while Δ m j = 0,±1,±2]. We apply the present selection rules to the so-called parity violating transition (such as 6s → 7s in atomic Cesium Cs) and show that it is possible according to the present selection rules.

Journal of Physics Conference Series•Nov 5, 2012•0 citations

Quantized magnetic flux through the electronic orbits of dirac hydrogen atom and its relation with the spin dependent selection rules and photons intrinsic flux

Ziya Saglam, M. Sağlam

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).

Journal of Physics Conference Series•Nov 1, 2009•1 citation

Non-Markovian treatment of the spontaneous 2P1/2to 1S1/2transition in the Dirac hydrogen atom

JOSIP SEKE

For the first time to the author's knowledge, a rigorous mathematical treatment of the spontaneous 2P 1/2 to 1S 1/2 transition, going beyond the usual Markov approximation, is presented in the case of the Dirac hydrogen atom. The relevant transition matrix elements of the Dirac Hamiltonian are calculated without the dipole approximation. Further, a non-Markovian equation of motion for the non-decay probability of the unstable 2P 1/2 2 state is derived, by using a self-consistent projection-operator method recently developed by the present author. By a rigorous analytical treatment of the non-Markovian equation, deviations from exponential decay for asymptotic times are obtained. Moreover, by careful error estimations deviations from exponential decay for finite times with definite validity range are also calculated. Finally, for the radiative lineshape a new quasi-Lorentzian distribution is obtained.

Journal of Physics A Mathematical and General•Feb 7, 1992•14 citations

Spin-dependent Bohm trajectories associated with an electronic transition in hydrogen

C Colijn, E R Vrscay

The de Broglie–Bohm causal theory of quantum mechanics with spin-dependence is used to determine electron trajectories when a hydrogen atom is subjected to (semiclassical) radiation. The transition between the 1s ground state and the 2p 0 state is examined. It is found that transitions can be identified along Bohm trajectories. The trajectories lie on invariant hyperboloid surfaces of revolution in R 3 . The energy along the trajectories is also discussed in relation to the hydrogen energy eigenvalues.

arXiv:quant-ph/0304203•Journal of Physics A Mathematical and General•Apr 8, 2003•13 citations
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.
Despite the fact that properties of atomic transitions are well known since the early days of quantum mechanics, the theoretical analysis of peculiarities of the spectroscopic data still attracts a great deal of interest (e.g., see recent monograph [1]). It is well known that some nanostructures like quantum dots and quantum wells behave like twoor multi-level atoms. For example, an exciton-polariton confined in a quantum well represents an ideal two-level atom, manifesting a number of specific phenomena such as collaps and revival of Rabi oscillations [2, 3, 4]. Similar effects can also be observed in quantum dots [5, 6]. Let us stress that those “artificial atoms” are considered nowadays in the context of design of a hardware for realization of quantum computing. It has been observed that the dipole transitions in excitons and some nanostructures can manifest spin-flip effects [7, 8]. In the article by M. Saglam et al, it is shown that even the conventional Dirac model of hydrogen atom surprisingly allows spin-flip effects. The corresponding rate seems to be quite high (more than 50%).
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).
For the first time to the author's knowledge, a rigorous mathematical treatment of the spontaneous 2P 1/2 to 1S 1/2 transition, going beyond the usual Markov approximation, is presented in the case of the Dirac hydrogen atom. The relevant transition matrix elements of the Dirac Hamiltonian are calculated without the dipole approximation. Further, a non-Markovian equation of motion for the non-decay probability of the unstable 2P 1/2 2 state is derived, by using a self-consistent projection-operator method recently developed by the present author. By a rigorous analytical treatment of the non-Markovian equation, deviations from exponential decay for asymptotic times are obtained. Moreover, by careful error estimations deviations from exponential decay for finite times with definite validity range are also calculated. Finally, for the radiative lineshape a new quasi-Lorentzian distribution is obtained.
The de Broglie–Bohm causal theory of quantum mechanics with spin-dependence is used to determine electron trajectories when a hydrogen atom is subjected to (semiclassical) radiation. The transition between the 1s ground state and the 2p 0 state is examined. It is found that transitions can be identified along Bohm trajectories. The trajectories lie on invariant hyperboloid surfaces of revolution in R 3 . The energy along the trajectories is also discussed in relation to the hydrogen energy eigenvalues.