Energy level shifts and transition probabilities in a relativistic atom

Лебедев, V. E. Cherkovets, S.V. Yusim

В. В. Скобелев

Christopher W. Churchill

The energy structures and transition energies of single-electron atoms and ions are presented. Five Nobel Prizes in Physics were awarded for the theories discussed in this chapter. We first review the Bohr model, which was based on quantized angular momentum and classical circular orbits. The wave model of Schrödinger followed, in which spherical boundary conditions quantized polar and azimuthal standing waves. The energies were identical to Bohr’s, but transition selection rules dictated the change in angular momentum of the system during absorption and emission. Dirac incorporated electron spin and relativistic energies, resulting in energy shifts and fine structure splitting of the energy levels for non-zero angular momentum states. Feynman and Swinger incorporated quantization of the electric vector potential. This physics broke energy degeneracies in the Dirac model and correctly predicted the famous Lamb shift. In this chapter, each of these models are described in detail. The final full characterization of the energy levels and transitions are presented. The chapter ends with a discussion on isotope shifting and transitions to the continuum (ionization/recombination).

Roger Boudet

В. Б. Терновський, О. В. Глушков, П. О. Заїчко +2 more

We have presented an effective relativistic approach for sensing and calculating energy of levels, probabilities and oscillator strengths (transition amplitudes, lifetimes) of a number of radiative transitions in the spectra of heavy Rydberg atoms of alkaline elements. It represents a new version of the relativistic model potential method. The approach is based on the relativistic many-body gauge-invariant perturbation theory with the improved Dirac-Kohn-Sham zeroth approximation and relativistic energy approach (S-matrix adiabatic Gell-Mann and Low formalism). We have shown that that during computing the energy and spectroscopic characteristics of the multielectron Rydberg atomic systems a new approach provides a precise accounting exchange-correlation effects, including effect of essentially non-Coulomb grouping of Rydberg levels, pressure continuum. There are received precise data on energy and spectroscopic parameters energy, radiation width, amplitude transitions, the lifetime) for Rydberg atoms Rb, Cs, Fr, particularly, transitions nS½→n’P½,3/2 (n=5,6; n’=10-70), nP½,3.2→n’D3/2,5/2 (n=5,6; n’=10-80) in the Rb, Cs spectra; for Rydberg Fr there are in most first calculated and predicted spectroscopic data on transition amplitude, lifetime of Rydberg states and transitions 7S½-nP½,3/2, 7P½,3.2-nD3/2,5/2 (n=20-80). Regarding the application of the obtained data it can be indicated on carrying out new types of radiative quantum sensors and frequency standards, quantum electronics and different quantum devices.

Mubarak Dirar Abd-Alla Yagoub, Mohammed El Idriss

Using generalized special relativistic energy-momentum relation the linear energymomentum Dirac relation was obtained. This equation was used to find Dirac generalized relativistic quantum equation. This equation was used to find the probability and the number of particles for each atomic energy level. The wave function found using this equation can give an expression for the number of electrons in each energy levels if the atomic radius is quantized and satisfy a certain relation.