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Revista Colombiana de Física

The Absorption Spectra of General Rydberg Atoms in Crossed Electric and Magnetic Fields: Quantum vs Classical Core Scattering

Rodrigo Carboni, Francisco Frutos─Alfaro

Published Sep 12, 2012• 0 citations
OpenAlex

Abstract

The photoabsorption spectra of general atoms in external fields depend on the scattering by the electronic core. Two theoretical approaches have been developed to investigate this process: The fully quantum mechanical treatment and the classical treatment of the scattering. In this article we implement the semiclassical closed-orbit theory to be used in the case of atoms in crossed fields with classical scattering and compare the results obtained for planar orbits by both approaches.

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The photoabsorption spectra of general atoms in external fields depend on the scattering by the electronic core. Two theoretical approaches have been developed to investigate this process: The fully quantum mechanical treatment and the classical treatment of the scattering. In this article we implement the semiclassical closed-orbit theory to be used in the case of atoms in crossed fields with classical scattering and compare the results obtained for planar orbits by both approaches.
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This paper reports on the investigation of excitation spectra of rubidium Rydberg atoms in crossed electric and magnetic fields. The quasi-Landau spectra were evaluated and their Fourier transforms calculated. The scaled spectral scans used for this purpose were obtained by changing the electric and magnetic fields as well as the laser frequency in an appropriate way. The observed resonances could be explained completely by semiclassical orbits. Only orbits showing overlap with the ground-state wave function are observed. The polarization dependence of certain components in the Fourier spectra can be explained by the shape of the semiclassical orbits. The electric dipole moments of the atoms resulting from the shift of the quasi-Landau structures in a changing electric field agree quite well with the corresponding semiclassical orbits.
Using a simple analytic formula from closed orbit theory, we have calculated the photoabsorption spectra of Li atom in different magnetic fields. Closed orbits in the corresponding classical system have also been obtained for B =5.96T. We demonstrate schematically that the closed orbits disappear gradually with the decrease of the magnitude of the magnetic field. This gives us a good method to control the closed orbits in the corresponding system by changing the magnetic field and thus changing the peaks in the photoabaorption spectra. By comparing the photoabsorption spectra of Li atom with those of hydrogen case, we find the core-scattered effects play an important role in multi-electron Rydberg atoms.
The problem of Rydberg atomic spectra in crossed electric F and magnetic B fields (combined Stark–Zeeman effects), as well as an oscillating electric field are under consideration. The main problem is the great array of radiative transitions between the Rydberg atomic states. The different versions of semiclassical approaches are applied for the solution of the problem. New approximate selection rules are established to simplify the matrix elements of radiative transitions, making it possible to reduce the complex expressions of Gordon’s hypergeometric series to the trivial trigonometric functions. Simple analytical formulas for the dipole matrix elements of a Rydberg hydrogen-like atom in external crossed electric and magnetic fields for Hnα are obtained. The specific calculations are presented for n = 10 to 9 transition both for parallel and perpendicular orientations of F–B fields. The result of Blokhintsev for a single Stark component in oscillating field is generalized for the array of radiative transitions between Rydberg atomic states. Such spectra with large values of modulation index are compared with static ones.
By combining the B-spline basis set with model potential (B-spline + MP), we present oscillator strength spectra of Rydberg Li atoms in external fields. The photoabsorption spectra are analyzed. Over the narrow energy ranges considered in this paper, the structure of the spectra can be independent of the initial state chosen for a given atom. Our results are in good agreement with previous high-precision experimental data and theoretical calculations, where the R-matrix approach together with multichannel quantum defect theory (R-matrix+MQDT) was used. It is suggested that the present methods can be applied to deal with the oscillator strength spectra of Rydberg atoms in crossed electric and magnetic fields.