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Journal of Anhui Normal University

A LAW OF SPECTRA FOR HYDROGEN ATOM IN A UNIFORM ELECTRIC FIELD

Changxin Zhang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

According to a simplified formula for the secular equation and energy levels in the first-order Stark effect on hydrogen atom,and the selection rules for light radiation,a law for the splitting of hydrogen atom spectra in a uniform electric field is developed.

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Annual Meeting Optical Society of America•Jan 1, 1989•0 citations
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.
A numerical calculation of the DC Stark effect for hydrogen and sodium atoms and Wannier-Mott excitons in an external uniform DC electric field is carried out within the operator perturbation theory method. New adequate model for description of the unique especialitites in the photoionization spectra of the hydrogenic atoms is proposed. It is found that the Stark shift for the n=2 state of excitons in the Cu2 O semiconductor (yellow series) at the electric field strength 600 V/cm results in — 3,1 10 -4 eV which agrees well with experimental data of Gross et al. It is indicated also that the analogous unique especialitites may possibly take a place in the Wannier-Mott excitons spectra near the threshold boundary
The prediction of the energy level shifts and intensity transfer in atomic hydrogen and helium spectra caused by an external electric field was one of the first applications of wave mechanics. Early measurements relied on electrical discharge sources for excited atoms; since discharge processes will not produce excited states with n > 7 in observable densities, very large (10s to 100s kV cm) electric fields were required to resolve spectral modifications. The development of high peak power lasers enabled excitation to high n (Rydberg) states, increasing field sensitivity down to millivolts/cm and allowing comparison of experiment and theory in well-defined conditions. Field modified selection rules can be used to measure the field direction as well as magnitude. Analysis of line shape simulations of Stark modified Rydberg spectra reveals pitfalls in commonly used field measurement techniques. An ambiguity in defining series termination results in a factor of 2 discrepancy in field measurements based on Inglis Teller line merging. Field-induced line broadening (unresolved manifold splitting) in triplet and singlet helium are shown to differ significantly, with triplet broadening nonlinear with field.