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Izvestiya vysshikh uchebnykh zavedenii Fizika

Spatial transitions of electron in hydrogen-like atom with photon radiation

В. В. Скобелев

Published Jan 1, 2021• 0 citations
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Abstract

For the first time, electron transitions in a hydrogen-like atom with a change in spatial dimension D = 3® D ¢ = 1, 2 and energy of its state, accompanied by photon radiation, are considered. Similar "conversions" for some atoms were observed experimentally, but there was no theoretical explanation for this effect. Calculations were carried out in parabolic coordinates, as a result of which this approach is also of methodological interest, since these coordinates are rarely used in the literature.

DOI
10.17223/00213411/64/7/132

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For the first time, electron transitions in a hydrogen-like atom with a change in spatial dimension D = 3® D ¢ = 1, 2 and energy of its state, accompanied by photon radiation, are considered. Similar "conversions" for some atoms were observed experimentally, but there was no theoretical explanation for this effect. Calculations were carried out in parabolic coordinates, as a result of which this approach is also of methodological interest, since these coordinates are rarely used in the literature.
To describe the microscopic properties of matter, quantum mechanics uses wave functions, whose structure and time dependence is governed by the Schrödinger equation. In atoms the charge distributions described by the wave function are rarely observed. The hydrogen atom is unique, since it only has one electron and, in a dc electric field, the Stark Hamiltonian is exactly separable in terms of parabolic coordinates (η, ξ, φ). As a result, the microscopic wave function along the ξ coordinate that exists in the vicinity of the atom, and the projection of the continuum wave function measured at a macroscopic distance, share the same nodal structure. In this Letter, we report photoionization microscopy experiments where this nodal structure is directly observed. The experiments provide a validation of theoretical predictions that have been made over the last three decades.
Electron transitions and emission of an atom interacting with a spatially inhomogeneous ultrashort electromagnetic pulse are considered. The excitation and ionization probabilities are obtained as well as the spectra and cross sections of the reemission of such a pulse by atoms. By way of an example, one-and two-electron inelastic processes accompanying the interaction of ultrashort pulses with hydrogen-and helium-like atoms are considered. The developed technique makes it possible to take into account exactly the spatial non-uniformity of the ultrashort pulse field and photon momenta in the course of reemission.
The radiative transition probabilities in hydrogen have been calculated for all Stark transitions through n=25n=25n=25. In general, the total transition probability and lifetime of a particular state are a function of the parabolic quantum numbers n1{n}_{1}n1​, n2{n}_{2}n2​, and mmm. For m>0m>0m>0 and to within an error of the order of one percent the radiative lifetimes are functions only of nnn, mmm. The radiative lifetimes are presented graphically for all states from n=2n=2n=2 through n=25n=25n=25.
The theory of collisions of Rydberg atoms with rare-gas atoms is generalized to include the effects of an applied static electric field. Two effects occur. First, the field causes the states to split, and the increased energy separations lead to a decrease in the inelastic cross sections. Second, there is a change in the form of the wave functions, because the various Stark states in the field have electron charge distributions that may be localized in very different regions of space. The present work focuses on this second effect. With the description of the initial and final Stark states of the Rydberg atom by the proper electronic wave functions obtained in parabolic coordinates, cross sections are obtained for a variety of specific transitions of Rydberg atoms (n=10,15,and20n=10, 15, \mathrm{and} 20n=10,15,and20) caused by collisions. The calculations are strictly valid for hydrogen, but exhibit general features that are expected to apply to other Rydberg atoms as well. The results show a dramatic effect on the cross section for particular transitions depending on the degree of overlap of the initial and final charge distributions. In addition, it is observed that transitions are favored that involve small changes in the azimuthal quantum number mmm. The origin of this tendency is discussed.