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Technical Physics

Features of the bremsstrahlung accompanying collisions with a hydrogen atom in an excited state

Andrei V. Korol, O. I. Obolensky, А. В. Соловьев

Published Oct 1, 1999• 4 citations

Abstract

The features of the bremsstrahlung appearing during a collision of a fast charged particle with a hydrogen atom (or hydrogenic ion) in an excited state are investigated. It is shown that the emission spectrum of photons with energies greater than the ionization potential of a given excited state (except the 2 s state) displays narrow lines, which are caused by de-excitation of the atom in an intermediate state. It is demonstrated that the scattering of a charged particle on an excited hydrogen atom produces a feature which is not observed in the case of scattering on a ground-state hydrogen atom. Expressions are obtained for the generalized dynamic polarizability of the hydrogen atom and hydrogenic ions in the 1 s , 2 s , and 3 s states. A method is developed for deriving expressions for the generalized dynamic polarizabilities of other excited states through the use of the Coulomb Green’s function and representation of the electronic wave function in terms of the differentiation of the generating functions of Laguerre polynomials. The bremsstrahlung cross sections for electrons and positrons colliding with hydrogen atoms in the 1 s , 2 s , and 3 s states are calculated.

DOI: 10.1134/1.1259487

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The features of the bremsstrahlung appearing during a collision of a fast charged particle with a hydrogen atom (or hydrogenic ion) in an excited state are investigated. It is shown that the emission spectrum of photons with energies greater than the ionization potential of a given excited state (except the 2 s state) displays narrow lines, which are caused by de-excitation of the atom in an intermediate state. It is demonstrated that the scattering of a charged particle on an excited hydrogen atom produces a feature which is not observed in the case of scattering on a ground-state hydrogen atom. Expressions are obtained for the generalized dynamic polarizability of the hydrogen atom and hydrogenic ions in the 1 s , 2 s , and 3 s states. A method is developed for deriving expressions for the generalized dynamic polarizabilities of other excited states through the use of the Coulomb Green’s function and representation of the electronic wave function in terms of the differentiation of the generating functions of Laguerre polynomials. The bremsstrahlung cross sections for electrons and positrons colliding with hydrogen atoms in the 1 s , 2 s , and 3 s states are calculated.

The authors demonstrate in this work that there is a peculiar source of low-frequency photon emission when a slow massive charged particle collides with an excited hydrogen atom. This radiation is generated by the rotating dipole moment of the hydrogen during the collision. The specific feature of the problem is in the appearance of the dipole moment of the excited hydrogen due to mixing of degenerated levels with different parity in the field of the projectile particle (linear Stark effect). The radiation associated with transitions between components of the Stark multiplet is also considered. Its contribution to the total radiation spectrum is shown to be important.

High-energy cross sections for the excitation of the 3s state of the hydrogen atom by simultaneous collision with electrons and photons are calculated under the second-order Bethe-Born approximation, both as functions of electron energy and of laser intensity. Resonant structures are shown to arise as a function of laser-photon frequency. The behaviour of these resonances is described and their origin explained. It is concluded that these resonances are characteristic of the simultaneous electron-photon excitation process itself and can occur for any atomic target, under suitable conditions.

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, \mathrm{and} 20

) 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

m

. The origin of this tendency is discussed.

We investigate the Bremsstrahlung originating from fast non-relativistic electron scattering on an atom in the spectral region near the Fano resonance including the polarization channel and interference term. It is shown that the account for polarization Bremsstrahlung leads to a significant increase of the total Bremstrahlung cross section near the Fano resonances. Numerical calculations are carried out for the first autoionization states 2l2l' of the Helium atom in the framework of the Born approximation that goes beyond the dipole approximation of the dynamic polarizability of the atom.

This paper is a theoretical discussion of a "coherence effect" in the excitation of hydrogen atoms to the

n=3

state by electron bombardment. By coherence is meant that the density matrix describing the atom after the collision has off-diagonal matrix elements in the field-free basis. The differential cross section for producing Balmer-$\ensuremath{\alpha}$ photons at 90\ifmmode^\circ\else\textdegree\fi{} to the electron beam is calculated as a function of an applied longitudinal electric field. The off-diagonal elements show up as a dependence of the observed light on the directions of the electric field. Theoretical results based on the Born approximation are compared with an experiment at 200 and 500 eV. It is pointed out that this method for measuring relative phases of scattering amplitudes can be generally applied and is not restricted to

n=3

excitation of hydrogen.