# Exchange effects in atomic K-shell ionisation

TL;DR: In this article, a modified form of the Ochkur approximation for the exchange amplitude is suggested for the calculation of doubly differential cross sections (d sigma /dE1 d Omega 1).

Abstract: Exchange effects in atomic K-shell ionisation have been re-examined. A modified form of the Ochkur approximation (1964) for the exchange amplitude is suggested. This is suitable for application to the calculation of doubly differential cross sections (d sigma /dE1 d Omega 1).

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TL;DR: In this paper, the energy spectrum of scattered particles in the K-shell ionization of medium to heavy atoms by relativistic electrons and positrons with exchange effects has been calculated for various kinematic conditions.

Abstract: The energy spectrum of scattered particles in the K-shell ionization of medium to heavy atoms by relativistic electrons and positrons with exchange effects has been calculated for various kinematic conditions. In this calculation, the final state is described by a non-relativistic multiple-scattering wavefunction of Das and Seal (1993a Phys. Rev. A 47 2978; 1998 J. Phys. B: At. Mol. Opt. Phys. 31 2355) multiplied by suitable spinors. Exchange effects in the atomic K-shell ionization of 47Ag atoms by relativistic electrons show better agreement with the available experimental data. The peaks are very similar to those observed in the relativistic K-shell ionization of 47Ag atoms by electrons at 500 keV energy (Schule and Nakel 1982 J. Phys. B: At. Mol. Phys. 15 L639). Some other theoretical computational results are also presented here for comparison. Experimental verification of the present results for higher incident energies and other theoretical calculations by similar wavefunction theories will be interesting.

6 citations

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TL;DR: In this article, a relativistic calculation of the cross section for the ionization from the K and L shells by high-energy electrons is presented, using the first-order Born approximation to treat the interaction between the scattered and atomic electrons.

Abstract: Results of a relativistic calculation of the cross section for the ionization from the K and L shells by high-energy electrons are presented. The calculation use the first-order Born approximation to treat the interaction between the scattered and atomic electrons. Plane waves are used to treat the high-energy scattered electron, while solutions of the Dirac equation in a Hartree-Slater central potential are used to describe the atomic electrons. Results are presented for a set of elements from Z = 18 to 92 and incident energies from 50 keV to 1 GeV. Calculated results are given for the correction due to the density effect arising from the polarizability of the medium. In the calculation of this correction, the medium is treated as composed of free electons.

147 citations

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TL;DR: Cross sections for the K-shell ionization of medium-heavy atoms by relativistic electrons have been calculated in a relativist framework in the Coulomb gauge to order ..cap alpha../sub 0/ ( = e/sup 2//hc) in the interaction Hamiltonian.

Abstract: Cross sections for the K-shell ionization of medium-heavy atoms by relativistic electrons have been calculated in a relativistic framework in the Coulomb gauge to order ..cap alpha../sub 0/ ( = e/sup 2//hc) in the interaction Hamiltonian. Here exchange is neglected. The incident- and scattered-electron wave functions are described by Dirac plane waves. Only the bound- and ejected-electron wave functions are described nonrelativistically for a screened Coulomb potential, used earlier by the present authors. Thus the screening effect is taken into account in this calculation in a satisfactory manner. The calculation is a repetition of what has been published recently by the present authors with one important exception: Here, the ejected-electron continuum state wave function that is used is determined variationally for the above screened Coulomb potential. Thereby some perturbation approximation of ad hoc nature could be avoided. As a consequence, considerable improvement is noticed in the total cross-section results. Comparison with experimental results for /sup 29/Cu, /sup 47/Ag, and /sup 79/Au shows a good agreement. The calculation may easily be extended to ionization from other shells.

31 citations

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TL;DR: In this paper, a theoretical study on the differential cross-section for inner-shell ionization of medium-heavy atoms has been made, and special attention has been paid to the study of the angular distribution of the scattered electrons, scattered after ionizing a 50Sn atom, and to the momentum distribution of electrons ejected from the atom.

Abstract: A theoretical study on the differential cross-section for the inner-shell ionization of medium-heavy atoms has been made. Special attention has been paid to the study of the angular distribution of the scattered electrons, scattered after ionizing a50Sn atom, and to the momentum distribution of the electrons ejected from the atom.

30 citations

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TL;DR: Inner shell ionization cross sections of silver and gold have been calculated from a result which uses the relativistic Sommerfeld-Maue wavefunction for the ejected electron as mentioned in this paper.

Abstract: Inner-shell ionization cross sections of silver and gold have been calculated from a result which uses the relativistic Sommerfeld-Maue wavefunction for the ejected electron. The results have been compared with the results of Das (see ibid., vol.7, 923 (1974)), which use the non-relativistic Coulomb wavefunction for the ejected electron. The comparison shows that there is only a few percent lowering in total cross section under these improved calculations and the overall trend of the curves for total cross section and the conclusion of Das are maintained.

25 citations

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TL;DR: In this paper, the emission of x-rays following the electron bombardment of an atom is caused by three processes: electron-nucleus (e-n) bremsstrah-lung, electron-electron bremsStrahlung and inner-shell ionisation.

Abstract: The emission of x-rays following the electron bombardment of an atom is caused by three processes: electron-nucleus (e-n) bremsstrah-lung, electron-electron (e-e) bremsStrahlung and inner-shell ionisation. The bremsStrahlung processes have continuous spectra of photon energy (k) and outgoing electron energy (T), the ionisation is accompanied by emission of characteristic x-rays and by a continous electron spectrum (Auger electrons are not considered here).

19 citations