A Modified Formal Theory on Semi-Relativistic Effects during Electron Emission from Metallic Surfaces upon the Impact of High Energy Particles

Affiliation(s)

Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong, Bangladesh.

Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong, Bangladesh.

ABSTRACT

In this paper we introduce a formal theory on unveiling relativistic effects during electron emission from clean metallic surfaces upon high charged particle impact using a Jellium-type wave function including suitable spinors. In addition image charge final state electron surface interactions have been initiated in the relativistic region as well as the scattering of the projectile from the multi-center bulk potential. Finally, a semi-relativistic condition is considered in place of the ionization mechanism of scattering from an aluminium semi-infinite solid target by non-relativistic electrons to determine multiple differential cross-section.

Cite this paper

S. Dhar, M. G. Hafez and A. Saha, "A Modified Formal Theory on Semi-Relativistic Effects during Electron Emission from Metallic Surfaces upon the Impact of High Energy Particles,"*Open Journal of Microphysics*, Vol. 3 No. 4, 2013, pp. 121-127. doi: 10.4236/ojm.2013.34018.

S. Dhar, M. G. Hafez and A. Saha, "A Modified Formal Theory on Semi-Relativistic Effects during Electron Emission from Metallic Surfaces upon the Impact of High Energy Particles,"

References

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http://dx.doi.org/10.1007/BF02822628

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http://dx.doi.org/10.1088/0953-4075/25/6/020

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http://dx.doi.org/10.1016/0370-2693(76)90115-5

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http://dx.doi.org/10.1088/0953-4075/25/20/025

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http://dx.doi.org/10.1007/s004600050028

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http://dx.doi.org/10.1088/0022-3700/15/17/013

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http://dx.doi.org/10.1088/0022-3700/20/10/022

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http://dx.doi.org/10.1088/0953-4075/24/6/026

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http://dx.doi.org/10.1088/0953-4075/31/10/021

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http://dx.doi.org/10.1007/s12043-007-0140-3

[12] S. Dhar, “The Energy Spectrum of Scattered Particles in the K-Shell Ionization of Medium Heavy Atoms by Relativistic Electrons and Positrons with Exchange Effects,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 41, No. 15, 2008, p. 155204.

http://dx.doi.org/10.1088/0953-4075/41/15/155204

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http://dx.doi.org/10.1088/0034-4885/54/6/001

[14] H. Ehrhardt, K. Jung, G. Knoth and P. Schlemmer, “Dif- ferential Cross Sections of Direct Single Electron Impact Ionization,” Zeitschrift für Physik D Atoms, Molecules and Clusters, Vol. 1, No. 1, 1986, pp. 3-32.

http://dx.doi.org/10.1007/BF01384654

[15] F. W. Byron Jr. and C. J. Joachain, “Theory of (e, 2e) Reactions,” Physics Reports, Vol. 179, No. 4, 1989, pp. 211-272. http://dx.doi.org/10.1016/0370-1573(89)90158-0

[16] C. T. Whelan, R. J. Allan, J. Rasch, H. R. J. Walters, X. Zhang, J. Roder, K. Jung and H. Ehrhardt, “Coulomb three-Body Effects in (e,2e) Collisions: The Ionization of H in Coplanar Symmetric Geometry,” Physical Review A, Vol. 50, No. 5, 1994, pp. 4394-4396.

http://dx.doi.org/10.1103/PhysRevA.50.4394

[17] J. N. Das and S. Seal, “Electron-Hydrogenatom Ioniza- tion Collisions at Intermediate (5I0-20I0) and High (≥20I0) Energies,” Physical Review A, Vol. 47, No. 4, 1993, pp. 2978-2986.

http://dx.doi.org/10.1103/PhysRevA.47.2978

[18] J. N. Das and S. Seal, Australian Journal of Physics, Vol. 47, 1994, p. 99.

[19] Sunil Dhar, “Electron Impact Ionisation of Metastable 2s-state Hydrogen Atoms,” Australian Journal of Physics, Vol. 47, No. 5, 1994, pp. 937-944.

http://dx.doi.org/10.1071/PH960937

[20] J. N.Das and S. Dhar, “Energy Spectrum of Ejected Electrons in Ionization of Hydrogen Atoms by Electrons,” Pramana, Vol. 53, No. 5, 1999, pp. 869-875.

http://dx.doi.org/10.1007/s12043-999-0121-9

[21] J. Berakdar, J. Roder, J. S. Brggs and H. Ehrhardt, “The Effect of Target Atom Polarization and Wavefunction Distortion in (e - 2e) Ionization of Hydrogen,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 29, No. 9, 1996, p. 1767.

http://dx.doi.org/10.1088/0953-4075/29/9/021

[22] P. J. Jenning, R. O. Jones, and M. Weinert, “Surface Barrier for Electrons in Metals,” Physical Review B, Vol. 37, No. 11, 1988, pp. 6113-6120.

http://dx.doi.org/10.1103/PhysRevB.37.6113

[23] J. Berakdar and M. P. Das, “Electron Ejection from Clean Metallic Surfaces upon Charged Particle Impact,” Physical Review A, Vol. 56, No. 2, 1997, pp. 1403-1413.

http://dx.doi.org/10.1103/PhysRevA.56.1403

[24] C. B. Duke, “Advances in Chemical Physies,” Wiley, New York, 1974.

[25] J. B. Pendry, “Low Energy Electron Diffraction,” Academic, London, 1974.

[26] U. Thumm and J. S. Briggs, Nuclear Instruments and Methods in Physics Research Section B, Vol. 43, 1989, p. 471.

[1] J. N. Das, “Differential Cross-Section for the Inner-Shell Ionization of Medium-Heavy Atoms by the Electrons,” Il Nuovo Cimento B, Vol. 12, No. 2, 1972, pp. 197-204.

http://dx.doi.org/10.1007/BF02822628

[2] J. N. Das and S. Chakraborthy, “Atomic Inner-Shell Ionization,” Physical Review A, Vol. 32, No. 1, 1985, pp. 176-180. http://dx.doi.org/10.1103/PhysRevA.32.176

[3] D. H. Jakubassa-Amundsen, “A Systematic Study of Re- lativistic (e, 2e) Collisions in Comparison with Experiment,” Journal of Physics B: Atomic, Molecular and Op- tical Physics, Vol. 25, No. 6, 1992, p. 1297.

http://dx.doi.org/10.1088/0953-4075/25/6/020

[4] X. Zhang, C. T. Whelan and H. R. J. Walters, “Local Supersymmetry for Spinning Particles,” Physics Letters B, Vol. 64, No. 4, 1976, pp. 435-438.

http://dx.doi.org/10.1016/0370-2693(76)90115-5

[5] Allan, P. Bickert and W. Hink, “(e, 2e) Cross Sections for Inner-Shell Ionization of Argon and Neon,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 25, No. 20, 1992, p. 4325.

http://dx.doi.org/10.1088/0953-4075/25/20/025

[6] S. Kellir, R. M. Dreizler. L. U. Ancarni and H. R. J. Walfers, Z. Phys. D, Vol. 37, 1996, p. 191.

http://dx.doi.org/10.1007/s004600050028

[7] E. Schüle and W. Nakel, “Triply-Differential Cross Section for K-Shell Ionisation Of silver by Relativistic Electron Impact,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 15, No. 17, 1982, p. L639.

http://dx.doi.org/10.1088/0022-3700/15/17/013

[8] H. Ruoff and W. Nakel, “Absolute Triply Differential Cross Section for K-Shell Ionisation by Relativistic Electron Impact for High Atomic Number,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 20, No. 10, 1987, p. 2299.

http://dx.doi.org/10.1088/0022-3700/20/10/022

[9] J. Bonfert, H. Graf and W. Nakel, “Relativistic (e,2e) Processes on Atomic Inner Shells,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 24, No. 6, 1991, p. 1423.

http://dx.doi.org/10.1088/0953-4075/24/6/026

[10] J. N. Das and S. Dhar, “Energy Spectrum of Scattered Electrons in K-Shell Ionization of Medium to Heavy Atoms by Relativistic Electrons,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 31, No. 10, 1998, p. 2355.

http://dx.doi.org/10.1088/0953-4075/31/10/021

[11] S. Dhar and M. R. Alam, “Computation of Triple Differential Cross-Sections with the Inclusion of Exchange Effects in Atomic K-Shell Ionization by Relativistic Electrons for Symmetric Geometry,” Pramana, Vol. 69, No. 3, 2007, p. 387.

http://dx.doi.org/10.1007/s12043-007-0140-3

[12] S. Dhar, “The Energy Spectrum of Scattered Particles in the K-Shell Ionization of Medium Heavy Atoms by Relativistic Electrons and Positrons with Exchange Effects,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 41, No. 15, 2008, p. 155204.

http://dx.doi.org/10.1088/0953-4075/41/15/155204

[13] I. E. Mc Carthy and E. Weigold, “Electron Momentum Spectroscopy of Atoms and Molecules,” Reports on Progress in Physics, Vol. 54, No. 6, 1991, p. 789.

http://dx.doi.org/10.1088/0034-4885/54/6/001

[14] H. Ehrhardt, K. Jung, G. Knoth and P. Schlemmer, “Dif- ferential Cross Sections of Direct Single Electron Impact Ionization,” Zeitschrift für Physik D Atoms, Molecules and Clusters, Vol. 1, No. 1, 1986, pp. 3-32.

http://dx.doi.org/10.1007/BF01384654

[15] F. W. Byron Jr. and C. J. Joachain, “Theory of (e, 2e) Reactions,” Physics Reports, Vol. 179, No. 4, 1989, pp. 211-272. http://dx.doi.org/10.1016/0370-1573(89)90158-0

[16] C. T. Whelan, R. J. Allan, J. Rasch, H. R. J. Walters, X. Zhang, J. Roder, K. Jung and H. Ehrhardt, “Coulomb three-Body Effects in (e,2e) Collisions: The Ionization of H in Coplanar Symmetric Geometry,” Physical Review A, Vol. 50, No. 5, 1994, pp. 4394-4396.

http://dx.doi.org/10.1103/PhysRevA.50.4394

[17] J. N. Das and S. Seal, “Electron-Hydrogenatom Ioniza- tion Collisions at Intermediate (5I0-20I0) and High (≥20I0) Energies,” Physical Review A, Vol. 47, No. 4, 1993, pp. 2978-2986.

http://dx.doi.org/10.1103/PhysRevA.47.2978

[18] J. N. Das and S. Seal, Australian Journal of Physics, Vol. 47, 1994, p. 99.

[19] Sunil Dhar, “Electron Impact Ionisation of Metastable 2s-state Hydrogen Atoms,” Australian Journal of Physics, Vol. 47, No. 5, 1994, pp. 937-944.

http://dx.doi.org/10.1071/PH960937

[20] J. N.Das and S. Dhar, “Energy Spectrum of Ejected Electrons in Ionization of Hydrogen Atoms by Electrons,” Pramana, Vol. 53, No. 5, 1999, pp. 869-875.

http://dx.doi.org/10.1007/s12043-999-0121-9

[21] J. Berakdar, J. Roder, J. S. Brggs and H. Ehrhardt, “The Effect of Target Atom Polarization and Wavefunction Distortion in (e - 2e) Ionization of Hydrogen,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 29, No. 9, 1996, p. 1767.

http://dx.doi.org/10.1088/0953-4075/29/9/021

[22] P. J. Jenning, R. O. Jones, and M. Weinert, “Surface Barrier for Electrons in Metals,” Physical Review B, Vol. 37, No. 11, 1988, pp. 6113-6120.

http://dx.doi.org/10.1103/PhysRevB.37.6113

[23] J. Berakdar and M. P. Das, “Electron Ejection from Clean Metallic Surfaces upon Charged Particle Impact,” Physical Review A, Vol. 56, No. 2, 1997, pp. 1403-1413.

http://dx.doi.org/10.1103/PhysRevA.56.1403

[24] C. B. Duke, “Advances in Chemical Physies,” Wiley, New York, 1974.

[25] J. B. Pendry, “Low Energy Electron Diffraction,” Academic, London, 1974.

[26] U. Thumm and J. S. Briggs, Nuclear Instruments and Methods in Physics Research Section B, Vol. 43, 1989, p. 471.