A final state wave function of multiple scattering theory developed by Das and
seal is utilized in the present study to calculate the triple differential cross sections
(TDCS) for the ionization of metastable 3S state hydrogen atoms at incident
electron energy of 250 eV with the exchange effects in the asymmetric
coplanar geometry for various kinematic conditions. Our present calculation
results are compared with the available hydrogenic ground state experimental
data and other existing theoretical results. A good qualitative agreement is
shown with those of compared results of the present study specifically with
hydrogenic ground state experimental data and metastable 2S and 2P state
with exchange effect results. These new results offer an extensive scope for
experimental verification in such ionization process.
References
[1]
Bethe, H. (1930) A Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie. Asymmetric Ann Phys, 5, 325. Handbuch der Physik Ed. A Smekal Aufbau Der Zusammenhangenden Materie. 1933, 24:273.
[2]
Madison, D.H. and Merzbacher, E. (1975) Semi Classical Transition Probabilities for the Electron-Impact Excitation of Hydrogeic Ions in Dense Plasma. Academic Press, New York, 1.
[3]
Das, J.N. (1972) Advances in Atomic and Molecular Physics. Il Nuovo Cimento B, 12, 17.
[4]
Das, J.N. and Chakraborty, S. (1985) An Improved Calculations for The Inner-Shell Ionization Problems. Physics Letters A, 32, 176.
[5]
Jakubasa-Amundsen, D.H. Relativistic Theory for K-Shell Ionization by Fast Electrons. Z. Phys., 1989, D11, 305; Journal of Physics, 1992, B25, 1297.
[6]
Keller, S., Dreizler, R.M., Ancarni, L.U., Watters, H.R.J., Ast, H. and Whelan, C.T. (1996) Theoretical Analysis of the Relativistic First Order Born Approximation for Inner Shell (e,2e) Processes. Z. Phys., D37, 191.
[7]
Schule, E and Nakel, W. (1982) Triply-Differential Cross Section for K-Shell Ionization of Silver by Relativistic Electron Impact. Journal of Physics, B15, L639.
[8]
Ruoff, H. and Nakel, W. (1987) Absolute Triply Differential Cross Section for K-Shell Ionization by Relativistic Electron Impact for High Atomic Number. Journal of Physics, B20, 2299.
[9]
Bonfert, J., Graf, H. and Nakel, W. (1991) Relativistic (e,2e) Collisions on Atomic Inner Shells in Symmetric Geometry. Journal of Physics, B24, 1423.
[10]
Massey H.S.W. and Mohr, C.B.O. (1933) Gaseous Reactions Involving Positronium. Proceedings of the Physical Society. Section A, 67, 695.
https://doi.org/10.1088/0370-1298/67/8/306
[11]
Ehrhardt, H., Hesselbacher, K.H., Jung, K. and Willman, K. (1972) Collisional Ionization of Helium by Slow Electrons. Journal of Physics B, 5, 1559.
[12]
Lahmann, B., McCarthy, I.E., Stelbovics, A.T. and Weigold, E. (1984) Electron-Impact Ionization of Atomic Hydrogen: Comparison of Asymmetric (e, 2e) Measurements with Theories. Physical Review A, 30, 758.
https://doi.org/10.1103/PhysRevA.30.758
[13]
Weigold, E., Noble, C.J., Hood, S.T. and Fuss, I. (1979) Electron Impact Ionization of Atomic Hydrogen: Experimental and Theoretical (e, 2e) Differential Cross Section. Journal of Physics B: Atomic, Molecular and Optical Physics, 12, 291.
https://doi.org/10.1088/0022-3700/12/2/019
[14]
Joachain, C.J. and Piraux, B. (1986) Theory of Coplanar Asymmetric (e, 2e) Reactions in Helium. Comments on Atomic and Molecular Physics, 17, 261.
[15]
Ehrhardt, H., Knoth, G., Schlemmer, P. and Jung, K. (1986) Differential Cross Sections of Direct Single Electron Impact Ionization. Zeitschrift für Physik D, 1, 3.
https://doi.org/10.1007/BF01384654
[16]
Byron, W.F., Joachain, J.C. and Piraux, B. (1980) Triple Differential Cross Sections for the Ionization of Atomic Hydrogen by Fast Electrons: A Second Born Treatment. Journal of Physics B: Atomic, Molecular and Optical Physics, 13, L673.
[17]
Das, J.N. and Seal, S. (1993) Electron-Hydrogen-Atom Ionization Collision at Intermediate (2l_0-20l_0) and High (≥20l_0) Energies. Physical Review A, 47, 2978.
https://doi.org/10.1103/PhysRevA.47.2978
[18]
Lahmann-Bennani, A. (1991) Recent Developments and Ne Trends in (e, 2e) and (e, 3e) Studies. Journal of Physics B, 24, 2401.
https://doi.org/10.1088/0953-4075/24/10/001
[19]
Das, J.N. and Dhar, S. (1999) Energy Spectrum of Ejected Electrons in Ionization of Hydrogen Atoms by Electrons. Pramana Journal of Physics, 47, 263-269.
[20]
Vucic, S., Potvliege, R.M. and Joachain, C.J. (1987) Second Born Triple-Differential Cross Sections for the Coplanar Asymmetric Ionization of H (2S) by Fast Electrons. Physical Review A, 35, 1446. https://doi.org/10.1103/PhysRevA.35.1446
[21]
Dal Cappello, C., Haddadou, A., Menas, F. and Roy, A.C. (2011) The Second Born Approximation fr the Single and Double Ionization of Atoms by Electrons and Positrons. Journal of Physics B: Atomic, Molecular and Optical Physics, 44, Article ID: 015204. https://doi.org/10.1088/0953-4075/44/1/015204
[22]
Ehrhardt, H., Schulz, M., Tekkat, T. and Willmann, K. (1969) Differential Cross Sections of Direct Single Electron Impact Ionization. Physical Review Letters, 22, 89.
[23]
Amaldi, U., Egidi, A., Marconero, R. and Pizzela, G. (1969) Use of a to Channeltron Coincidence in a New Line of Research in Atomic Physics. Review of Scientific Instruments, 40, 1001. https://doi.org/10.1063/1.1684135
[24]
Byron, F.W., Joachain, C.J. and Piraux, B. (1886) Theory of Coplanar Asymmetric (e, 2e) Reactions in Helium. Journal of Physics B: Atomic, Molecular and Optical Physics, 19, 1201. https://doi.org/10.1088/0022-3700/19/8/015
[25]
Byron, F.W., Joachain, C.J. and Piraux, B. (1985) Triple Differential Cross Sections for the Ionization of Atomic Hydrogen by Fast Electrons: A Second Born Treatment. Journal of Physics B: Atomic, Molecular and Optical Physics, 18, 3203.
[26]
Das, J.N. (1990) Momentum-Space Analysis of Scattering States with Possible Application to Atomic Ionization. Physical Review A, 42, 1376.
https://doi.org/10.1103/PhysRevA.42.1376
[27]
Das, J.N. and Seal, S. (1993) Electron-Hydrogen-Atom Ionization Collision at Intermediate (2l_0-20l_0) and High (≥20l_0) Energies. Physical Review A, 40, 253.
[28]
Das, J.N. and Dhar, S. (1999) Energy Spectrum of Ejected Electrons in Ionization of Hydrogen Atoms by Electrons. Pramana Journal of Physics, 53, 869.
https://doi.org/10.1007/s12043-999-0121-9
[29]
Jones, S. and Madison, D.H. (2000) Ionization of Hydrogen Atoms by Fast Electrons. Physical Review A, 62, Article ID: 042701.
https://doi.org/10.1103/PhysRevA.62.042701
[30]
Jones, S. and Madison, D.H. (2002) Scaling Behavior of the Fully Differential Cross Section for Ionization of Hydrogen Atoms by the Impact of Fast Elementary Charged Particles. Physical Review A, 65, Article ID: 052727.
https://doi.org/10.1103/PhysRevA.65.052727
[31]
Li, S., Berakdar, J., Zhang, S.T. and Chen, J. (2005) Laser Assisted (e, 2e) Reaction in One Electron Atoms and Ions. Journal of Physics B: Atomic, Molecular and Optical Physics, 38, 1291. https://doi.org/10.1088/0953-4075/38/8/017
[32]
Das, J.N. and Dhar, S. (1998) 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, 31, 2355.
https://doi.org/10.1088/0953-4075/31/10/021
[33]
Bransden, B.H. and Joachain, C.J. (1983) Physics of Atoms and Molecules. 2nd Edition, Pearson Education, New York.
[34]
Brauner, M., Briggs, J.S. and Klar, H. (1989) Triply-Differential Cross Sections for Ionization of Hydrogen Atoms by Electrons and Positrons. Journal of Physics B: Atomic, Molecular and Optical Physics, 22, 2265-2287.
https://doi.org/10.1088/0953-4075/22/14/010
[35]
Ray, H. and Roy, A.C. (1988) Triply Differential Cross Sections for the Coplanar Asymmetric Ionization of H (2S) by Fast Electrons. Journal of Physics B: Atomic, Molecular and Optical Physics, 21, 3243.
https://doi.org/10.1088/0953-4075/21/19/014
[36]
Hafid, H., Joulakian, B. and Cappelo, C.D. (1993) Theoretical Study of the Differential Cross Section of the Ionization of Hydrogen (2S) by Electron Impact. Journal of Physics B: Atomic, Molecular and Optical Physics, 26, 3415.
https://doi.org/10.1088/0953-4075/26/19/028
[37]
Das, J.N and Seal, S. (1993) Electron-Hydrogen-Atom Ionization Collision at Intermediate (2l_0-20l_0) and High (≥20l_0) Energies. Physical Review A, 47, 2978.
https://doi.org/10.1103/PhysRevA.47.2978
[38]
Dhar, S. (1996) Electron Impact Ionization of Metastable 2S-State Hydrogen Atoms. Australian Journal of Physics, 49, 937. https://doi.org/10.1071/PH960937
[39]
Das, J.N. and Dhar, S. (1998) Calculation of Triple Differential Cross-Sections of K-Shell Ionization of Medium-Heavy Atoms by Electrons for Symmetric Geometry. Pramana Journal of Physics, 51, 751. https://doi.org/10.1007/BF02832607
[40]
Kyle, H.L. and Omidvar, K. (1968) Passage of Charged Particles through Matter. Physical Review, 176, 164. https://doi.org/10.1103/PhysRev.176.164
[41]
Berakdar, J., Engelns, A. and Klar, H. (1996) Oriented and Aligned Two-Electron Continue. Journal of Physics B: Atomic, Molecular and Optical Physics, 29, 1109.
https://doi.org/10.1088/0953-4075/29/5/019
[42]
Karnali, M.Z.M., Ratnavelu, K. and Zhou, Y. (2008) Electron Impact Excitation of 2P and 3P States of Hydrogen at Intermediate Energies. The European Physical Journal D, 46, 267-279. https://doi.org/10.1140/epjd/e2007-00317-0
[43]
Qi, Y.Y., Ning, L.N., Wang, J.G. and Qu, Y.Z. (2013) Plasma Effect on Fast-Electron-Impact-Ionization from 2P State of Hydrogen-Like Ions. Physics of Plasmas, 20, Article ID: 123301. https://doi.org/10.1063/1.4833616
[44]
Lewis, R.R. (1956) Potential Scattering of High-Energy Electrons in Second Born Approximation. Physical Review, 102, 537. https://doi.org/10.1103/PhysRev.102.537
[45]
Dhar, S. and Nahar, N. (2015) Electron Impact Ionization of Metastable 2P-State Hydrogen Atoms in the Coplanar Geometry. Results in Physics, 5, 3-8.
[46]
Dhar, S. and Nahar, N. (2015) Energy Spectrum of Ejected Electrons of H (2P) Ionization by Electrons in Coplanar Asymmetric Geometry. American Journal of Modern Physics, 4, 132. https://doi.org/10.11648/j.ajmp.20150403.15
[47]
Dhar, S. and Nahar, N. (2016) Triple Differential Cross-Sections for the Ionization of Metastable 2P-State Hydrogen Atoms by Electrons with Exchange Effects. Pramana Journal of Physics, 87, 69.
[48]
Dhar, S., Noor, T. and Chowdhury, F.S. (2015) Electron Impact Ionization of Metastable 3S-State Hydrogen Atoms by Electrons in Coplanar Geometry. American Journal of Modern Physics, 4, 361-366. https://doi.org/10.11648/j.ajmp.20150406.11
[49]
Dhar, S., Akter, S. and Nahar, N. (2016) The First Born Triple Differential Cross Sections for Ionization of H (3P) by Electron Impact in the Asymmetric Coplanar Geometry. Open Journal of Medical Psychology, 6, 15-23.
https://doi.org/10.4236/ojm.2016.61002
[50]
Bartschat, K. (2002) Electron-Impact Excitation of Helium from the 1S and 2S States. Journal of Physics B: Atomic, Molecular and Optical Physics, 35, L527.
https://doi.org/10.1088/0953-4075/35/23/104
