Nuclear Physics and Atomic Energy

ядерна ф≥зика та енергетика
Nuclear Physics and Atomic Energy

  ISSN: 1818-331X (Print), 2074-0565 (Online)
  Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine
  Languages: Ukrainian, English, Russian
  Periodicity: 4 times per year

  Open access peer reviewed journal


 Home page   About 
Nucl. Phys. At. Energy 2016, volume 17, issue 3, pages 226-231.
Section: Nuclear Physics.
Received: 14.07.2016; Accepted: 19.10.2016; Published online: 13.12.2016.
PDF Full text (ru)
https://doi.org/10.15407/jnpae2016.03.226

Cross-section of the photoeffect averaged over the atomic electrons

S. N. Fedotkin*

Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine

*Corresponding author. E-mail address: sfedot@kinr.kiev.ua

Abstract: Simple approximate method for calculation of the cross sections of the photoeffect averaged over all atomic electrons is suggested. This method is based on the statistical Thomas - Fermi model with a new additional assumption. The proposed approach allows to calculate rather simply the average probabilities of various processes with participation of all atomic electrons. For this purpose averaged density of the atomic electrons is calculated analytically. Good agreement between the total cross-sections for all atomic electrons calculated in the described approach and in the framework of the quantum mechanics is obtained.

Keywords: photoeffect, Thomas - Fermi model, atomic shell.

References:

1. M.J. Amusia. Atomic photoeffect (Moskva: Fizmatgiz, 1987) 272 p. (Rus) Google Books

2. A.I. Akhiezer, V.B. Berestetskiy. Quantum electrodynamics (Moskva: Fizmatgiz, 1959) 656 p. (Rus) Google Books

3. J.H. Scofield. K- and L-shell ionization of atoms by relativistic electrons. Phys. Rev. A 18 (1978) 963. https://doi.org/10.1103/PhysRevA.18.963

4. U.I. Safronova, M.S. Safronova. Third-order relativistic many-body calculations of energies, transition rates, hyperfine constants, and blackbody radiation shift in 171Yb+. Phys. Rev. A 79 (2009) 022512. https://doi.org/10.1103/PhysRevA.79.022512

5. C.F. Fischer. The Hartree - Fock method for atoms (N.Y., London: JohnWiley & Sons, 1977). Google Books

6. M.Ya. Amusia, V.K. Ivanov, V.A. Kupchenko. The effect of atomic rearrangement on the photoionisation cross section for 3d subshells of the isoelectronic Xe series. J. Phys. B 18 (1985) 3871. https://doi.org/10.1088/0022-3700/18/19/010

7. M.Ya. Amusia, N.A. Shards, L.V. Chernysheva, V.K. Ivanov. Theory of many-electron effects in atomic processes (Sankt-Peterburg: Nauka, 2006) 385 p. (Rus) Book

8. Electronic and Atomic Collision. Ed. by G. Watel, P.G. Burke (North-Holland, Amsterdam-N-Y-Oxford, 1978) 201 p.

9. K. Smith, R.J.W. Henry, P.G. Burke. Scattering of Electrons by Atomic Systems with Configurations 2pq and 3pq. Phys. Rev. 147 (1966) 21. https://doi.org/10.1103/PhysRev.147.21

10. W. Brandt, S. Lundqvist. Atomic Oscillations in the Statistical Approximation. Phys. Rev. 139 (1965) A612. https://doi.org/10.1103/PhysRev.139.A612

11. A.V. Vinogradov, O.I. Tolstikhin. Resonant photoabsorption and polarizability of inhomogeneous dielectric particles. Sov. Phys. JETP 69(1) (1989) 32. http://www.jetp.ac.ru/cgi-bin/dn/e_069_01_0032.pdf

12. J.M. Rost. Analytical total photo cross section for atoms. J. Phys. B 28 (1995) L601. https://doi.org/10.1088/0953-4075/28/19/002

13. B.O. Ndinya, S.O. Okeyo. Analytical Absorption Cross-Section for Photon by a Hydrogen 2s Atom. Commun. Theor. Phys. 55 (2011) 659. https://doi.org/10.1088/0253-6102/55/4/26

14. L.H. Thomas. The calculation of atomic fields. Proc. Camb. Phil. Soc. 23 (1927) 542. https://doi.org/10.1017/S0305004100011683

15. E. Fermi. Statistical method to determine some properties of atoms. C. Acc. Lincei 6 (1927) 602; http://www.michelepavanello.com/pdf/TF/Fermi_1927.pdf

Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente. Z. Phys. 48 (1928) 73. https://doi.org/10.1007/BF01351576

16. P. Gombas. Die statistische theorie des atoms und ihre anwendungen (Wien: Springer-Verlag, 1949) 399 p. Book

17. Theory of the inhomogeneous electron gas. Ed. by S. Lundqvist, N. H. March (New York and London: Plenum Press, 1983). Book

18. M. Brack, R.K. Bhaduri. Semiclassical Physics (USA: Westview Press, Boulder, 2003) 458 p. Google Books

19. S. Seriy. Modern Ab-Initio Calculations on Modified Tomas-Fermi-Dirac Theory. Open Journal of Modelling and Simulation 3 (2015) 96. https://doi.org/10.4236/ojmsi.2015.33010

20. V.Ya. Karpov, G.V. Shpatakovskaya. Inclusion of the discreteness of the electronic spectrum in the statistical model of free ions. JETP Letters 98 (2013) 348. https://doi.org/10.1134/S0021364013190065

21. G.V. Shpatakovskaya. Semiclassical model of the structure of matter. Phys. Usp. 55 (2012) 429. https://doi.org/10.3367/UFNe.0182.201205a.0457

22. T. Tietz. Simple Analytical Eigenfunctions of Electrons in Thomas - Fermi Atoms. Zs. Naturfosch. 23a (1968) 191. http://zfn.mpdl.mpg.de/data/Reihe_A/23/ZNA-1968-23a-0191_n.pdf

23. W. Heitler. Quantum Theory of Radiation (London: Oxford University Press, 1954) 453 p. Google Books

24. H.A. Bethe, E.E. Salpeter. Quantum mechanics of one- and two-electron atoms (Berlin-Gottingen-Heidelberg: Springer-Verlag, 1957) 562 p. Google Books

25. E. Fermi, E. Amaldi. Mem. Acc. Italia 6 (1934) 117. http://operedigitali.lincei.it/Fermi/Fermi-omnia1_2_Prefazione_Nota-biografica.pdf