Methodological notes

Semiclassical method of analysis and estimation of the orbital binding energies in many-electron atoms and ions

M.V. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russian Federation

The orbital binding energies, obtained in the experiments or in the quantum-mechanical calculations, are studied in the ground state of many-electron elements. Their dependences on the atomic number and on the degree of ionization are analyzed. The semiclassical quantization condition of Bohr—Sommerfield is used and a filled shell orbital binding energy scaling is shown approximately. The scaling is similar to one in the Thomas—Fermi model, but with other two coefficient functions. The effective method of the demonstration of binding energies in a large number of atoms through these two functions is proposed. In addition the special features of the elements of main and intermediate groups and the influence of relativistic effects are visually manifested. The simple interpolation expressions are built for the two functions. One can use them to estimate orbital binding energies in the filled shells of many-electron atoms and ions to within 10% for the average elements and from 10% to 30% for the heavy ones. The estimation can be used as the initial approximation in precessional atomic computations and also for the rough calculations of the ionization cross sections of many-electron atoms and ions by electrons and heavy particles failing more precise data.

Fulltext is available at IOP
Keywords: periodic system, semiclassic approximation, electron-binding energy, atomic number scaling, ionization state, orbital angular momentum
PACS: 03.65.−w, 31.10.+z, (all)
DOI: 10.3367/UFNe.2018.02.038289
Citation: Shpatakovskaya G V "Semiclassical method of analysis and estimation of the orbital binding energies in many-electron atoms and ions" Phys. Usp. 62 186–197 (2019)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 18th, October 2017, revised: 20th, January 2018, 9th, February 2018

Оригинал: Шпатаковская Г В «Квазиклассический метод анализа и оценки орбитальных энергий связи в многоэлектронных атомах и ионах» УФН 189 195–206 (2019); DOI: 10.3367/UFNr.2018.02.038289

References (26) Cited by (5) Similar articles (20) ↓

  1. K.V. Chukbar “Harmony in many-particle quantum problem61 389–396 (2018)
  2. E.D. Trifonov “On the spin-statistics theorem60 621–622 (2017)
  3. E.E. Nikitin, L.P. Pitaevskii “Imaginary time and the Landau method of calculating quasiclassical matrix elements36 (9) 851–853 (1993)
  4. B.I. Sturman “Ballistic and shift currents in the bulk photovoltaic effect theory63 407–411 (2020)
  5. V.G. Bagrov, D.M. Gitman, A.S. Pereira “Coherent and semiclassical states of a free particle57 891–896 (2014)
  6. Yu.M. Tsipenyuk “Zero point energy and zero point oscillations: how they are detected experimentally55 796–807 (2012)
  7. N.P. Klepikov “Types of transformations used in physics, and particle ’exchange’30 644–648 (1987)
  8. V.L. Ginzburg “The laws of conservation of energy and momentum in emission of electromagnetic waves (photons) in a medium and the energy-momentum tensor in macroscopic electrodynamics16 434–439 (1973)
  9. S.V. Goupalov “Classical problems with the theory of elasticity and the quantum theory of angular momentum63 57–65 (2020)
  10. S.V. Petrov “Was Sommerfeld wrong? (To the history of the appearance of spin in relativistic wave equations)63 721–724 (2020)
  11. I.F. Ginzburg “Particles in finite and infinite one-dimensional chains63 395–406 (2020)
  12. A.V. Belinsky, M.Kh. Shulman “Quantum nature of a nonlinear beam splitter57 1022–1034 (2014)
  13. A.A. Grib “On the problem of the interpretation of quantum physics56 1230–1244 (2013)
  14. V.K. Ignatovich “The neutron Berry phase56 603–604 (2013)
  15. S.N. Gordienko “Irreversibility and the probabilistic treatment of the dynamics of classical particles42 573–590 (1999)
  16. V.I. Bodnarchuk, L.S. Davtyan, D.A. Korneev “Geometrical phase effects in neutron optics39 169–177 (1996)
  17. A.S. Tarnovskii “The Bohr-Sommerfeld quantization rule and quantum mechanics33 (1) 86–86 (1990)
  18. G.A. Vardanyan, G.S. Mkrtchyan “A solution to the density matrix equation33 (12) 1072–1072 (1990)
  19. K.S. Vul’fson “Angular momentum of electromagnetic waves30 724–728 (1987)
  20. V.L. Ginzburg “The nature of spontaneous radiation26 713–719 (1983)

The list is formed automatically.

© 1918–2021 Uspekhi Fizicheskikh Nauk
Email: Editorial office contacts About the journal Terms and conditions