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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 pdf (322 KB)
Fulltext is also available at DOI: 10.3367/UFNe.2018.02.038289
Keywords: periodic system, semiclassic approximation, electron-binding energy, atomic number scaling, ionization state, orbital angular momentum
PACS: 03.65.−w, 31.10.+z, 31.15.bt (all)
DOI: 10.3367/UFNe.2018.02.038289
URL: https://ufn.ru/en/articles/2019/2/e/
000466030200005
2-s2.0-85067789561
2019PhyU...62..186S
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)
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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 (10) Similar articles (20) ↓

  1. K.V. Chukbar “Harmony in many-particle quantum problem” 61 389–396 (2018)
  2. S.E. Kuratov, D.S. Shidlovski et al “Two scales of quantum effects in a mesoscopic system of degenerate electrons” 64 836–851 (2021)
  3. E.D. Trifonov “On the spin-statistics theorem” 60 621–622 (2017)
  4. E.E. Nikitin, L.P. Pitaevskii “Imaginary time and the Landau method of calculating quasiclassical matrix elements” 36 (9) 851–853 (1993)
  5. B.I. Sturman “Ballistic and shift currents in the bulk photovoltaic effect theory” 63 407–411 (2020)
  6. V.G. Bagrov, D.M. Gitman, A.S. Pereira “Coherent and semiclassical states of a free particle” 57 891–896 (2014)
  7. Yu.M. Tsipenyuk “Zero point energy and zero point oscillations: how they are detected experimentally” 55 796–807 (2012)
  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 electrodynamics” 16 434–439 (1973)
  9. S.V. Goupalov “Classical problems with the theory of elasticity and the quantum theory of angular momentum” 63 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 chains” 63 395–406 (2020)
  12. A.N. Rubtsov “On the question of measurement in quantum mechanics” 66 734–740 (2023)
  13. A.V. Belinsky, M.Kh. Shulman “Quantum nature of a nonlinear beam splitter” 57 1022–1034 (2014)
  14. V.K. Ignatovich “The neutron Berry phase” 56 603–604 (2013)
  15. A.A. Grib “On the problem of the interpretation of quantum physics” 56 1230–1244 (2013)
  16. S.N. Gordienko “Irreversibility and the probabilistic treatment of the dynamics of classical particles” 42 573–590 (1999)
  17. V.I. Bodnarchuk, L.S. Davtyan, D.A. Korneev “Geometrical phase effects in neutron optics” 39 169–177 (1996)
  18. G.A. Vardanyan, G.S. Mkrtchyan “A solution to the density matrix equation” 33 (12) 1072–1072 (1990)
  19. A.S. Tarnovskii “The Bohr-Sommerfeld quantization rule and quantum mechanics” 33 (1) 86–86 (1990)
  20. K.S. Vul’fson “Angular momentum of electromagnetic waves” 30 724–728 (1987)

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