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 UFN, 2012, Volume 182, Number 5, Pages 457–494 (Mi ufn2798)

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Semiclassical model of the structure of matter

G. V. Shpatakovskaya

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow

Abstract: The modern semiclassical method developed over the past few decades and used for describing the properties of the electronic subsystems of matter is reviewed, and its application to quantum physics problems is illustrated. The method involves the Thomas–Fermi statistical model and allows an extension by including additive corrections that take the shell structure of the electronic spectrum and other physical effects into account. Applying the method to the study of matter and finite systems allowed the following, inter alia: (1) an analysis of the total electron energy oscillations as a function of the number of particles in a 1D quantum dot; (2) a description of spatial oscillations of the electron density in atoms and atomic clusters; (3) a description of the stepwise temperature dependence of the ionicity and ionization energy in a Boltzmann plasma; (4) an evaluation of free ion ionization potentials; (5) an interpretation and evaluation of the difference in the patterns of oscillations in the mass spectra of metal clusters.

DOI: https://doi.org/10.3367/UFNr.0182.201205a.0457

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English version:
Physics–Uspekhi, 2012, 55:5, 429–464

Bibliographic databases:

PACS: 31.15.bt, 36.40.Cg, 52.25.Kn, 64.10.+h, 71.10.-w, 71.15.Mb
Revised: July 15, 2011
Accepted: August 2, 2011

Citation: G. V. Shpatakovskaya, “Semiclassical model of the structure of matter”, UFN, 182:5 (2012), 457–494; Phys. Usp., 55:5 (2012), 429–464

Citation in format AMSBIB
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Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. Ya. Karpov, G. V. Shpatakovskaya, “Inclusion of the discreteness of the electronic spectrum in the statistical model of free ions”, JETP Letters, 98:6 (2013), 348–352
2. Christian Castrejon-Martinez, V.V.. Grimalsky, L.M.anuel Gaggero-Sager, S.V.. Koshevaya, “Combined method for simulating electron spectrum of $\delta$-doped quantum wells in N-Si with many-body corrections”, PIER M, 31 (2013), 215–229
3. J. W. Abraham, M. Bonitz, “Quantum Breathing Mode of Trapped Particles: From Nanoplasmas to Ultracold Gases”, Contrib. Plasma Phys., 54:1 (2014), 27
4. Sergey Dyachkov, Pavel Levashov, “Region of validity of the finite–temperature Thomas–Fermi model with respect to quantum and exchange corrections”, Phys. Plasmas, 21:5 (2014), 052702
5. Sergey Seriy, “Modern Ab-Initio Calculations on Modified Tomas-Fermi-Dirac Theory”, OJMSi, 03:03 (2015), 96
6. Kadatskiy M.A., Khishchenko K.V., “Comparison of Hugoniots Calculated For Aluminum in the Framework of Three Quantum-Statistical Models”, Xxx International Conference on Interaction of Intense Energy Fluxes With Matter (Elbrus 2015), Journal of Physics Conference Series, 653, IOP Publishing Ltd, 2015, 012079
7. Shpatakovskaya G.V., Karpov V.Ya., “Shell Correction To the Thomas-Fermi Statical Model of Plasma With Different Atomic Compostion At High and Low Temperatures”, Xxx International Conference on Interaction of Intense Energy Fluxes With Matter (Elbrus 2015), Journal of Physics Conference Series, 653, IOP Publishing Ltd, 2015, UNSP 012074
8. Dyachkov S., Levashov P., Minakov D., “Region of validity of the Thomas–Fermi model with corrections”, Phys. Plasmas, 23:11 (2016), 112705
9. Poklonski N.A. Vyrko S.A. Poklonskaya O.N. Kovalev A.I. Zabrodskii A.G., “Ionization equilibrium at the transition from valence-band to acceptor-band migration of holes in boron-doped diamond”, J. Appl. Phys., 119:24 (2016), 245701
10. Poklonski N.A., Vyrko S.A., Poklonskaya O.N., Zabrodskii A.G., “Role of electrostatic fluctuations in doped semiconductors upon the transition from band to hopping conduction (by the example of p-Ge:Ga)”, Semiconductors, 50:6 (2016), 722–734
11. Dyachkov S.A., Levashov P.R., Minakov D.V., “Region of Validity of the Thomas Fermi Model With Quantum, Exchange and Shell Corrections”, Xxxi International Conference on Equations of State For Matter (Elbrus 2016), Journal of Physics Conference Series, 774, IOP Publishing Ltd, 2016, UNSP 012006
12. Kadatskiy M.A. Khishchenko K.V., “Shock Compressibility of Iron Calculated in the Framework of Quantum-Statistical Models With Different Ionic Parts”, Xxxi International Conference on Equations of State For Matter (Elbrus 2016), Journal of Physics Conference Series, 774, IOP Publishing Ltd, 2016, UNSP 012005
13. Khishchenko K.V., “Equation of State For Titanium At High Energy Densities”, Xxxi International Conference on Equations of State For Matter (Elbrus 2016), Journal of Physics Conference Series, 774, IOP Publishing Ltd, 2016, UNSP 012001
14. Shpatakovskaya G.V., Karpov V.Ya., “Atomic Number Scaling of Electron Spectra in the Free Atoms”, Xxxi International Conference on Equations of State For Matter (Elbrus 2016), Journal of Physics Conference Series, 774, IOP Publishing Ltd, 2016, UNSP 012002
15. I. V. Lomonosov, S. V. Fortova, “Wide-range semiempirical equations of state of matter for numerical simulation on high-energy processes”, High Temperature, 55:4 (2017), 585–610
16. V. Ya. Karpov, G. V. Shpatakovskaya, “On the Atomic-Number Similarity of the Binding Energies of Electrons in Filled Shells of Elements of the Periodic Table”, J. Exp. Theor. Phys., 124:3 (2017), 369–378
17. Chikina I., Shikin V., “Barium Ions in Liquid Helium”, Low Temp. Phys., 44:5 (2018), 401–409
18. Kuratov S.E., Shidlovski D.S., Blinnikov S.I., “Inhomogeneous Spatial Distribution of Electrons in a Compressed Gas Bubble of Submicron Size”, 11Th International Conference Aerophysics and Physical Mechanics of Classical and Quantum Systems (Aphm-2017), Journal of Physics Conference Series, 1009, ed. Surzhikov S., IOP Publishing Ltd, 2018, UNSP 012013
19. G. V. Shpatakovskaya, “Dependence on ionization degree and relativistic effects in electron binding energies in free atoms and ions”, Preprinty IPM im. M. V. Keldysha, 2018, 184, 12 pp.
20. Kyarov A.Kh., Savintsev A.P., Xxxii International Conference on Interaction of Intense Energy Fluxes With Matter (Elbrus 2017), Journal of Physics Conference Series, 946, IOP Publishing Ltd, 2018
21. Levashov P.R. Minakov D.V., Xxxii International Conference on Interaction of Intense Energy Fluxes With Matter (Elbrus 2017), Journal of Physics Conference Series, 946, IOP Publishing Ltd, 2018
22. G. V. Shpatakovskaya, “Atomic-number similarity of the $K$ and $L$ X-ray terms in multielectron atoms”, JETP Letters, 108:11 (2018), 768–771
23. Kadatskiy M.A., Khishchenko K.V., “Theoretical Investigation of the Shock Compressibility of Copper in the Average-Atom Approximation”, Phys. Plasmas, 25:11 (2018), 112701
24. G. V. Shpatakovskaya, “Semiclassical method of analysis and estimation of the orbital binding energies in many-electron atoms and ions”, Phys. Usp., 62:2 (2019), 186–197
25. Shemyakin O.P., Levashov P.R., Krasnova P.A., “Tfmix: a High-Precision Implementation of the Finite-Temperature Thomas-Fermi Model For a Mixture of Atoms”, Comput. Phys. Commun., 235 (2019), 378–387
26. Kuratov S.E., Shidlovski D.S., Blinnikov S.I., “Quantum Shell Effects in Compressed Mesoscopic System”, Phys. Plasmas, 26:2 (2019), 022709
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