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Exchange interaction of weakly delocalized multielectron systems

Abstract

The polar model of a metal developed by Bogolyubov [1] is extended to the case of a group of equivalent electrons on each of the atoms that form a crystal. A procedure is suggested for treating the second-quantized Hamiltonian that includes the interconfigurational interaction with the help of the double tensor operators W πq иκ . The relationship between these operators and the unitary operators α a , which act separately in the space of the spin and orbital functions, is pointed out. The conditions for the applicability of the Heisenberg model are analyzed.

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Literature cited

  1. 1.

    N. N. Bogolyubov, Lectures on Quantum Statistics [in Russian], Ukrainian School, Kiev (1949).

  2. 2.

    Yu. A. Izyumov and R. P. Ozerov, Magnetic Neutron Diffraction [in Russian], Fizmatgiz (1966).

  3. 3.

    Yu. P. Irkhin, Zh. Éksp. Teor. Fiz.,50, 12, 379 (1966).

  4. 4.

    V. V. Druzhinin, Fiz. Tverd. Tela,9, 2463 (1967); V. V. Druzhin in and A. S. Moskvin, Fiz. Met. i Metal.,26, 3, 415 (1968).

  5. 5.

    P. M. Levy, Phys. Rev., 177, 2, 509 (1969).

  6. 6.

    V. L. Pokrovskii and G.V. Uimin, Zh. Éksp. Teor. Fiz. (Letters),11, 206 (1970).

  7. 7.

    A. A. Sidorov, Izv. Vuzov SSSR, Fizika, No. 3, 59 (1969).

  8. 8.

    B. R. Judd, Second Quantization and Atomic Spectroscopy [Russian translation], Mir, Moscow (1970).

  9. 9.

    E. Wigner, Gruppentheorie und ihre Anwendung auf die Qwantenmechanik der Atomspektren, Braunschweig (1931).

  10. 10.

    G. Racah, Phys. Rev.,63, 367 (1943).

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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 80–87, May, 1973.

In conclusion I wish to thank B. V. Karpenko for the statement of this problem and for numerous consultations and discussions.

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Sidorov, A.A. Exchange interaction of weakly delocalized multielectron systems. Soviet Physics Journal 16, 658–663 (1973). https://doi.org/10.1007/BF00898804

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Keywords

  • Exchange Interaction
  • Heisenberg Model
  • Polar Model
  • Tensor Operator
  • Orbital Function