Abstract
An approximate equation of state is considered that contains a correction for electron-gas inhomogeneity in the exchange-correlation and kinetic energies in the quasi-classical approximation. The problem of finding the model parameters satisfying the condition P=0 has been solved for metals at a normal density. The results of numerical solution of the model equations are presented for degrees of compression. The values of the quasi-classical parameter determining the approximation accuracy are found. The results are illustrated by the dependences on the degree of compression plotted in the range ρ/ρ0=1–106 and by the spatial dependences. Our approach to construction of the equation of state provides for a quite simple but sufficiently accurate approach to the experimental values of the model parameters. Moreover, the proposed model gives much more self-consistent information as compared to conventional approximations. In particular, the ionicity is calculated for an increase in the density. The model equation can also be used instead of the well-known effective bound-electron potential approximation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Gambás, The Statistical Theory of Atoms and Its Applications (Die Statistische Theorie des Atoms und Ihre Anwendungen) (Springer-Verlag, Vienna, 1949; Inostrannaya Literatura, Moscow, 1951).
C. F. von Weizsacker, Z. Phys. 96, 431 (1935).
A. S. Kompaneets and E. S. Pavlovskii, Zh. Éksp. Teor. Fiz. 31(3), 115 (1956).
D. A. Kirzhnits, Zh. Éksp. Teor. Fiz. 32(1), 115 (1957) [Sov. Phys. JETP 5, 64 (1957)].
W. Kohn and J. Sham, Phys. Rev. 140, A1133 (1965).
N. N. Kalitkin, Zh. Éksp. Teor. Fiz. 38, 1534 (1960) [Sov. Phys. JETP 11, 1106 (1960)].
J. W. Zink, Phys. Rev. 176, 279 (1968).
B. F. Rozsnyai, Phys. Rev. A 5, 1137 (1972).
D. A. Kirzhnits, Yu. E. Lozovik, and G. V. Shpatakovskaya, Usp. Fiz. Nauk 117, 3 (1975) [Sov. Phys. Usp. 18, 649 (1975)].
A. F. Nikiforov, V. G. Novikov, and V. B. Uvarov, Quantum Statistical Models of High-Temperature Plasma (Fizmatlit, Moscow, 2000) [in Russian].
N. N. Kalitkin, Mat. Model. 1, 64 (1989).
A. V. Andriyash and V. A. Simonenko, Fiz. Plazmy 14, 1201 (1988) [Sov. J. Plasma Phys. 14, 703 (1988)].
G. V. Sin’ko, Teplofiz. Vys. Temp. 21, 1041 (1983).
N. N. Kalitkin and L. V. Kuz’mina, Fiz. Plazmy 2, 858 (1976) [Sov. J. Plasma Phys. 2, 478 (1976)].
F. Perrot and M. W. C. Dharma-Wardana, Phys. Rev. E 52, 5352 (1995).
V. V. Prut, Preprint No. 6465/9, IAE (Kurchatov Institute of Atomic Energy, Moscow, 2003).
D. Pines and P. Noziéres, The Theory of Quantum Liquids (Benjamin, New York, 1966; Mir, Moscow, 1967).
S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980).
K. S. Singwi and M. P. Tosi, Solid State Phys. 36, 177 (1981).
S. Ichimaru, Rev. Mod. Phys. 54, 1017 (1982).
M. Gell-Mann and K. A. Brueckner, Phys. Rev. 106, 364 (1957).
W. J. Carr and A. A. Maradudin, Phys. Rev. 133, A371 (1964).
W. J. Carr, R. A. Coldwell-Horsfall, and A. E. Fein, Phys. Rev. 124, 747 (1961).
D. M. Ceperly and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980).
J. G. Zabolitzky, Phys. Rev. B 22, 2353 (1980).
P. Vashishta and K. S. Singwi, Phys. Rev. B 6, 875 (1972).
L. J. Lantto, Phys. Rev. B 22, 1380 (1980).
J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
T. Endo, M. Horiuchi, Y. Takada, and H. Yasuhara, Phys. Rev. B 59, 7367 (1999).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1989, 4th ed.; Pergamon, New York, 1977, 3rd ed.).
J. P. Perdew, J. A. Chevary, S. H. Vosko, et al., Phys. Rev. B 46, 6671 (1992).
J. F. Dobson, J. Wang, and T. Gould, Phys. Rev. B 66, 081108 (2002).
E. Engel and S. H. Vosko, Phys. Rev. B 50, 10498 (1994).
J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
P. Fromy, C. Deutch, and G. Maynard, Phys. Plasmas 3, 714 (1996).
E. N. Avrorin, B. K. Vodolaga, V. A. Simonenko, and V. E. Fortov, Usp. Fiz. Nauk 163, 1 (1993) [Phys. Usp. 36, 337 (1993)].
V. V. Prut, Preprint No. 6464/9, IAE (Kurchatov Institute of Atomic Energy, Moscow, 2003).
Author information
Authors and Affiliations
Additional information
__________
Translated from Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 74, No. 12, 2004, pp. 10–20.
Original Russian Text Copyright © 2004 by Prut.
Rights and permissions
About this article
Cite this article
Prut, V.V. Equation of state in the quasi-classical approximation. Tech. Phys. 49, 1546–1557 (2004). https://doi.org/10.1134/1.1841402
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1134/1.1841402