HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 62 (1979) > Number 6
| Next Article >

Prog. Theor. Phys. Vol. 62 No. 6 (1979) pp. 1533-1549

[ Full Text PDF : FREE ACCESS (1377K) ]

Static Density Response Function of a Degenerate Electron Gas Calculated by Quantal Hyper-Netted Chain Equation

Junzo Chihara and Ken Sasaki

Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 319-11

(Received July 26, 1979)

Abstract:

The density distribution n(r∣v) around a fixed electron in an electron gas with density n0 is calculated by the two quantal versions (QHNC and QHNC') of the hyper-netted chain (HNC) equation, which gives the radial distribution funcion g(r) in the best fir with the computer simulation of the classical electron liquid. The one (QHNC) is derived from the Hohenberg-Kohn-Sham formalism by treating the kinetic energy in an exact manner and the other (QHNC') is obtained by approximating it as in the Thomas-Fermi theory. The result is compared with those of the Hartree and Sjölander-Stott equations. In the high density region (rs=1) where the exchange-correlation effect is small, the QHNC n(r∣v) is virtually identical with the Hartree n(r∣v): this may be considered as providing a numerical evidence for the validity of the Ansatz that the Fourier transform of n(r∣v)-n0 is represented in terms of the static density-density response function χQ. With the aid of this Ansatz, χQ is calculated from the QHNC and QHNC' equations. The local-field factor G(Q) in χQ calculated by QHNC has a maximum and two types of singularities in its slope at Q=2QF (QF; the Fermi wave-vector) and approaches a constant value 1-n(r=0∣v)/n0 in the large wave-vector limit, while the QHNC' G(Q) increases monotonically with Q, which is similar to that of Singwi's group. This difference indicates that in the calculation of G(Q) it is important to treat the kinetic energy in an exact manner.


URL : http://ptp.ipap.jp/link?PTP/62/1533/
DOI : 10.1143/PTP.62.1533

[ Full Text PDF : FREE ACCESS (1377K) ] Citation:

References:

  1. A. A. Kugler, J. Stat. Phys. 12 (1975), 35.
  2. For example, G. Mukhopadyay and A. Sjölander, Phys. Rev. B 17 (1978), 3589[APS].
  3. J. P. Hansen, I. R. McDonald and E. L. Pollock, Phys. Rev. A 11 (1975), 1025[APS].
    J. Bosse and K. Kubo, Phys. Rev. A 18 (1978), 2337[APS].
  4. S. Takeno and F. Yoshida, Prog. Theor. Phys. 60 (1978), 1304[PTP].
  5. J. Chihara, Prog. Theor. Phys. 47 (1972), 395[PTP].
  6. J. Hubbard, Proc. R. Soc. A 243 (1957), 336.
  7. D. J. W. Geldart and R. Taylor, Can. J. Phys. 48 (1970), 155.
  8. L. Dangens, J. of Phys. C 4 (1971), L165[IoP STACKS].
  9. A. K. Rajagopal, Phys. Rev. A 6 (1972), 1239[APS].
  10. D. N. Tripathy and S. S. Mandal, Phys. Rev. B 16 (1977), 231[APS].
  11. F. Brosens, L. F. Lemmens and J. T. Devreese, Phys. Stat. Sol. (b) 81 (1977), 551.
  12. F. Toigo and T. O. Woodruff, Phys. Rev. B 2 (1970), 3958[APS]; ibid. 4 (1971), 371[APS]; ibid. 4 (1971), 4312[APS].
  13. D. J. W. Geldart and R. Taylor, Can. J. Phys. 48 (1970), 167.
  14. K. S. Singwi, M. P. Tosi, R. H. Land and A. Sjölander, Phys. Rev. 176 (1968), 589[APS].
  15. K. S. Singwi, A. Sjölander, M. P. Tosi and R. H. Land, Phys. Rev. B 3 (1970), 1044[APS].
  16. P. Vashishta and K. S. Singwi, Phys. Rev. B 6 (1972), 875[APS].
  17. G. Niklasson, Phys. Rev. B 10 (1974), 3052[APS].
  18. J. Chihara, Prog. Theor. Phys. 58 (1977), 1709[PTP].
  19. P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964), B864[APS].
    W. Kohn and L. J. Sham, Phys. Rev. 140 (1965), A1133[APS].
  20. J. Chihara, Prog. Theor. Phys. 59 (1978), 76[PTP].
  21. J. Chihara, Prog. Theor. Phys. 50 (1973), 1156[PTP].
  22. J. K. Percus, The Equilibrium Theory of Classical Fluids, edited by H. L. Frish and L. Lebowitz (Benjamin, 1964), II-33.
  23. S. Ichimaru, Phys. Rev. A 2 (1970), 494[APS].
  24. A. Sjölander and K. J. Stott, Phys. Rev. B 5 (1972), 2109[APS].
  25. J. H. Rose, Jr. and H. B. Shore, Solid State Commun. 17 (1975), 327[CrossRef].
    M. Manninen, R. Nieminen and P. Hautojärvi, Phys. Rev. B 12 (1975), 4012[APS].
    E. Zaremba, L. M. Sander, H. B. Shore and J. H. Rose, J. of Phys. F 7 (1977), 1763[IoP STACKS].
  26. R. D. Cowan and J. G. Kirkwood, Phys. Rev. 3 (1958), 1460[APS].
  27. J. Chihara, Prog. Theor. Phys. 53 (1975), 400[PTP].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 64 No. 1 (1980) pp. 40-53 :
    Local-Field Correction and Dynamical Structure Factor of Electron Liquids
    Fukuo Yoshida, Shozo Takeno and Hiroshi Yasuhara
  2. Progress of Theoretical Physics Vol. 70 No. 2 (1983) pp. 331-342 :
    Comparison of Local-Density and Quantal Hypernetted-Chain Approximations in the Calculation of Electron Density Distribution
    Junzo Chihara
  3. Progress of Theoretical Physics Vol. 72 No. 5 (1984) pp. 940-955 :
    Pair Correlation Functions in Liquid Metallic Hydrogen
    Junzo Chihara

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.