Radial Distribution Function of a Gas of Hard Spheres and the Superposition Approximation

B. R. A. Nijboer; L. Van Hove

doi:10.1103/PhysRev.85.777

Access by Xinjiang University

Radial Distribution Function of a Gas of Hard Spheres and the Superposition Approximation

B. R. A. Nijboer

L. Van Hove^*

Institute for Theoretical Physics, University of Utrecht, Utrecht, Holland

University of Brussels, Brussels, Belgium

^*Associé du Fonds National de la Recherche Scientifique (Belgium).

PDF

Phys. Rev. 85, 777 – Published 1 March, 1952

DOI: https://doi.org/10.1103/PhysRev.85.777

Abstract

The term $g_{2} (r)$ proportional to the square of the density in the expansion of the radial distribution function $g (r)$ of an imperfect gas in powers of the density is calculated exactly in the case of a gas consisting of hard spheres. The result is checked by means of Boltzmann's value of the 4th virial coefficient of such a gas. The integral equation for $g (r)$ , obtained on applying the superposition approximation introduced by Kirkwood and by Born and Green, can also be solved by an expansion in powers of the density. For the case of hard spheres the approximate ${g_{2}}^{'} (r)$ found in this way is compared with the exact $g_{2} (r)$ . As a further application of our result on $g_{2} (r)$ a certain integral is discussed, which is of interest in the treatment of interference effects in neutron scattering problems.

References (15)

J. de Boer, "Reports on Progress in Physics," Phys. Soc. (London) 12, p. 305 (1949)
J. de Boer and A. Michels, Physica 6, 97 (1939)
J. G. Kirkwood, J. Chem. Phys. 3, 300 (1935)
Hart, Wallis, and Pode, J. Chem. Phys. 19, 139 (1951)
G. S. Rushbrooke and H. I. Scoins, Nature 167, 366 (1951) Phil. Mag. 42, 582 (1951)
M. Born and H. S. Green, Proc. Roy. Soc. (London) A188, 10 (1946)
B. R. A. Nijboer et L. Van Hove, Proc. Koninkl. Nederlandse Akad. Wetenschappen B54, 256 (1951)
Placzek, Nijboer and Van Hove, Phys. Rev. 82, 392 (1951)
W. Magnus und F. Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik (Julius Springer, Berlin, 1943), p. 119
L. Boltzmann, Verslag. Gewone Vergadering Afd. Natuurk. Nederlandse Akad. Wetensch. 7, 484 (1899) H. Happel, Ann. Physik 21, 342 (1906) R. Majumdar, Bull. Calcutta Math. Soc. 21, 107 (1929)
Omitted endnote
Kirkwood, Maun, and Alder, J. Chem. Phys. 18, 1040 (1950)
R. J. Riddell, thesis (Ann Arbor, 1951)
Omitted endnote
Kirkwood (private communication)

[c1] J. de Boer, "Reports on Progress in Physics," Phys. Soc. (London) 12, p. 305 (1949)

[c2] J. de Boer and A. Michels, Physica 6, 97 (1939)

[c3] J. G. Kirkwood, J. Chem. Phys. 3, 300 (1935)

[c4] Hart, Wallis, and Pode, J. Chem. Phys. 19, 139 (1951)

[c5] G. S. Rushbrooke and H. I. Scoins, Nature 167, 366 (1951) Phil. Mag. 42, 582 (1951)

[c6] M. Born and H. S. Green, Proc. Roy. Soc. (London) A188, 10 (1946)

[c7] B. R. A. Nijboer et L. Van Hove, Proc. Koninkl. Nederlandse Akad. Wetenschappen B54, 256 (1951)

[c8] Placzek, Nijboer and Van Hove, Phys. Rev. 82, 392 (1951)

[c9] W. Magnus und F. Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik (Julius Springer, Berlin, 1943), p. 119

[c10] L. Boltzmann, Verslag. Gewone Vergadering Afd. Natuurk. Nederlandse Akad. Wetensch. 7, 484 (1899) H. Happel, Ann. Physik 21, 342 (1906) R. Majumdar, Bull. Calcutta Math. Soc. 21, 107 (1929)

[c11] Omitted endnote

[c12] Kirkwood, Maun, and Alder, J. Chem. Phys. 18, 1040 (1950)

[c13] R. J. Riddell, thesis (Ann Arbor, 1951)

[c14] Omitted endnote

[c15] Kirkwood (private communication)

Physical Review Journals Archive

Export citation

Export citation

Radial Distribution Function of a Gas of Hard Spheres and the Superposition Approximation

Abstract

References (15)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation