Résumé
On montre que la sommation d’une large class de diagrammes dans un développement du type « cluster » permet l’établissement d’une équation intégrale pour la fonction de corrélation dans les fluides classiques. Après une approximation, cette équation se réduit à celle de Born, Green et Kirkwood, et elle reproduit plus exactement que celle-ci les coefficients du viriel. On donne les termes correctifs, de plus en plus compliqués, qui permettent de rendre exacte notre équation. On calcule enfin la fonction de corrélation à trois corps, qui, introduite dans l’équation d’Yvon-Born-Green, permet de calculer la fonction de corrélation à deux corps. On confirme ainsi le calcul direct de cette fonction, et on montre que notre équation intégrale inclut des corrections à l’approximation de superposition.
Riassunto
Si mostra che la somma di una larga classe di diagrammi in uno sviluppo del tipo « cluster » permette di scrivere una equazione integrale per la funzione di correlazione nei fluidi classici. Con una approssimazione, questa equazione si riduce a quella di Born, Green e Kirkwood e riproduce più esattamente di quella i coefficienti del viriale. Si danno i termini correttivi, sempre più complicati, che permettono di rendere esatta la nostra equazione. Si calcola infine la funzione di correlazione a tre corpi, che, introdotta nell’equazione di Yvon-Born-Green, permette di calcolare la funzione di correlazione a due corpi. Si conferma così il calcolo diretto di questa funzione, e si mostra che la nostra equazione integrale include delle correzioni all’approssimazione di sovrapposizione.
References
At the moment when this paper was ready to be sent, Prof.Yvon kindly communicated us preprints of a work due to Dr.E. Meeron which is in many points similar to the present paper.
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After this paper was written, we realized that this integral equation was contained, with different derivations, in the paper of Meeron quoted in ref. (6) and in a paper byJ. M. J. Van Leuwen, J. Groenveld andJ. de Boer:Physica,25, 792 (1959).
J. Yvon:Suppl. Nuovo Cimento,9, 144 (1958);Actualités scientifiques et industrielles (Paris, 1935), no. 203.
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Note added in proof. - In an article which appeared recently (Progr. Theor. Phys.,23, 829 (1960))Morita has added to his preceeding expansion the missing terms. He thus obtains the eqs. (37–38) of the present paper: moreover, the same author has given the expression of the correction terms to the integral equation as in the preprint of Dr.Meeron and as in the present paper (Progr. Theor. Phys.,23, 385 (1960)).
See ref. (1) andL. Goldstein:Phys. Rev.,84, 466 (1951).
A. Eisenstein andN. S. Gingrich:Phys. Rev.,62, 261 (1942).
J. G. Kirkwood, V. A. Lewinson andB. J. Alder:Journ. Chem. Phys.,20, 929 (1952).
Various authors have investigated this problem by considering the first few terms of the expansion of (81):Yvon: private communication;R. Abe:Progr. Theor. Phys.,21, 421 (1959).
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Supported in part by the United States Air Force through the European Office, Air Research and Development Command.
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Verlet, L. On the theory of classical fluids. Nuovo Cim 18 (Suppl 1), 77–101 (1960). https://doi.org/10.1007/BF02726040
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DOI: https://doi.org/10.1007/BF02726040