Theorie statistique du mouvement de translation des atomes dans un liquide simple : II. Modèle de la cage mobile et déformable
The theory developed in a previous paper to calculate the correlation function of the velocity of an atom or of a spherical molecule in a liquid, has been generalized to introduce the mobility and the softness of the cage which contains the atom under study. Moreover, the deformation of the cage depends upon the initial velocity of the atom. To take into account this effect, the possibility of an irreversible exchange of kinetic momentum between the atom and the nearest neighbours that it knocks on its way, has been introduced. The irreversible character of this exchange is due to the fact that the nearest neighbours themselves are in thermal contact with the whole liquid. By also introducing, as it was done in the previous work, the irreversibility of the energy exchanges between the atom and its environment, one gets two coupled integral equations. The solution of these equations yields for the correlation function of the velocity a spectrum which exhibits a maximum and at least one shoulder. These are interpreted as corresponding respectively to the collective behaviour of the couple formed by the atom and its cage and to the individual oscillatory motion of the atom itself in the cage. There exists a good quantitative agreement between the spectrum calculated in this theory and the spectrum obtained, for the same physical conditions, by simulation from the molecular dynamics (liquid argon) or by scattering of neutrons (liquid sodium).