Interatomic dispersion forces and small angle scattering from rare gas fluids

Abstract

The structure factor S(q) and the direct correlation function c(q) of rare gases are expected to have a nonanalytic mod q mod 3 term at small q. This term is due, in addition to the well known long-range r-6 tail of the two-body interaction, also to the three-body Axilrod-Teller interaction. The coefficient c3 of the mod q mod 3 term of c(q) has a particularly simple state dependence, T-1 in temperature and linear in density, when the AT interaction is present. If no three-body interaction is present C3 is density independent. Therefore the experimental determination of the density dependence of c3 will give unequivocable evidence of three-body forces. On the basis of the integral equation method the authors determine that it will be easier to detect the mod q mod 3 term if the scattering data are analysed in term of c(q) and for measurements at density and temperature not far from the critical point. Under these favourable conditions scattering measurements in the range 1-4 nm-1 will give a precise determination of the mod q mod 3 term. The role of retardation, which changes the r-6 tail into r-7, on the small-q behaviour of S(q) and c(q) is also evaluated and this effect is predicted to be measurable for q<0.5 nm-1.

Long Range Potential Effects in Low Density Krypton Gas

“…(2) below], which is the Fourier transform of the direct correlation function c͑r͒, are expected to have at small k a nonanalytic k 3 term directly related to the r 26 tail of the microscopic van der Waals interaction potential in the fluid. In particular, the theory of Reatto and Tau [7] takes into account the effect of retardation which modifies k 3 to k 4 as k ! 0.…”

“…This connection has been pointed out by Enderby, Gaskell, and March [3], who emphasized the importance of direct observation of such terms. Several papers have been devoted to this subject [4][5][6], and recently this matter has been discussed by Reatto and Tau [7]. The main result of these papers is that for classical fluid insulators, like noble gases, S͑k͒ and c͑k͒ [Eq.…”

“…By means of theoretical calculations of c͑k͒, performed with the modified hypernetted chain equation, Reatto and Tau [7] have shown that in low density noble gases, the k range useful for the determination of the k 3 dependence is 0.5 , k , 3.5 nm 21 . This range is experimentally accessible with modern SANS instrumentation.…”

“…The agreement between the two sets of experimental data is reasonable in the overlapping region. In very low density systems the interaction law can be written retaining only the pair and triplet contributions and it has been demonstrated [7] that, within suitable approximations, the asymptotic behavior of c͑r͒ is given by…”

“…Moreover, if the irreducible three-body interaction is assumed to be of the AT form [12], it can be demonstrated [7,16] that the asymptotic behavior of C͑r͒ is C͑r͒ 2͑8p͞3͒ bnn͞r 6 , as r !`.…”