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The universal critical-scattering function ͑CSF͒ has been measured on a CO 2 sample at critical density by small-angle neutron scattering. The experiment was designed and conducted in such a way as to reach an accuracy of 0.3% in the determination of the CSF in the large-Q range. Several approximate equations proposed in the literature are used to model the results, and their validity is discussed, but the main purpose of this work was to produce accurate data in the region of the crossover between the Ornstein-Zernike and critical regimes. ͓S0163-1829͑98͒06042-1͔

Small angle neutron scattering (SANS) in low density 86 Kr gas has been performed in order to measure the small-k behavior of the static structure factor S͑k͒. Three number densities between 1.52 and 2.42 nm 23 along the T 297 K isotherm have been studied. The small-k dependence of the Fourier transform c͑k͒ of the direct correlation function c͑r͒ has been derived. The experimental determination of the k 3 term in the behavior of c͑k͒ has led to a direct measurement of the London dispersion interaction in the pair potential of krypton. Also the contribution of the three-body potential in the asymptotic behavior of c͑r͒ has been observed and related to the magnitude of the three-body interaction potential.[ S0031-9007(97) The London dispersion energy due to the induced dipole interactions determines the form of the long range potential of pairs, as well as the form of the long range irreducible three-body interaction in ground state atoms [1,2]. One possibility for a direct assessment of these long range interactions among the particles in a fluid is given by the connection between the small-k behavior of the static structure factor S͑k͒ [Eq. (1) below] and the long range microscopic forces. 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. (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. Moreover, they confirm that measurements of the k 3 behavior of c͑k͒ in low density gases can, in principle, give an experimental direct verification of the r 26 power law of the pair potential and might determine the long range behavior of the dressed three-body vertex. However, we shall show that in the present case the k 2 term includes a larger and more useful measure of the dressed three-body vertex, giving a direct and unique experimental access to the long range interaction.Neutron diffraction measurements, when possible with high accuracy, have been proven to be a direct method for the determination of the interaction potential between pairs of atoms in gases [8,9]. Recently, both normal diffraction and SANS experiments have been performed in argon gas in order to measure the k 3 dependence of c͑k͒ and give an experimental value of the amplitude B of the long range 2B͞r 6 pair potential [10,12] in agreement with that determined by more traditional methods. Here we report the results of the measurements of the smallk dependence of the c͑k͒ of krypton at low density from which the stren...

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We show that diffraction measurements can reach the precision needed to test different models of interatomic interaction also in a dense fluid. Our measurements have been performed in krypton at several temperatures and densities in the liquid phase. Our theoretical calculations show that the density derivative of the static structure, contrary to the function itself, is sensitive to the shape of the interaction and the comparison with the experimental data gives another test of the interaction models.PACS numbers: 61.25.Bi, 61.20.GyOne of the motivations for the accurate determination of the static structure of a fluid is that the radial distribution function g{r) and the related static structure factor S(k) contain detailed information on the interatomic interaction. Recently [1] it has been shown that S(k) can be determined now by neutron scattering with the accuracy necessary to obtain an unambiguous determination of the pair interatomic interaction U2(r) in low density fluid argon. In that case S(k) directly reflects u 2 . The situation is quite different in a dense fluid where the structure is dominated by excluded-volume effects, i.e., by the strong repulsive forces which are present at short interatomic distances. In fact it is well known that S(k) of such diverse fluids like liquid argon or molten sodium can be modeled very simply by the structure factor of hard spheres. What is an asset in the theory of liquids [2], i.e., the weak dependence of S(k) on the detailed shape of the interatomic forces, makes it very difficult to extract information on these forces from the measured S(k). This is particularly true in rare gases in which the repulsive forces are very harsh and it was not clear that different models of interatomic interaction could be really tested by a measurement of S(k) in the dense phase. The case of krypton is particularly significant because the rather large deviation between the measured [3] S(k) and the computed one [4] with the best models [5, 6] of the interatomic interaction raised questions on the accuracy of these models of interaction and on the role of many-body forces.With this in view we have performed a new set of measurements of S(k) in liquid Kr at several densities and temperatures and over an extended k range. We find that the higher accuracy with which now S(k) can be determined allows for an unambiguous test of different models of interatomic interaction. By using an accurate theory of liquid structure, the modified hypernetted chain (MHNC) equation [7] extended, when needed, to include three-body forces [8], we show that the hard sphere and the Lennard-Jones (LJ) potentials give an inadequate representation of the forces whereas the Barker [5] and the Aziz HFD-B models [6] of ^(r) are very satisfactory. Our diffraction data taken together with thermodynamic data indicate also that many-body forces must be present and the Axilrod-Teller-Muto (ATM) [9] triple dipole U3(ri,r2,r3) gives a first good account for these forces for the description of the static properties of th...

By means of neutron Compton scattering, we have measured the momentum distribution of 4 He, on the isotherm Tϭ6.1 K, in the pressure range between 0 and 500 bars. The second moment of the distribution gives the value of the kinetic energy. This is a function of density that increases from the classical value 3 2 k B T up to ϳ5 times this value in the compressed solid. The kinetic energy data show a change in the density behavior at melting. This suggests that the change of symmetry influences the single-particle distribution function.

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The center-of-mass structure factor of liquid para hydrogen has been measured, using neutron diffraction, in four thermodynamic states close to the triple point. Path integral Monte Carlo simulations have been carried out at the same temperatures and densities. The present experimental data are in reasonable quantitative agreement with the simulations and closer to these results than previous neutron determinations available in the literature. The thermodynamic derivatives of the structure factor, from both experiment and simulation, have been compared to previous measurements obtaining a quantitative consistency.