Interatomic Correlations in LiquidHe4

Abstract

The direct correlation functions, of generally short-range character over most of the liquid temperature interval, have been obtained with the liquid ${\mathrm{He}}^{4}$ x-ray scattering data of Reekie, using the 701 IBM Electronic Calculator. The geometrical simplicity of these functions when compared with the indirect correlation functions, of more intuitive physical significance, is automatically demonstrated. They closely satisfy two types of integral test relations, and this fact proves their over-all correct character and the internal consistency of the numerical analysis.The previously obtained indirect correlation functions will be used here in studying the interference properties of the liquid in slow-neutron scattering processes, in the limiting static approximation. At temperatures not too close to the critical region, the static interference integrals are always negative as a result of the preponderant destructive interference effects arising from the local density defects from the mean density, outweighing the local density excesses. At short and moderate neutron wavelengths, where the use of the static interference integrals is better justified, the total slow-neutron scattering cross sections in liquid ${\mathrm{He}}^{4}$, and in liquids in general, always increase with increasing temperature. The static interference integrals will be shown to provide an additional integral test on the indirect correlation functions. The latter were found to satisfy this test relation with good accuracy.Part of this paper is devoted to a numerical evaluation of mean kinetic energies per liquid ${\mathrm{He}}^{4}$ atom as a function of the temperature. The existence of a large zero-point kinetic energy of the liquid as compared with the kinetic energy of thermal origin is demonstrated. Furthermore, the previously given qualitative proof of the kinetic energy origin of the lambda transition could be made semiquantitative. Finally, root-mean-square forces acting on a liquid atom are evaluated, this physical quantity of elementary character having become, in principle at least, accessible through the experimental investigation of slow-neutron scattering properties of liquids.