The surface of liquid 4He, based on the idea that ? i<j f(r ij) describes a droplet

Abstract

We argue that the wave function 11 f(rij) describes the ground state of a droplet of liquid 4He. With this wave function, expressions for the surface energy e and the surface tension cr of liquid aBe at T = 0 are derived. Choosing particular f(r) and density profile, and the simplest pair correlation function, we plot the variation of e and cr with surface thickness t. For slow variation of density at the surface, e becomes proportional to t. The surface thickness is found to be about 4 ~. The inclusion of phonon zero-point motion correlations in the wave function leads (at T = O) to a-R 2 log R term in the energy of a droplet of radius R, implying a logarithmic divergence in both e and o'. At T > 0 the phonon correlations give a log T dependence of e and r and a negative bulk specific heat, Suggestions as to the reason for these problems are explored, but no definite conclusions are reached.

Surface oscillations and the surface thickness of classical and quantum droplets

“…For He 4, using a=0.373 erg/cm 2 [13], equation (40) gives (~)01/8___ 1.54 A, so t~ ~ 3.5 A and t r = 4.2 A. The first result can be compared with the calculations of reference [14], w167 3 and 4, which give t~___3"9 A and 3.4 A respectively.…”

“…To facilitate comparison with other estimates of the surface thickness we shall evaluate (~2) for two specific density profiles, and then express it in terms of the 10-90 thickness t, defined as the distance over which the density falls from 90 per cent to 10 per cent of its bulk value. (For other definitions of the surface thickness, and comparisons between them, as well as a survey of theoretical estimates for simple classical liquids and He 4, see [11].) First we will consider droplets that are large compared to the size of the constituent particles (R >>t), so we can approximate the density profile by its plane surface form.…”

“…The theory so far is quite general. (27) applies to any self-bound system whose surface oscillations are well represented by the hamiltonian (11). This includes droplets of HO, possibly He a and nuclei, and droplets of classical liquids and of liquid metals.…”

Measurements of the surface thickness of liquid4He

“…At a liquid--vapour interface, the density p ( z ) of a fluid does not change abruptly but changes continuously from liquid density to vapour density over a vertical distance of some Bngstroms. Following the ideas of Lekner and Henderson (1978a), it is convenient to define a surface thickness t as the difference in height between the point where the densityisp: t 0.9(p2pl) andthepointwherethedensityisp, + O.l(pzp l ) . p1 and p2 being the densities of bulk vapour and bulk iiquid.…”