Many-Body Theory

Abstract

This thesis is a collection of theoretical investigations into a number of separate topics in many-body physics, These topics are related in that they all deal, if indirectly in some cases, with the properties of interfaces, in particular the liquid-vapour interface. A good proportion of the work presented here is contained in three papers supplied with the thesis. Part A deals with the reflection of light from a liquid-vapour interface. I work towards developing a theory which relates the atomic properties of an interface to the reflected amplitudes of light incident on it. In AI I calculate the local field near the surface of both a crystalline solid and. a liquid, for the case of an incident field of zero frequency. This work leads to a relation between the density profile n(z) and dielectric profile E(z) of a liquid-vapour interface. We find a smaIl dependence of E(z) on the polarisation of the incoming light, In AII we consider the problem of relating the dielectric profile E(z) to the reflected amplitudes Rs and. Rp of s and. p polarised Iight incident on the interface. The low order departures of Rs and.Rp from those expected for a step interface are calculated. We obtain Rs to second order in wave number times interface thickness but Rg to only first order. In part B I consider quantum liquids. In BI the surface energy and surface tension of the ground state of He3 are calculated, BII deals with the ground state phonons that exist in He4 t absolute zero. Current theories of the surface energy and. surface tension of He4 involve divergences when these phonons are included.. I consider the possibility that the phonon wave function depends on the shape of the system, but find the same wave function applies to a spherical system as to a rectangular system. By summing the zero-point energies of the phonon modes expressions for the phonon contribution to the bulk and surface energies of He4 are obtained if the total number of phonon modes is 3N these expressions .give values unrealistically high. In C I consider the coexistence of the Liquid and vapour phases of a fluid. A theory has been developed which relates the densities of these coexisting phases to the correlations In the interface. By using approximations for these correlations one obtains an equation for the Liquid-vapour coexistence curve of the fluid. The bulk of the work I have done on this has been in applying this theory to molecular fluids (such as water). The results give good agreement with experiment for all fluids considered. I also derive a liquid.-vapour coexistence curve for two-dimensional fluids.