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A nu -dimensional system of particles with two-body potential q(r)+ gamma nu K( gamma r) is considered. Various correlation functions are defined and evaluated in the limit gamma to 0. Some of the results describe two-phase states, and others are closely related to the Ornstein- Zernike theory.

A theoretical discussion of helicon wave propagation in non-resistive plasmas is presented. The boundary conditions are derived and applied in cylindrical geometry to give results consistent with experiment. The problem is more complicated in spherical geometry because of the non-separability of the wave equation. However, by separating in cylindrical coordinates and rearranging in a series of spherical waves, solutions are obtained in the form of an infinite set of integral equations. Approximate solutions are obtained and the first few natural frequencies are identified. Wave fields for the principal mode are calculated and displayed graphically.

The free energy and crystal structure of some particular cases of a cell model of melting are obtained. These include (i) a class of one-dimensional cases with interactions extending to many neighbouring cells, (ii) the plane hexagonal, bcc and triangular lattices with nearest-neighbour interactions, (iii) a case of the plane, square lattice with first- and second-neighbour (diagonal) interactions, and others. The solutions for the simple cubic lattices in all dimensions were obtained in a previous paper (abstr. A46569 of 1971). It is shown that some of the 2, 3, etc dimensional cases are closely related ('isomorphic') to one-dimensional cases.