Simple Plane Waves Research Articles

Calculation of the Interatomic Distance at which a Model of Compressed Solid Helium becomes a Metal

In this paper, a calculation is attempted of the interatomic distance at which a face-centred cubic lattice of helium atoms becomes a metal, i.e., at which valence and conduction bands begin to overlap. Furthermore, the pressure which corresponds to this interatomic distance is estimated by means of the Thomas-Fermi equation of state. In one model used (the `ionic' one) an electron in the crystal sees a helium ion at the lattice position to which it is nearest, and neutral helium atoms at the other lattice positions; thus the `Fermi hole' is crudely accounted for. A slightly more refined model deals with exchange and correlation in a way similar to that of Bohm and Pines. In both cases, points of high symmetry in the Brillouin zone are used, and the Bloch wave functions are expanded in terms of the corresponding suitable linear combinations of simple plane waves; the convergence problem involved is discussed.

SOUND SCATTERING AND TRANSMISSION BY THIN ELASTIC RECTANGULAR PLATES

Scattering and transmission of sound waves of somewhat more general form than simple plane waves are analysed for soatterers in the form of a thin elastio simply-supported rectangular plate in a rigid inflnite baffle. The plate is assumed to separate two different fluid media, and the sound radiation from the plate undergoing forced vibrations under the influence of the incident wave pressure is studied. Unlike the solid scatterer, whose dynamic characteristics are little different in vacuum and in certain fluid media, the characteristics of elastic plates are profoundly altered by fluid reaction. By correlating the general solution of the wave equation in the fluid media with that of the Lagrange equations of the elastic plate at the plate-fluid media interfaces, the deflexion of the plate motion is determined. A transmission coefficient t is then defined and derived. In the appendixes, expressions for an energy ratio η and the reactions at the plate supports are given.