Some magnetic properties of metals - IV. Properties of small systems of electrons

Abstract

The first part of the paper consists of a calculation of the magnetic properties of a system of electrons contained within a cylinder of very small radius placed with its axis parallel to the field direction. Perturbation theory is used to find the energy levels, and from these the number of occupied states in a two-dimensional system is determined by summation over the quantum numbers; the results are then generalized to the three-dimensional case. The expressions for the magnetic susceptibility, thermodynamic potential, and specific heat are found to contain a steady term which remains of significant magnitude at all temperatures, together with terms periodic in the field which are significant only at very low temperatures. The influence of electron spin on both steady and periodic terms is discussed. The second part consists of similar calculations for a small spherical system.