On the relativistic dynamics of polarized systems. III: The case of atoms and molecules with electric and magnetic dipole moments and electric quadrupole moments

Abstract

The derivation of the classical relativistic equations of motion for electric and magnetic dipole atoms or molecules in an external electromagnetic field of force, given in two previous papers (I and II), is extended in the present paper to the case that these atoms possess also electric quadrupole moments. Again Møller's equations of motion for relativistic systems with an internal angular momentum are taken as the starting point. We only consider the form of these equations in which the term describing the unphysical trembling motion of the atoms is eliminated (see paper II). The resulting equations of motion are used in order to derive the relativistic atomic energy-momentum tensor for a system, consisting of a (large) number of these atoms. It is found that the field part of this tensor is not of the same form as in the pure dipole case and also no longer expressible only in terms of quantities appearing in the atomic field equations.