Relativistic Basis Set Methods

Abstract

Relativity, like gravitation, cannot be switched off. Whilst relativistic effects on the physics of light elements are often tiny, they grow rapidly with nuclear charge and become progressively harder to ignore as we go down the Periodic Table. We have seen in this meeting, for example, that at energies of several hundred keV, which is comparable with the rest energy of the electron, relativistic effects in electron impact ionization are significant and need a full-blooded relativistic treatment [1]. This is partly because of the relativistic character of the dynamics of fast electrons, but also because the many-electron target atom, molecule, atomic cluster or solid may also reveal relativistic effects. Relativistic theories of many-electron systems can be regarded as a branch of quantum electrodynamics (QED) (see any good text, for example, [2]). The geometry of space-time is described by the group of inhomogeneous Lorentz transformations. The corresponding Lie algebra is built from the infinitesimal generators for space and time displacements, rotations and boosts (which relate 4-vectors in inertial frames moving with different velocities). These generators can be identified with quantum mechanical operators: linear 4-momentum, angular momentum and so on. The irreducible representations can be labelled by the particle's rest mass, m and its angular momentum in the rest frame of the particle, 5, the intrinsic spin : 1/2 for electrons, 1 for photons (which have zero mass). The time-like component of linear 4-momentum is the particle energy which, unlike nonrelativistic mechanics, can be either positive or negative. The infinitesimal generators of rotations about coordinate directions are operators describing the total angular momentum, j = 1 + s where, as usual the orbital angular momentum 1 = r x p, where r is the (3-)vector of position and p is the linear momentum operator, — i