Spin-Orbit Coupling for f-Electrons in a Crystalline Field

The notion of a spin-orbit interaction arises from consideration of dynamics of multielectron atoms, i.e. systems of N electrons in a spherical potential. This notion is essentially a single-particle one. We sketch its origin as a second-order correction when Dirac four-component wave equations for an electron in external electromagnetic fields are simplified to the two-component Pauli spinors. The constraints in spinorial degrees of freedom consist, roughly speaking, in neglecting the small component of the electron four-function. The spin-orbit interaction term serves to compensate effects of the small component. The crystalline field induces some deviations from spherical symmetry of an isolated atom, which yields some modifications of the spherical form of the spin-orbit interaction operator. These modifications can be described in terms of a number of tensor operators adapted to appropriate chains of subgroups of the spherical symmetry group. We present a classification of independent tensor operators and discuss the relevant parameters for f-ions.