In previous papers [1-3] we have reported experimental measurements of the relaxation rates of the k-multipole moments in the 4D level of sodium and the 3S-4D optical coherence. In the present paper we compare the experimental values with those obtained theoretically for different types of potentials. We show that the Van der Waals C6R -6 interaction is not sufficiently anisotropic to describe the relaxation of the k multipole moments. For Ar, Kr and Xe, much better results are obtained by taking into account the next term C8R-8 in the expansion of the long-range interaction. The potentials of Pascale and Vandeplanque [4] give very good results for helium. The results are also satisfactory for Ar, Kr and Xe, but the agreement could still be improved.
We derive algebraic expressions for the atomic multipole moments
mk,q(F) describing the steady-state polarization of an atomic ensemble with angular momentum
F in a static magnetic field of arbitrary direction and general multipole relaxation rates ${\ensuremath{\Gamma}}_{q}^{(k)}$. The longitudinal moments
mk,0 are given in terms of truncated continued fractions, while the transverse moments ${m}_{k,q\ensuremath{\ne}0}$, representing the ensemble coherence, are given by products of truncated continued fractions. The special case of isotropic relaxation leads to particularly simple and elegant expressions. Our results are relevant for all domains of physics that consider the evolution of a spin system interacting with vector-type perturbations.