  The spontaneous relaxation rates for an atom in free space and close to an
absorbing surface are calculated to various orders of the electromagnetic
multipole expansion. The spontaneous decay rates for dipole, quadrupole and
octupole transitions are calculated in terms of their respective primitive
electric multipole moments and the magnetic relaxation rate is calculated for
the dipole and quadrupole transitions in terms of their respective primitive
magnetic multipole moments. The theory of electromagnetic field quantization in
magnetoelectric materials is used to derive general expressions for the decay
rates in terms of the dyadic Green function. We focus on the decay rates in
free space and near an infinite half space. For the decay of atoms near to an
absorbing dielectric surface we find a hierarchy of scaling laws depending on
the atom-surface distance z.
