  We provide a simple explanation, based on an effective field, for the
precession damping rate due to the spin-orbit interaction. Previous effective
field treatments of spin-orbit damping include only variations of the state
energies with respect to the magnetization direction, an effect referred to as
the breathing Fermi surface. Treating the interaction of the rotating spins
with the orbits as a perturbation, we include also changes in the state
populations in the effective field. In order to investigate the quantitative
differences between the damping rates of iron, cobalt, and nickel, we compute
the dependence of the damping rate on the density of states and the spin-orbit
parameter. There is a strong correlation between the density of states and the
damping rate. The intraband terms of the damping rate depend on the spin-orbit
parameter cubed while the interband terms are proportional to the spin-orbit
parameter squared. However, the spectrum of band gaps is also an important
quantity and does not appear to depend in a simple way on material parameters.
