We have investigated the efficiency of pulsed Raman sideband cooling in the
presence of multiple decay and excitation channels. By applying sum rules
we identify parameter regimes in which multiple scattering of photons can b
e described by an effective wave vector. Using this method we determine the
rate of heating caused by optical pumping inside and outside the Lamb-Dick
e regime. On this basis we discuss also the efficiency of a recently propos
ed scheme for ground-state cooling outside the Lamb-Dicke regime [Europhys.
Lett. 39 (1997) 13]. (C) 2001 Elsevier Science B.V. All rights reserved.