We study the scattering of light by a single ultracold trapped atom in
itially in the ground state of the trapping harmonic potential. We hav
e found interesting features of scattering in the regime where the ato
mic recoil energy is much larger than the separation between oscillato
ry trap levels. Although we present the quantum-mechanical expression
for the scattering cross section, special attention is paid to the sem
iclassical analysis of the process. We show that the major characteris
tics of the scattering might be deduced from two conservation laws: co
nservation of energy and momentum in absorption and emission of photon
process separately. These conservation laws impose a strong correlati
on between scattered light characteristics and the position of the tra
pped atom at the moment of photon emission.