  We investigate the dynamics of a cold trapped ion coupled to the quantized
field inside a high-finesse cavity, considering exact resonance between the
ionic internal levels and the field (carrier transition). We derive an
intensity-dependent hamiltonian in which terms proportional to the square of
the Lamb-Dicke parameter ($\eta$) are retained. We show that different
nonclassical effects arise in the dynamics of the ionic population inversion,
depending on the initial states of the vibrational motion/field and on the
values of $\eta$.
