  First order Doppler effects are usually ignored in laser driven trapped ions
when the recoil frequency is much smaller than the trapping frequency
(Lamb-Dicke regime). This means that the central, carrier excitation band is
supposed to be unaffected by vibronic transitions in which the vibrational
number changes. While this is strictly true in the Lamb-Dicke limit (infinitely
tight confinement), the vibronic transitions do play a role in the Lamb-Dicke
regime. In this paper we quantify the asymptotic behaviour of their effect with
respect to the Lamb-Dicke parameter. In particular, we give analytical
expressions for the frequency shift, ``pulling'' or ``pushing'', produced in
the carrier absorption band by the vibronic transitions both for Rabi and
Ramsey schemes. This shift is shown to be independent of the initial
vibrational state.
