  We consider an XXZ spin-1/2 chain coupled to optical phonons with non-zero
frequency $\omega_0$. In the adiabatic limit (small $\omega_0$), the chain is
expected to spontaneously dimerize and open a spin gap, while the phonons
become static. In the antiadiabatic limit (large $\omega_0$), phonons are
expected to give rise to frustration, so that dimerization and formation of
spin-gap are obtained only when the spin-phonon interaction is large enough. We
study this crossover using bosonization technique. The effective action is
solved both by the Self Consistent Harmonic Approximation (SCHA)and by
Renormalization Group (RG) approach starting from a bosonized description. The
SCHA allows to analyze the lowfrequency regime and determine the coupling
constant associated with the spin-Peierls transition. However, it fails to
describe the SU(2) invariant limit. This limit is tackled by the RG. Three
regimes are found. For $\omega_0\ll\Delta_s$, where $\Delta_s$ is the gap in
the static limit $\omega_0\to 0$, the system is in the adiabatic regime, and
the gap remains of order $\Delta_s$. For $\omega_0>\Delta_s$, the system enters
the antiadiabatic regime, and the gap decreases rapidly as $\omega_0$
increases. Finally, for $\omega_0>\omega_{BKT}$, where $\omega_{BKT}$ is an
increasing function of the spin phonon coupling, the spin gap vanishes via a
Berezinskii-Kosterlitz-Thouless transition. Our results are discussed in
relation with numerical and experimental studies of spin-Peierls systems.
