  In this paper we analyze the effects induced by rotation on low mass
Asymptotic Giant Branch stars. We compute two sets of models, M=2.0 Msun at
[Fe/H]=0 and M=1.5 Msun at [Fe/H]=-1.7, respectively, by adopting Main Sequence
rotation velocities in the range 0 - 120 km/s. At high metallicity, we find
that the Goldreich-Schubert-Fricke instability, active at the interface between
the convective envelope and the rapid rotating core, contaminates the
13C-pocket (the major neutron source) with 14N (the major neutron poison), thus
reducing the neutron flux available for the synthesis of heavy elements. As a
consequence, the yields of heavy-s elements (Ba, La, Nd, Sm) and, to a less
extent, those of light-s elements (Sr, Y, Zr) decrease with increasing rotation
velocities up to 60 km/s. However, for larger initial rotation velocities, the
production of light-s and, to a less extent, that of heavy-s begins again to
increase, due to mixing induced by meridional circulations. At low metallicity,
the effects of meridional circulations are important even at rather low
rotation velocity. The combined effect of Goldreich-Schubert-Fricke instability
and meridional circulations determines an increase of light-s and, to a less
extent, heavy-s elements, while lead is strongly reduced. For both
metallicities, the rotation-induced instabilities active during the interpulse
phase reduce the neutrons-to-seeds ratio, so that the spectroscopic indexes
[hs/ls] and [Pb/hs] decrease by increasing the initial rotation velocity. Our
analysis suggests that rotation could explain the spread in the s-process
indexes, as observed in s-process enriched stars at different metallicities.
