We present new evolutionary calculations for a 3 M. star of Population
I starting from the zero-age main sequence and followed up to the 25t
h thermal pulse of the asymptotic giant branch. The third dredge-up is
found to occur in a self-consistent way from the 14th pulse on. We sh
ow that any amount of C-13 possibly synthesized at the H/He interface
during the interpulse period is completely burnt through (alpha, n) re
actions before the next pulse develops. As a consequence, s-elements a
re produced in a radiative environment, at a neutron density of at mos
t a few 10(7) n cm(-3). They are then engulfed and diluted into the ne
xt convective pulse, where a second (minor) neutron burst occurs, driv
en by the Ne-22(alpha, n)Mg-25 reaction marginally activated near the
end of the He-shell instability. Despite the differences of the presen
t model with respect to past calculations, we predict s-process distri
butions very close to those computed by allowing C-13 to burn in conve
ctive pulses: C-13 burning and the ensuing s-processing are confirmed
to account for the main observational and experimental constraints. Th
e reasons for this are briefly discussed. Since no C-13 survives the i
nterpulse phase, we conclude that no modifications of the pulse shape
due to the energy feedback from the C-13(alpha, n)O-16 reaction occur.