  Thermally pulsating asymptotic giant branch (AGB) stars are the main
producers of slow neutron capture (s-) process elements, but there are still
large uncertainties associated with the formation of the main neutron source,
13C, and with the physics of these stars in general. Observations of s-process
element enhancements in stars can be used as constraints on theoretical models.
For the first time we apply stellar population synthesis to the problem of
s-process nucleosynthesis in AGB stars, in order to derive constraints on free
parameters describing the physics behind the third dredge-up and the properties
of the neutron source. We utilize a rapid evolution and nucleosynthesis code to
synthesize different populations of s-enhanced stars, and compare them to their
observational counterparts to find out for which values of the free parameters
in the code the synthetic populations fit best to the observed populations.
These free parameters are the amount of third dredge-up, the minimum core mass
for third dredge-up, the effectiveness of 13C as a source of neutrons and the
size in mass of the 13C pocket. We find that galactic disk objects are
reproduced by a spread of a factor of two in the effectiveness of the 13C
neutron source. Lower metallicity objects can be reproduced only by lowering by
at least a factor of 3 the average value of the effectiveness of the 13C
neutron source needed for the galactic disk objects. Using observations of
s-process elements in post-AGB stars as constraints we find that dredge-up has
to start at a lower core mass than predicted by current theoretical models,
that it has to be substantial ($\lambda$ >~ 0.2) in stars with mass M <~ 1.5
M_sun and that the mass of the 13C pocket must be about 1/40 that of the
intershell region.
