  A recent survey of a large sample of Galactic intermediate-mass (>3 Msun)
asymptotic giant branch (AGB) stars shows that they exhibit large
overabundances of rubidium (Rb) up to 100--1000 times solar. These observations
set constraints on our theoretical notion of the slow neutron capture process
(s process) that occurs inside intermediate-mass AGB stars. Lithium (Li)
abundances are also reported for these stars. In intermediate-mass AGB stars,
Li can be produced by proton captures occuring at the base of the convective
envelope. For this reason the observations of Rb, Zr, and Li set complementary
constraints on different processes occurring in the same stars. We present
predictions for the abundances of Rb, Zr, and Li as computed for the first time
simultaneously in intermediate-mass AGB star models and compare them to the
current observational constraints. We find that the Rb abundance increases with
increasing stellar mass, as is inferred from observations but we are unable to
match the highest observed [Rb/Fe] abundances. Inclusion of a partial mixing
zone (PMZ) to activate the 13C(a,n)16O reaction as an additional neutron source
yields significant enhancements in the Rb abundance. However this leads to Zr
abundances that exceed the upper limits of the current observational
constraints. If the third dredge-up (TDU) efficiency remains as high during the
final stages of AGB evolution as during the earlier stages, we can match the
lowest values of the observed Rb abundance range. We predict large variations
in the Li abundance, which are observed. Finally, the predicted Rb production
increases with decreasing metallicity, in qualitative agreement with
observations of Magellanic Cloud AGB stars. However stellar models of Z=0.008
and Z=0.004 intermediate-mass AGB stars do not produce enough Rb to match the
observed abundances.
