Thermally-pulsating asymptotic giant branch (TP-AGB) stars are hundreds of times larger and several tens of thousand times more luminous than than the Sun. They are composed of a compact carbon and oxygen core and an extended hydrogen convective envelope. These stars are intermediate-mass objects in their last stages of evolution, just before they die as a cooling compact star called a white dwarf. TP-AGB stars are the main producers of slow neutron capture (s-) process elements, which are elements heavier than iron such as strontium, yttrium, zirconium, caesium, barium, lanthanum and cerium. There are still large uncertainties associated with the formation of the main neutron source needed for the synthesis of these elements 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 TP-AGB stars and have constrained the free parameters describing the physics of the mixing process of these elements into the stellar envelope and the properties of the neutron source. We show that the amount of 13C which effectively contributes as a neutron source to s-process element synthesis tends to decrease with metallicity and that it is constrained to a narrower range of values than that previously believed. We also find that the mixing of s-process elements into the stellar envelope happens in stars of lower initial mass than those predicted by theoretical models. Binary systems which contained a TP-AGB star, now observed as a white dwarf, show significant orbital eccentricity. However, the strong tidal interaction which should have taken place due to the large size of a TP-AGB star must have dissipated significant amounts of energy and consequently circularised the orbit. This indicates that a mechanism which enhances the orbital eccentricity must take place in order to explain the observations. We propose a model for TP-AGB stars in binary systems in which their mass-loss is enhanced when the system components are closer to each other. This uneven mass-loss along the orbit provides a mechanism which enhances the orbital eccentricity in such a way that it competes with the tidal circularisation. We show that by applying this mechanism it is possible to explain the eccentric orbit of systems such as Sirius and of many barium stars, which so far had no explanation under the standard assumptions considering only tidal dissipation
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