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Germanium Production in Asymptotic Giant Branch stars: Implications for Observations of Planetary Nebulae

Observations of planetary nebulae (PNe) by Sterling, Dinerstein and Bowers have revealed abundances in the neutron-capture element Germanium (Ge) from solar to factors of 3 -- 10 above solar. The enhanced Ge is an indication that the slow-neutron capture process (s process) operated in the parent star during the thermally-pulsing asymptotic giant branch (TP-AGB) phase. We compute the detailed nucleosynthesis of a series of AGB models to estimate the surface enrichment of Ge near the end of the AGB. A partial mixing zone of constant mass is included at the deepest extent of each dredge-up episode, resulting in the formation of a 13C pocket in the top ~1/10th of the He-rich intershell. All of the models show surface increases of [Ge/Fe] less than about 0.5, except the 2.5Msun, Z=0.004 case which produced a factor of 6 enhancement of Ge. Near the tip of the TP-AGB, a couple of extra TPs could occur to account for the composition of the most Ge-enriched PNe. Uncertainties in the theoretical modeling of AGB stellar evolution might account for larger Ge enhancements than we predict here. Alternatively, a possible solution could be provided by the occurrence of a late TP during the post-AGB phase. Difficulties related to spectroscopic abundance estimates also need to be taken into consideration. Further study is required to better assess how the model uncertainties affect the predictions and, consequently, if a late TP should be invoked.