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(Abridged) We examine the effects of cool bottom processing (CBP) on severalisotopic ratios in the convective envelope during the TP-AGB phase of evolutionin a 1.5 M_sun initial-mass star of solar initial composition. We use aparametric model which treats extra mixing by introducing mass flow between theconvective envelope and the underlying radiative zone. The parameters of thismodel are the mass circulation rate (Mdot) and the maximum temperature (T_P)experienced by the circulating material. The effects of nuclear reactions inthe flowing matter were calculated using a set of structures of the radiativezone selected from a complete stellar evolution calculation. The compositionsof the flowing material were obtained and the resulting changes in the envelopedetermined. Abundant ^26Al was produced by CBP for log T_P > 7.65. While^26Al/^27Al depends on T_P, the isotopic ratios in CNO elements dependdominantly on the circulation rate. The correspondence is shown between modelsof CBP as parameterized by a diffusion formalism within the stellar evolutionmodel and those using the mass-flow formalism employed here. The isotopicratios are compared with the data on circumstellar dust grains. It is foundthat the ratios ^{18}O/^{16}O, ^{17}O/^{16}O, and ^26Al/^27Al observed foroxide grains formed at C/O < 1 are reasonably well-understood. However, the^15N/^14N, ^12C/^13C, and ^26Al/^27Al in carbide grains (C/O > 1) require manystellar sources with ^14N/^15N at least a factor of 4 below solar. The raregrains with ^12C/^13C < 10 cannot be produced by any red-giant or AGB source.Comment: 35 pages, plus 18 included figures. Scheduled for January 10, 2003  issue of Ap

Cool Bottom Processes on the Thermally Pulsing Asymptotic Giant Branch and the Isotopic Composition of Circumstellar Dust Grains