If a simple linear relationship or a sinusoidal relationship is assumed for the time dependence of temperature, the ratios of abundances attained at the surface in a given time are the same whether the time is spent in a single transit to the surface or in several transits back and forth from the bottom of the hydrogen-burning zone to the surface of the star. Analysis is made of the effect of convection with microscopic mixing on CN material passing through a hydrogen-burning zone. The resonance at 65 keV in the O' (p, a) N'4 reaction is responsible for the temperature dependence of ratios involving O' nuclei. General features of the curves of abundance ratios for C12, C'3, N14, N'2, and 016 nuclei as functions of protons consumed are found to be insensitive to the temperature at which the reactions take place. It is suggested that the MS stars are AGB stars and that their compositions reflect the addition of C-12 and s-process material from He-burning thermal pulses.Differential equations of the CNO bi-cycle are solved to obtain the abundances of carbon, nitrogen, and oxygen nuclei as functions of protons consumed per initial nucleus for hydrogen burning in the temperature range 10-50 x 106 K. A range of integrated neutron exposures is evident with one star showing a large enhancement of Ba and Nd relative to Sr, Y, and Zr, while the other two show much lower enhancements of Ba and Nd.
The three MS giants studied all show enhancements of the s-process elements Sr, Y, Zr, Ba, and Nd. The CNO abundances clearly show the effects of CN-processed material being dredged to the surface, while one MS giant shows an excess of C-12, probably the result of He-burning products being dredged up during thermal pulses on the asymptotic giant branch (AGB). The CNO abundances are based on molecular lines from CO, OH, and CN. The abundances of the Fe-peak and heavier elements are based on atomic lines and are referenced to a comparison red giant, alpha Tau, to minimize non-LTE effects. The source material are high-resolution, high signal-to-noise digital spectra in the infrared and near-infrared. Carbon, nitrogen, oxygen, Fe-peak, and heavy, s-process elemental abundances have been determined for nine red giants of type M and MS.
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