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tokens: Other channels may account for the most carbon-rich early-R stars. 4. Conclusion and Discussion The merger of an HeWD with an RGB star in a CE provides a possible model for the origin of lithium- and carbon-rich stars. By adopting a grid of approximate initial conditions for such mergers informed by previous SPH simulations, we have made one-dimensional mesa calculations of the post-merger evolution of a wide range of possible systems. Using BSPS we have computed the frequency and distribution of HeWD + RGB binary-star systems that are likely to merge. Analysis of the post-merger evolution models show that the final surface abundances depend on the masses of the progenitor HeWDs. The Li-rich giants form from low-mass HeWDs, i.e., ; the C-rich giants form from low-mass HeWDs, i.e., . The pathway to either of these categories is related to the temperature of the helium-core-burning shell and the balance of nuclear products during initial shell burning. Analysis of the distribution of post-merger systems, as given by BSPS and mesa evolution tracks, shows that predictions for HeWD+RGB mergers are consistent with observations of most Li-rich giants in terms of surface effective temperature ( T eff ), surface gravity (log g ), surface luminosity (log L ), surface abundance ( A (Li) and 12 C/ 13 C), and the Galaxy disk space density of . They are also consistent with the properties of some early-R carbon stars, in terms of T eff , log g , C/O, A (Li), 12 C/ 13 C, and a space density of (3.5−5.9) × 10 −7 pc −3 . According to the models, the post-merger objects are helium-core-burning stars, which means that they are all in the red clump stage of evolution, i.e., they are red giants with nondegenerate helium cores. However, only a few Li-rich giants have had their precise evolutionary stage determined by asteroseismology. Those stars that have been analyzed in this way correspond well with our results. Hence, we strongly argue that the Li-rich red clump stars and the majority of early-R carbon stars most likely form following the merger of an HeWD with an RGB star. A few problems still need to be addressed: (i) Post-merger evolution calculations depend on evolution during the CE phase that is determined by the progenitors of the merger, the amount of mass loss during the CE phase, and the structure of the CE. However, our knowledge of CE phase in binary-star evolution is still poor. Future theoretical studies and simulations will improve this deficiency. Also, as the products of post-CE mergers, further observations of Li-rich red clump stars will provide additional data for studies of the CE phase. (ii) Some of the observed Li-rich giants have measured rotation velocities, but we have not calculated rotation speeds for post-merger models immediately following CE ejection. Our model will be improved with more knowledge of angular momentum transport during the merger. (iii) The HeWD+RGB merger model provides a successful explanation for Li-rich red