adopt a more accurate treatment for the H-burning network (see § \[numtreat\]). In passing, we note that our models support the suggestion by @HIF90, according to which a more realistic treatment of the H burning should have the only effect of producing a wider H-burning shell.

However, at odds with the results obtained by @HIF90, in our computations of the HEFM the He-burning luminosity attains negligible values, and the structure is fully supported by the H-burning shell. Besides, due to the H-flash the size of the He core is significantly reduced in comparison with the value reached just before the He-flash.

About 100,000 years after the HEFM, the convective envelope deepens and merges with the convective zone located above the H-burning shell (the ), the lower boundary of which has, as also shown by @HIF90, moved outward. At the end of this process, a huge amount of matter processed by both H and He burning is carried to the surface of the star, polluting its initially metal free chemical composition. Thus, the stellar surface is strongly enriched by helium ($Y_{\rm surf}\approx0.5$) and the global metallicity is equal to $Z=0.0131$. However, unlike a Pop. I star, the most abundant heavy elements 