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Notes:
At some point the temperature in the inert He core becomes high enough for He fusion. Fusing 2 He particles into beryllium does not release energy, and the beryllium will quickly unbind again. However, if before this happens another He nucleus is added, one can make Carbon. Net, therefore, 3 particles are fused into Carbon.
Fig. 17.14 of the book, as well as a figure from the first -year astronomy lecture notes of Prof. Verbunt at Utrecht University.