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The chemical evolution of the Universe and several phases of the stellar lifeare regulated by minute nuclear reactions. The key point for each of thesereactions is the value of cross sections at the energies at which they takeplace in stellar environments. Direct cross-section measurements are mainlyhampered by the very low counting rate and by cosmic background, neverthelessthey have become possible by combining the best experimental techniques withthe cosmic silence of an underground laboratory. In the nineties the LUNA(Laboratory for Underground Nuclear Astrophysics) collaboration opened the eraof underground nuclear astrophysics installing first a home-made 50 kV andlater on, a second 400 kV accelerator under the Gran Sasso mountain in Italy:in 25 years of experimental activity, important reactions responsible forhydrogen burning could have been studied down to the relevant energies thanksto the high current proton and helium beams provided by the machines. Theinterest to the next and warmer stages of star evolution (i.e. post mainsequence, helium and carbon burning) drove a new project based on an ionaccelerator in the MV range called LUNA-MV, able to deliver proton, helium andcarbon beams. The present contribution is aimed to discuss the state-of-the-artfor some selected key processes of post main sequence stellar phases: the 12Cagand the 12C+12C fundamental for helium and carbon burning phases, and 13Can and22Neag that are relevant to the synthesis of heavy elements in AGB stars. Theperspectives opened by an underground MV-facility will be highlighted.

The study of key reactions shaping the post main-sequence evolution of massive stars in underground facilities