Context : Motivated by recent reports concerning the observation of limited enrichment in He but excess K in stars of globular clusters , we revisit the H-burning conditions that lead to the chemical properties of multiple stellar populations in these systems .

Aims : In particular , we are interested in correlations of He and K with other elements , like O , Na , Al , Mg and Si , reported in stars of NGC 2808

Methods : We perform calculations of nucleosynthesis at constant temperature and density , exploring the temperature range of 25 to 200 10 ^ { 6 } K ( 25 to 200 MK ) , using a detailed nuclear reaction network and the most up-to-date nuclear reaction rates .

Results : We find that Mg is the most sensitive `` thermometer '' of hydrostatic H-burning conditions , pointing to a temperature range of 70-80 MK for NGC 2808 , while He is a lesser - but not negligible - constraint .
K can be produced at the levels reported for NGC 2808 at temperatures > 180 MK and Si at T > 80 MK .
However , in the former temperature range Al and Na are totally destroyed and no correlation can be obtained , in contrast to the reported observations .
None of the putative polluter sources proposed so far seem to satisfy the ensemble of nucleosynthesis constraints .

Conclusions :