Fully evolutionary models have been built to follow the phases of Asymptotic Giant Branch ( AGB ) evolution with mass loss , for metal mass fractions from Z = 2 \times 10 ^ { -4 } to Z = 4 \times 10 ^ { -3 } .
The Hot Bottom Burning ( HBB ) at the base of the convective envelope is followed by fully coupling nuclear burning and non instantaneous mixing .
The models also show the occurrence of a spontaneous ( not induced by overshooting ) third dredge-up .
For the first time we find that temperatures close or even larger than 10 ^ { 8 } K are achieved at low Z : the full CNO cycle operates at the basis of the envelope , the ^ { 16 } O abundance for the most metal poor models of mass 4 and 5 M _ { \odot } is drastically reduced , and sodium and aluminium production by proton capture on neon and magnesium can occur .
Lithium is first largely produced in the envelope and then burned completely , so the average lithium abundance in the expelled envelope is a factor up to 5 times smaller than the initial one , but it is never completely depleted .

These results may be relevant for the evolution of primordial massive Globular Clusters : we suggest that the low mass stars may have been polluted at the surface by accretion from the gas lost from the evolving intermediate mass stars at early ages ( 1-2 \times 10 ^ { 8 } yr ) .
In this hypothesis , we should expect that the polluted stars show smaller abundance of oxygen , larger abundances of products of advanced nucleosynthesis as Na and Al , and lower , but never negligible , abundances of lithium .
The abundance spreads should be smaller in clusters of higher metallicities , where the lithium in the polluted stars could be larger than in the non polluted stars .