We present full stellar evolution and parametric models of the surface abundance evolution of ^ { 16 } \mathrm { O } , ^ { 22 } \mathrm { Ne } , ^ { 23 } \mathrm { Na } , and the magnesium isotopes in an extremely metal-poor intermediate mass star ( { \cal M } _ { ZAMS } = 5 { \cal M } _ { \odot } , Z = 0.0001 ) . ^ { 16 } \mathrm { O } and ^ { 22 } \mathrm { Ne } are injected into the envelope by the third dredge-up following thermal pulses on the asymptotic giant branch .
These species and the initially present ^ { 24 } \mathrm { Mg } are depleted by hot bottom burning ( HBB ) during the interpulse phase .
As a result , ^ { 23 } \mathrm { Na } , ^ { 25 } \mathrm { Mg } and ^ { 26 } \mathrm { Mg } are enhanced .
If the HBB temperatures are sufficiently high for this process to deplete oxygen efficiently , ^ { 23 } \mathrm { Na } is first produced and then depleted during the interpulse phase .
Although the simultaneous depletion of ^ { 16 } \mathrm { O } and enhancement of ^ { 23 } \mathrm { Na } is possible , the required fine tuning of the dredge-up and HBB casts some doubt on the robustness of this process as the origin of the O–Na anti-correlation observed in globular cluster stars .
However , a very robust prediction of our models are low ^ { 24 } \mathrm { Mg } / ^ { 25 } \mathrm { Mg } and ^ { 24 } \mathrm { Mg } / ^ { 26 } \mathrm { Mg } ratios whenever significant ^ { 16 } \mathrm { O } depletion can be achieved .
This seems to be in stark contrast with recent observations of the magnesium isotopic ratios in the globular cluster NGC 6752 .