  We study the production of Na and Al around the hydrogen shell of two
red-giant sequences of different metallicity in order to explain the abundance
variations seen in globular cluster stars in a mixing scenario. Using detailed
stellar models together with an extensive nuclear reaction network, we have
calculated the distribution of the various isotopic abundances around the
hydrogen shell at numerous points along the red-giant branch. These
calculations allow for the variation in both temperature and density in the
shell region as well as the timescale of the nuclear processing, as governed by
the outward movement of the hydrogen shell. The reaction network uses updated
rates over those of Caughlin \& Fowler (1988). We find evidence for the
production of Na and Al occurring in the NeNa and MgAl cycles. In particular,
Na is significantly enhanced throughout the region above the hydrogen shell.
The use of the newer reaction rates causes a substantial increase in the
production of $^{27}$Al above the hydrogen shell through heavy leakage from the
NeNa cycle and should have an important effect on the predicted surface
abundances. We also find that the nuclear processing is considerably more
extensive at lower metallicities.
