  We follow the static abundance profiles of the C, N, O, Ne, Na, Mg, and Al
isotopes around the hydrogen-burning shell (H shell) of globular cluster
red-giant-branch (RGB) stellar models in order to study the observed abundance
anomolies associated with these elements. We do this by combining four
"realistic" stellar evolutionary sequences of different metallicities with a
detailed nuclear reaction network. This approach allows for the variation in
the temperature and density around the H shell as well as structural changes in
the H shell caused by advancing evolution and variations in metallicity. In
addition, our reaction network allows us to explore the effects of the
uncertainties in the reaction rates on the abundance profiles.
  Our results are qualitatively consistent with the observed C vs. N, and O vs.
N, Na, and Al anticorrelations as well as with the observed luminosity- and
metallicity-dependent variations in the abundances and isotopic ratios. We find
that the source of the large Al enhancements in some clusters is 24Mg, but
contrary to the results of Shetrone (1996b;1997) we are unable to deplete the
24Mg abundance due to leakage from the NeNa cycle via the 23Na(p,gamma)24Mg
reaction. We discuss possible remedies to this discrepancy.
