  By means of analytical calculations, we explore the self-enrichment scenario
for Globular Cluster formation. According to this scenario, an initial burst of
star formation occurs inside the core radius of the initial gaseous
distribution. The outward-propagating shock wave sweeps up a shell in which
gravitational instabilities may arise, leading to the formation of a second,
metal-enriched, population of stars. We find a minimum mass of the
proto-globular cluster of the order of 10^6 solar masses. We also find that the
observed spread in the Magnitude-Metallicity relation can be explained assuming
cluster-to-cluster variations of some parameters like the thermalization
efficiency, the mixing efficiency and the Initial Mass Function, as well as
variations of the external pressure.
