  We explore the self-enrichment hypothesis for globular cluster formation with
respect to the star formation aspect. Following this scenario, the massive
stars of a first stellar generation chemically enrich the globular progenitor
cloud up to Galactic halo metallicities and sweep it into an expanding
spherical shell of gas. This paper investigates the ability of this swept
proto-globular cloud to become gravitationally unstable and, therefore, to seed
the formation of second generation stars which may later on form a globular
cluster. We use a simple model based on a linear perturbation theory for
transverse motions in a shell of gas to demonstrate that the pressures by which
the progenitor clouds are bound and the supernova numbers required to achieve
Galactic halo metallicities support the successful development of the shell
transverse collapse. Interestingly, the two parameters controling the
metallicity achieved through self-enrichment, namely the number of supernovae
and the external pressure, also rule the surface density of the shell and thus
its ability to undergo a transverse collapse. Such a supernova-induced origin
for the globular cluster stars opens therefore the way to the understanding of
the halo metallicity distributions. This model is also able to explain the
lower limit of the halo globular cluster metallicity.
