Star formation within globular clusters:discrete multiple bursts and
  top-light mass functions
  The observed discrete multiple stellar populations and internal abundance
spreads in r- and s-process elements within globular clusters (GCs) have been
suggested to be explained self-consistently by discrete star formation events
over a longer timescale (10^8 yr). We here investigate whether such star
formation is really possible within GCs using numerical simulations that
include effects of dynamical interaction between individual stars and the
accumulated gas ("star-gas interaction") on star formation. The principal
results are as follows. Small gas clouds with densities larger than $10^{10}$
atoms cm^{-3} corresponding to first stellar cores can be developed from gas
without turbulence. Consequently, new stars can be formed from the gas with
high star formation efficiencies (>0.5) in a bursty manner. However, star
formation can be suppressed when the gas mass fractions within GCs (f_g) are
less than a threshold value (f_g, th). This f_g, th is larger for GCs with
lower masses and larger gas disks. Star-gas interaction and gravitational
potentials of GCs can combine to suppress the formation of massive stars (i.e.,
"top-light" stellar initial mass function). Formation of He-rich stars directly
from gas of massive AGB stars is possible in massive GCs due to low f_g, th
(<0.01). Short bursty star formation only for f_g>f_g, th can be partly
responsible for discrete multiple star formation events within GCs.
