  Bright, ultracompact X-ray binaries observed in dense star clusters, such as
Galactic globular clusters, must have formed relatively recently, since their
lifetimes as persistent bright sources are short (e.g., ~10^8 yr above 10^36
erg/s for a 1.4 Msun neutron star accreting from a degenerate helium companion
with an initial mass of ~0.2 Msun). Therefore, we can use the present
conditions in a cluster core to study possible dynamical formation processes
for these sources. Here we show that direct physical collisions between neutron
stars and red giants can provide a sufficient formation rate to explain the
observed numbers of bright sources. These collisions produce tight, eccentric
neutron star -- white dwarf binaries that decay to contact by gravitational
radiation on timescales ~10^6-10^10 yr, usually shorter and often much shorter
than the cluster age.
