  We have computed models for ultraluminous X-ray sources ("ULXs") consisting
of a black-hole accretor of intermediate mass ("IMBH"; e.g., ~1000 Msun) and a
captured donor star. For each of four different sets of initial donor masses
and orbital separations, we computed 30,000 binary evolution models using a
full Henyey stellar evolution code. To our knowledge this is the first time
that a population of X-ray binaries this large has been carried out with other
than approximation methods, and it serves to demonstrate the feasibility of
this approach to large-scale population studies of mass-transfer binaries. In
the present study, we find that in order to have a plausible efficiency for
producing active ULX systems with IMBHs having luminosities > 10^{40} ergs/sec,
there are two basic requirements for the capture of companion/donor stars.
First, the donor stars should be massive, i.e., > 8 Msun. Second, the initial
orbital separations, after circularization, should be close, i.e., < 6-30 times
the radius of the donor star when on the main sequence. Even under these
optimistic conditions, we show that the production rate of IMBH-ULX systems may
fall short of the observed values by factors of 10-100.
