  We compute the probability that intermediate mass black holes (IMBHs) capture
companions due to dynamical interactions and become accreting sources, and
explore the possibility that the accreting IMBHs would appear as ultra-luminous
X-ray sources (ULXs). We focus on IMBHs originating from low-metallicity
Population III stars. Two channels of IMBH formation are considered: from
primordial halos in the framework of hierarchical clustering, and from
non-mixed, zero-metallicity primeval gas in galactic discs. IMBHs can form
binary systems due to tidal captures of single stars and exchange interactions
with existing binary systems in galactic discs. We find that neither formation
mechanism of the accreting IMBH binary is able to provide enough sources to
explain the observed population of ULXs. Even at sub-ULX luminosity, the total
number of accreting IMBHs with $L> 10^{36}$ erg s$^{-1}$ with dynamically
captured companions is found to be $< 0.01$ per galaxy.
