  Close encounters between two initially unbound objects can result in a binary
system if enough energy is released as gravitational waves (GWs). We address
the scenario in which such encounters occur in merging elliptical galaxies.
There is evidence that elliptical galaxies can harbor intermediate-mass black
holes. Therefore, these systems are potentially the breeding grounds of sources
of gravitational waves corresponding to inspiraling compact objects onto a
massive black hole due to the dynamics, the large densities, and the number of
compact remnants they contain. We show that this process is efficient for
intermediate-mass black holes (IMBHs) with masses ranging from M $\in
(10^3,10^5)$ M$_{\odot}$ and results in the formation of intermediate
mass-ratio inspirals (IMRIs). We consider a set of IMBHs and smaller black
holes with masses $m_2 \in (10,10^3)$ M$_{\odot}$ to estimate the IMRI
formation rate. We find rates ranging between 10$^{-8}$ yr$^{-1}$, and
10$^{-5}$ yr$^{-1}$, and the IMRI formation rate per comoving volume in merging
galaxies as a function of the redshift. The peak frequencies of the
gravitational radiation emitted when these IMRIs are formed are within the
detection band of space-borne detectors such as LISA and TianQin; taking into
account the observable volume of these detectors, the total amount of IMRI
detections per year is significant.
