  Dark energy is modelled by a Bose-Einstein gas of particles with an
attractive interaction. It is coupled to cold dark matter, within a flat
universe, for the late-expansion description, producing variations in
particle-number densities. The model's parameters, and physical association,
are: $\Omega_{G0}$, $\Omega_{m0}$, the dark-energy rest-mass energy density and
the dark-matter term scaling as a mass term, respectively; $\Omega_{i0}$, the
self-interaction intensity; $x$, the energy exchange rate. Energy conservation
relates such parameters. The Hubble equation omits $\Omega_{G0}$, but also
contains $h$, the present-day expansion rate of the flat
Friedman--Lem\^aitre--Robertson--Walker metric, and $\Omega_{b0}$, the baryon
energy density, used as a prior. This results in the four effective chosen
parameters $\Omega_{b0}$, $h$, $\Omega_{m0}$, $\Omega_{i0}$, fit with the
Hubble expansion rate $H(z)$, and data from its value today, near distance, and
supernovas. We derive wide $1\sigma$ and $2\sigma$ likelihood regions
compatible with definite positive total CDM and IBEG mass terms. Additionally,
the best-fit value of parameter $x$ relieves the coincidence problem, and a
second potential coincidence problem related to the choice of $\Omega_{G0}$.
