  In bound states in the continuum (BIC) the mass of a composite particle is
greater than the total mass of its constituents. Using the ladder
Bethe-Salpeter equation, the BIC state in a system of two charged particles $a$
and $b$ with different masses ($m_{b}>>m_{a}$) is investigated. We demonstrate
that for the positive binding energy, there are two momentum space regions in
which the electromagnetic interaction between the particles is strongly
enhanced, and the effective coupling constant turns out to be equal to $\alpha
\sqrt{m_{b}/m_{a}}$, where $\alpha$ is the fine structure constant. The
interaction resonance leads to confinement of the constituents in the BIC state
with the positive binding energy which is of the order of the mass of the
lighter particle from the pair.
