Resonance enhancement of the electromagnetic interaction between two charged particles in the bound state in the continuum

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 $\alpha \sqrt{m_b\mathrm{/}{m}_a}$, 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.