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

TL;DR

This paper investigates how electromagnetic interactions are significantly enhanced in bound states in the continuum (BIC) of two charged particles, revealing resonance effects that lead to confinement and an effective coupling constant dependent on mass ratio.

Contribution

It demonstrates the resonance enhancement of electromagnetic interaction in BIC states using the Bethe-Salpeter equation, introducing a new effective coupling constant related to particle masses.

Findings

Electromagnetic interaction is strongly enhanced in two momentum regions.

The effective coupling constant is proportional to lpha \, fsqrt{m_b/m_a}.

Resonance leads to confinement of constituents with positive binding energy.

Abstract

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.