# The Electron-Proton Bound State in the Continuum with the Positive Binding Energy of 1.531 of the Electron Mass

### Abstract

In the bound states in the continuum (BIC), the binding energy is positive, and the mass of a composite particle is greater than the total mass of its constituents. In this work, the BIC state is studied for the electron-proton system using the ladder Bethe-Salpeter equation. We demonstrate that there is a momentum space region in which the electromagnetic interaction between the particles is strongly enhanced, and the effective coupling constant is α p mp/me = 0.313, where α is the fine structure constant, and mp and me are the proton and the electron masses. This interaction resonance causes the confinement of the pair in the BIC state with the positive binding energy of 1.531me. The integral equation for the bispinor wave function is derived. This normalized wave function, which must be complex, was found numerically. It

turned out that in the BIC state, the average radius for the electron is 48 Fm, and that for the proton is 1.1 Fm. This composite boson can exist exclusively in the free state, in which its properties, such as its form factors, should only be studied. In bound states with other particles, the composite loses its individuality. In Stern-Gerlach experiments, the electron-proton composite boson will demonstrate the properties of a spin 1/2 fermion.

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