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.
References
[2] F.H. Stillinger, D.R. Herrick, Bound states in the continuum, Phys. Rev. A 1975, 11, 446.
[3] C.W. Hsu, B. Zhen, A.D. Stone, J.D. Joannopoulos, M. Soljačić, Bound states in the continuum, Nat. Rev. Mater. 2016, 1, 16048.
[4]A.F. Sadreev. Interference traps waves in open system: Bound states in the continuum, Reports on Progress in Physics 2021, 84, 055901.
[5] M. Robnik, A simple separable Hamiltonian having bound states in the continuum. J. Phys. A: Math. Gen. 1986, 19, 3845.
[6] F. Capasso, C. Sirtori, J. Faist, D.L. Sivco, S.-N. G. Chu, A.Y. Cho, Observation of an electronic bound state above a potential well. Nature 1992, 358, 565.
[7] S.I. Azzam, A.V. Kildishev, Photonic bound states in the continuum: from basics to applications, Adv. Opt. Mater. 2021, 9, 2001469.
[8] F. Odeh, Note on differential operators with purely continuous spectrum, Proc. Amer. Math. Soc. 1965, 16, 363.
[9] T. Kato, Some Mathematical Problems in Quantum Mechanics, Prog. Theor. Phys. Suppl. 1967, 40, 3.
[10] B. Simon, On positive eigenvalues of one-body Schrödinger operators, Commun. Pure Appl. Math. 1969, 22, 531–538.
[11] N. Nakanishi, A General survey of the theory of the Bethe-Salpeter equation, Prog. Theor. Phys. Suppl. 1969, 43, 1.
[12] H.A. Bethe and E.E. Salpeter, A Relativistic Equation for Bound-State Problems, Phys. Rev. A 1951, 84, 1232.
[13] R.P. Feynman, The Theory of Positrons, Phys. Rev. 1949, 76, 749.
[14] A.I. Agafonov, Massless Composite Bosons Formed by the Coupled Electron-Positron Pairs and Two-Photon Angular Correlations in the Colliding
Beam Reaction $e^{-}e^{+}\to B\gamma\gamma$ with Emission of the Massless Boson, Volume 2018, Article ID 6137380.
[15] Ya.B. Zel'dovich, V. S.Popov, Electronic structure of superheavy atoms, Sov. Phys. Usp. 1972, 14, 673.
[16] V.B. Berestesky, E.M. Lifshits, L.P. Pitaevsky, Quantum electrodynamics, Fizmatlit, Moscow, 2002.
[17] A.I. Agafonov, Resonance enhancement of the electromagnetic interaction between two charged particles in the bound state in the continuum,
Mod. Phys. Lett. A, https://doi.org/10.1142/S0217732323500700.
[18] J.E. Sherwood, T.E. Stephensen, S. Bernstein, Stern-Gerlach Experiment on Polarized Neutrons, Phys. Rev. 1954, 96, 1546.
[19] D.J. Hughes, M.T. Burgy, Reflection of Neutrons from Magnetized Mirrors, Phys. Rev. 1951, 81, 498.
[20] T.E. Phipps, The Magnetic Moment of the Hydrogen Atom, Phys. Rev. 1927, 29, 309.
[21] C.G. Shull, U. Billman, F.A. Wedgwood, Experimental Limit for the Neutron Charge, Phys. Rev. 1967, 153, 1415.
[22] H. Rauch, A. Zeilinger, G. Badurek, A. Wilfing, W. Bauspiess, U. BonseH, Verification of coherent spinor rotation of fermions, Phys. Lett. A 1975, 54, 425.
[23] S.A. Werner, R. Collela, A.W. Overhauser, C.F. Eagen, Observation of the Phase Shift of a Neutron Due to Precession in a Magnetic Field, Phys Rev Lett, 1975, 35, 1053.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Letters in High Energy Physics (LHEP) is an open access journal published by Andromeda Publishing and Education Services. The articles in LHEP are distributed according to the terms of the creative commons license CC-BY 4.0. Under the terms of this license, copyright is retained by the author while use, distribution and reproduction in any medium are permitted provided proper credit is given to original authors and sources.
Terms of Submission
By submitting an article for publication in LHEP, the submitting author asserts that:
1. The article presents original contributions by the author(s) which have not been published previously in a peer-reviewed medium and are not subject to copyright protection.
2. The co-authors of the article, if any, as well as any institution whose approval is required, agree to the publication of the article in LHEP.
