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Relativistic wave equation for the bound states of a system of interacting particles

  • Atoms, Spectra, Radiation
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Abstract

A method for obtaining the relativistic wave equation for the bound states of a system of interacting charged particles without consideration of spin is proposed. An expansion of the wave function of the system in a complete basis of orthonormal wave functions of vacuum states for each type of particle is used in this equation. It is shown that this equation contains two types of solutions for a proton + electron system. The first type corresponds to Bohr bound states. Exact expressions are obtained for the energy and Bohr radius of the ground state with consideration of the finite mass of the particles. An influence of the energy of translational motion of the system as a whole on the structure of the atomic levels in the laboratory frame is predicted. This effect is due to the finite value of m/M, and leads to removal of the degeneracy of the levels with respect to orbital angular momentum l, and partial removal of the degeneracy with respect to its projection. The second type of solution represents states of the system with binding energy \(E_b = M + m - \sqrt {|M^2 - m^2 |} \) and an exponential wave function damping radius equal to the Compton wavelength of the electron. A complete description of this state requires consideration of the electronic vacuum polarization.

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Authors and Affiliations

  1. Kurchatov Institute, 123182, Moscow, Russia

    A. I. Agafonov & É. A. Manykin

Authors
  1. A. I. Agafonov
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  2. É. A. Manykin
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Zh. Éksp. Teor. Fiz. 112, 50–62 (July 1997)

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Agafonov, A.I., Manykin, É.A. Relativistic wave equation for the bound states of a system of interacting particles. J. Exp. Theor. Phys. 85, 27–33 (1997). https://doi.org/10.1134/1.558311

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  • DOI: https://doi.org/10.1134/1.558311

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