Numerical solutions of the equations of quantum field theory describing bound s-states of systems of two scalar particles have been found for the following three cases: a one-boson exchange potential, a superposition of such potentials, and also the Coulomb potential in the relativistic configuration representation. On the basis of these solutions, the elastic scattering form factors and decay constants for decay of a two-particle system into two photons have been obtained. It is shown that the number of zeros of the elastic form factors coincides with the number of zeros of the wave functions and is equal to the quantum number of the state of the system minus one. The obtained energy spectra and decay constants are compared with the experimentally measured values for positronium.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 71–8, April, 2013.
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Grishechkin, Y.A., Kapshai, V.N. Numerical solution of relativistic problems on bound states of systems of two spinless particles. Russ Phys J 56, 435–443 (2013). https://doi.org/10.1007/s11182-013-0053-1
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DOI: https://doi.org/10.1007/s11182-013-0053-1