Abstract
A two-particle system is described by integral equations whose kernels are dependent on the total energy of the system. Such equations can be reduced to an eigenvalue problem featuring an eigenvalue-dependent operator. This nonlinear eigenvalue problem is solved by means of an iterative procedure developed by the present authors. The energy spectra of a two-fermion system formed by particles of identical masses are obtained for two cases, that where the total spin of the system is equal to zero and that where the total spin of the system is equal to unity. The splitting of the ground-state levels of positronium and dimuonium, the frequency of the transition from the ground state of orthopositronium to its first excited state, and the probabilities of parapositronium and paradimuonium decays are computed. The results obtained in this way are found to be in good agreement with experimental data.
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Translated from Yadernaya Fizika, Vol. 66, No. 1, 2003, pp. 100–106.
Original Russian Text Copyright © by Skachkov, Solov'eva.
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Skachkov, N.B., Solov'eva, T.M. Results of numerically solving an integral equation for a two-fermion system. Phys. Atom. Nuclei 66, 99–104 (2003). https://doi.org/10.1134/1.1540662
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DOI: https://doi.org/10.1134/1.1540662