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The constant growth of energies in particle accelerators gives grounds to raise the question of studying few-nucleon atomic nuclei within the framework of the relativistic approach. The well-studied quantum mechanical formalisms of Faddeev [1] and Yakubovsky [2] are not suitable for this due to their non-relativistic nature.
In our recent work [3], we carried out a relativistic generalization of the non-relativistic FY equation [2] to the relativistic case using the method developed in [4,5] for the three-particle case. In this work, we also solved the resulting system of integral equations by the iteration method and calculated the binding energy and the amplitudes of the states of the helium-4 nucleus. But in doing so, we made a number of assumptions, namely, we omitted the terms corresponding to the “2+2” subchannel from the equation.
In the present work, the relativistic FY equation was considered in its full form, taking into account the “2+2” subchannel. Rank-one separable potentials were used as nucleon–nucleon interaction potentials. Only states with zero orbital angular momentum were considered. The integral equation was solved by the iteration method. The binding energy and amplitudes of the helium-4 nucleus states were found. Calculations showed that taking into account the “2+2” subchannel leads to a decrease in the binding energy by 2–7 MeV depending on the potential and the considered state of the nucleus. This change shifts the calculation result closer to the experimental data. The studies conducted in this paper show that calculations using the relativistic generalization of the FY equation give realistic results. This gives reason to believe that replacing the simplest components of the formalism with more advanced ones will yield results superior in accuracy to non-relativistic calculations, as was the case in the study of the triton and helion using the BSF formalism. Namely, it is planned to use more accurate multi-rank NN-interaction potentials first.
1.Л. Д. Фаддеев, ЖЭТФ т. 39, стр. 1459 (1960)
2.O. A. Jacubovsky, Sov. J. Nucl. Phys. V. 5, P. 1312 (1967)
3.С. Г. Бондаренко, С.А. Юрьев, Ядерная Физика т. 87, № 6, стр. 822-828 (2024)
4.G. Rupp, J. A. Tjon, Phys. Rev. C V. 37, P. 1729 (1988)
5.G. Rupp, J. A. Tjon, Phys. Rev. C V. 45, P. 2133 (1992)
