Mass Correction in $AAA$ Model for $nnp$ and $ppn$ Systems*

Within the framework of the isospin formalism, the neutron and proton are indistinguishable particles (I=1/2) having different masses. 3$N$ theoretical considerations often ignore the difference in masses, considering the particles to be identical within the framework of the $AAA$ model. Based on the Faddeev differential equations for the $AAA$ model, we perform AV14 calculations for $^3$H and $^3$He nuclei varying the averaged nucleon mass and scaling the pair potential depth to show the mass-energy compensation effect. Comparing the results of different authors, we conclude that the contribution of the three-body attraction potential to the Hamiltonian can be compensated by increasing the nucleon mass. Thus, the effective nucleon mass is determined (see also [1]). The theoretical explanation for this approach is based on the well-known mass correction for the $AAA$ model [2]. This correction imitates the natural $AAB$ model for the $nnp$ and $ppn$ systems by correcting the averaged nucleon masses to physical masses to achieve better agreement with the experimental data for the three-body binding energy. The discrepancy between the $AAA$ model and the mass defect formula for these nuclei is discussed.

[1] I. Filikhin, A. Karoui and B. Vlahovic, Int. J. Modern Phys. E 2250098 (2022).

[2] J. L. Friar, B. F. Gibson, and G. L. Payne, Phys. Rev. C 42, 1211 (1990).