Mass-Energy Equivalence in Bound Three-Nucleon Systems

The mass defect formula reflects the equivalence of mass and energy for bound nuclear systems. We consider the three-nucleon systems 3 H and 3 He assuming the neutron and proton to be indistinguishable particles (AAA model) or taking into account realistic masses for neutrons and protons (AAB model). We discuss the disagreement between the AAA model and the mass defect formula, which is related naturally to the AAB model. Also, we demonstrate that ignoring the neutron-proton mass difference leads to the uncertainty for AAA calculations of several keV that overlap the realistic calculations accuracy estimated before in the literature. To show another manifestation of the mass-energy equivalence, we perform AAA realistic calculations varying nucleon mass and scaling the depth of pair potential to show the mass-energy compensation effect. Comparing the results of different authors, we show that the contribution of attractive three-body potential to the Hamiltonian can be compensated by increasing the nucleon mass. For the binding energy calculations, we apply the differential Faddeev equations.