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Mass–Energy Equivalence in Bound Three-Nucleon Systems

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Abstract

The mass defect formula reflects the equivalence of mass and energy for bound nuclear systems. We study three-nucleon systems \({}^{3}\)H and \({}^{3}\)He, considering the neutron and proton as indistinguishable particles (AAA model) or taking into account the real masses of neutrons and protons (AAB model). We have focused on conceptual problems of the AAA model, which is widely used for 3\(N\) calculations. In particular, the AAA model is incompatible with the mass defect formula, which naturally corresponds to the AAB model. In addition, the AAA model has a cyclic permutation symmetry, which is breaking in the natural AAB model. The latter problem cannot be eliminated within the perturbative AAA approach, in which the mass difference effect is simulated by correcting the kinetic energy operator. Earlier it was reported that the accuracy of such AAA calculations is 1 keV. An example of the AAB calculation, we numerically estimate the effect of the difference between the neutron and proton masses on the energy calculated without any approximation with the accuracy of 0.1 keV. Another manifestation of the equivalence of mass \(m\) and energy \(E\) can be expressed by the formula \(dE/dm=\textrm{Const}\). To show this dependence of the three-body energy on the nucleon mass, we performed realistic calculations within the AAA approximation, varying the averaged nucleon mass. The mass–energy compensation effect for the three-body Hamiltonian is shown. According to this, we have determined the effective nucleon mass required to compensate for the perturbative effect of a three-body potential.

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Funding

This work was supported by US National Science Foundation, HRD-1345219 award and the Department of Energy/National Nuclear Security Administration, award NA0003979.

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  1. CREST, North Carolina Central University, NC 27707, Durham, USA

    I. Filikhin, V. M. Suslov & B. Vlahovic

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Filikhin, I., Suslov, V.M. & Vlahovic, B. Mass–Energy Equivalence in Bound Three-Nucleon Systems. Phys. Atom. Nuclei 86, 931–945 (2023). https://doi.org/10.1134/S1063778824010186

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