Investigation of three-body forces from atomic mass data

Although two-nucleon (NN) interactions successfully explain many aspects of nuclear structure, recent studies are pointing to the important role of three-body (3N) forces in the predictions of neutron-rich nuclei and in the evolution of shell structure [1], in particular from an ab-initio point of view.
The aim of this work is to investigate whether we can describe atomic masses using valence-shell corrections that include both NN and 3N forces in the mass formulae. The focus lies on pinpointing indications of NN and 3N forces in the residuals of the mass formulae fits from the standpoint of their dependence on the valence particles (or holes).
Starting from the Bethe–Weizsäcker formula, an investigation on the effects of NN and 3N forces by performing local fits to the experimental mass compilation AME2016 [2,3], was made. By introducing inert cores and a valence-configuration space, a search to identify hints of NN and 3N forces was conducted mainly around the traditional magic numbers 8, 20, 28, 50, 82 and 126 of neutrons and/(or) protons. Additionally, a modified Bethe–Weizsäcker mass formula was employed to estimate its ability to better fit the doubly magic nuclei.
The results show that the addition of the suggested terms of NN and 3N to the mass formulae are applicable to describe the trend observed around the doubly magic nuclei for some atomic mass regions. Although this is a fact, we cannot directly claim that these expressions correspond to the NN and 3N body forces.
Moreover, a shell correction [4] was employed to extend the Bethe–Weizsäcker mass formula. The results obtained from a fit using this modified formula show an agreement between the valence-shell corrections of the present investigation and the suggested ones, in the description of the parabolic-like behavior of the residuals between two doubly magic nuclei.