Relativistic effects and three-body interactions in atomic nuclei

Based on the leading-order covariant pionless effective field theory, a relativistic nuclear Hamiltonian is derived and solved using the variational Monte Carlo approach for $A\le 4$ nuclei by representing the nuclear many-body wave functions with a symmetry-based artificial neural network. It is found that the relativistic effects rescue the renormalizability of the theory, and overcome the energy collapse problem for $^3$H and $^4$He without promoting a repulsive three-nucleon interaction to leading order as in nonrelativistic calculations. Nevertheless, to exactly reproduce the experimental ground-state energies, a three-nucleon interaction is needed and its interplay with the relativistic effects plays a crucial role. The strongly repulsive relativistic effects suppress the energy contribution given by the three-nucleon interactions, so a strong strength for the three-nucleon interaction could be required to reproduce the experimental energies. These results shed light on a consistent understanding of relativistic effects and three-body interactions in atomic nuclei.