Nuclei with Up to $$\varvec{A=6}$$ Nucleons with Artificial Neural Network Wave Functions

Abstract

The ground-breaking works of Weinberg have opened the way to calculations of atomic nuclei that are based on systematically improvable Hamiltonians. Solving the associated many-body Schr\"odinger equation involves non-trivial difficulties, due to the non-perturbative nature and strong spin-isospin dependence of nuclear interactions. Artificial neural networks have proven to be able to compactly represent the wave functions of nuclei with up to $A=4$ nucleons. In this work, we extend this approach to $^6$Li and $^6$He nuclei, using as input a leading-order pionless effective field theory Hamiltonian. We successfully benchmark their binding energies, point-nucleon densities, and radii with the highly accurate hyperspherical harmonics method.