Nuclei with up to $\mathbf{A}=6$ 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 Schrödinger 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.

15 pages, 3 figures, invited contribution to the special issue in Few-Body Systems "Celebrating 30 years of Steven Weinberg's papers on Nuclear Forces from Chiral Lagrangians"