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

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 Li and 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. A. Gnech Theory Center, Jefferson Lab, Newport News, VA 23606, USA E-mail: agnech@jlab.org C. Adams Physics Division and Leadership Computing Facility, Argonne National Laboratory, Argonne, Illinois 60439, USA E-mail: corey.adams@anl.gov N. Brawand Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA E-mail: nbrawand@anl.gov G. Carleo Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland E-mail: giuseppe.carleo@epfl.ch A. Lovato Physics Division and Computational Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA E-mail: lovato@anl.gov N. Rocco Theoretical Physics Department, Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510, USA E-mail: nrocco@fnal.gov ar X iv :2 10 8. 06 83 6v 1 [ nu cl -t h] 1 5 A ug 2 02 1