Distilling the essential elements of nuclear binding via neural-network quantum states

TL;DR

This paper introduces a neural-network quantum state approach to compute ground-state properties of light nuclei, revealing shell structure emergence and magnetic moments using a variational Monte Carlo method with a novel protocol involving external magnetic fields.

Contribution

It presents a highly-expressive neural-network ansatz and a new computational protocol for studying nuclear properties, including magnetic moments, from pionless effective field theory.

Findings

Accurate binding energies and charge radii for nuclei up to A=20.

Emergence of shell structure without explicit encoding.

Method to evaluate magnetic moments via external magnetic fields.

Abstract

In pursuing the essential elements of nuclear binding, we compute ground-state properties of atomic nuclei with up to $A=20$ nucleons, using as input a leading order pionless effective field theory Hamiltonian. A variational Monte Carlo method based on a new, highly-expressive, neural-network quantum state ansatz is employed to solve the many-body Schr\"odinger equation in a systematically improvable fashion. In addition to binding energies and charge radii, we accurately evaluate the magnetic moments of these nuclei, as they reveal the self-emergence of the shell structure, which is not a priori encoded in the neural-network ansatz. To this aim, we introduce a novel computational protocol based on adding an external magnetic field to the nuclear Hamiltonian, which allows the neural network to learn the preferred polarization of the nucleus within the given magnetic field.