Nuclei with up to $\boldsymbol{A=6}$ nucleons with artificial neural network wave functions

TL;DR

This paper extends neural network wave function methods to calculate properties of nuclei with up to six nucleons, demonstrating successful benchmarking against established methods using pionless effective field theory.

Contribution

It introduces neural network wave functions for $A=6$ nuclei, expanding prior work limited to smaller nuclei, and benchmarks results with hyperspherical harmonics.

Findings

Neural network wave functions accurately reproduce binding energies.

Point-nucleon densities and radii match hyperspherical harmonics results.

Extension to $A=6$ nuclei demonstrates scalability of the approach.

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.