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In pursuing the essential elements of nuclear binding, we computeground-state properties of atomic nuclei with up to $A=20$ nucleons, using asinput a leading order pionless effective field theory Hamiltonian. Avariational Monte Carlo method based on a new, highly-expressive,neural-network quantum state ansatz is employed to solve the many-bodySchr\"odinger equation in a systematically improvable fashion. In addition tobinding energies and charge radii, we accurately evaluate the magnetic momentsof 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, weintroduce a novel computational protocol based on adding an external magneticfield to the nuclear Hamiltonian, which allows the neural network to learn thepreferred polarization of the nucleus within the given magnetic field.

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