This paper reports a first‑principles, or ab initio, calculation that reproduces the famous two‑neutron halo of the nucleus lithium‑11 (11Li) directly from nuclear forces and the full many‑body dynamics. The authors use a neural‑network variational Monte Carlo method to build a flexible quantum wave function and show that the extended size and weak binding of 11Li come out of the calculation rather than being put in by hand.

The team represents the many‑nucleon wave function with a neural‑network ansatz called FeynmanNet, which combines known shell structure with flexible correlation pieces (a Slater‑Jastrow‑backflow form). They optimize that wave function by stochastic (Monte Carlo) methods. The nuclear Hamiltonian they use includes two‑nucleon (NN) and three‑nucleon (3N) forces that are fixed only by very light systems (A ≤ 4, meaning up to helium‑4). Because that minimal Hamiltonian underbinds some nuclei, they add a short‑range spin‑orbit interaction (a term that couples a nucleon’s motion to its spin) and fix its strength by reproducing the splitting of P‑wave phase shifts in neutron–alpha (neutron–helium‑4) scattering. The spin‑orbit parameter they find is Cso = −2.8 fm4.

With this setup the calculations reproduce the binding energies and the neutron separation energies along the lithium isotopic chain, including the small but positive two‑neutron separation energy of 11Li. The root‑mean‑square deviation for the separation energies is reported as about 0.36 MeV. The matter radii calculated for 6–9Li agree with experiment, and the radius shows a sharp increase at 11Li, signaling the halo. The computed 11Li radius is somewhat smaller than the experimental value. The authors report that numerical uncertainties from choices in the wave‑function representation are small (below ~0.1 MeV for energies and ~0.02 fm for radii) and that independent training runs give consistent results.