The atomic nucleus is like a musical box: inside, nucleons (protons and neutrons) move along their orbits, like pins plucking the comb. But in some nuclei, such as magnesium-32, this box plays a tune you wouldn't expect from the usual shell-filling scheme. Physicists call such regions 'islands of inversion.' To understand how a neutron 'sounds' when it collides with such a nucleus, you need to describe their interaction, and until now, that meant relying on crude global models fitted to average data.

In the new work, an optical potential (a mathematical representation of how the nucleus scatters a neutron) has been built for magnesium isotopes 24, 26, 28, and 32 directly from nuclear structure. Instead of fitting parameters, the researchers used first-principles calculations: the symmetry-adapted no-core shell model (SA-NCSM) provides translationally invariant densities that describe both structure and reaction on equal footing. This approach requires no free parameters — everything is determined by the fundamental interactions of nucleons.

The result for stable magnesium-24 matched experimental data for total, reaction, and elastic neutron scattering at energies from 65 to 250 MeV. It's as if the melody predicted from the box's blueprint matched the actual sound. Then the same 'melody' was played for heavier isotopes: magnesium-26 and 28, as well as the unstable magnesium-32. Comparison with popular global potentials (Koning-Delaroche and Weppner-Penney) and ENDF evaluations showed where these models go wrong, especially near the island of inversion at N=20.

This first-principles approach opens the way to more accurate descriptions of nuclear reactions for exotic isotopes, which are important in astrophysics (for example, in nucleosynthesis in stars) and in nuclear technologies. Now, instead of trusting a universal 'average melody,' you can calculate an individual score for each nucleus.