An electron flying through a heavy nucleus behaves like a tennis ball sent through a picket fence. If the pickets are unevenly spaced (denser here, sparser there) the ball will deflect differently. In the nucleus, protons and neutrons play the role of 'pickets,' and the electron senses the difference between them thanks to the weak interaction — the very one responsible for certain types of radioactivity.

This very phenomenon, the violation of mirror symmetry (parity) in electron scattering, was measured by the CREX and PREX collaborations on calcium-48 and lead-208 nuclei. But extracting information about the neutron 'fur coat' of the nucleus from the data requires very precise calculations. The authors of the work performed them for the first time ab initio: that is, from first principles, relying on realistic nuclear forces without adjustable parameters. And they fully accounted for how the nucleus's electric field bends the path of the incoming electron.

The result surprised: the calculations gave a slightly smaller asymmetry for calcium and a slightly larger one for lead than experiments see. The discrepancy is not dramatic—1.9 sigma, but it forces a recheck of both measurements and theory. When the authors recalculated the neutron 'fur coat' of lead (the difference between the radii of the neutron and proton clouds), they got 0.187 femtometers — noticeably smaller than PREX II claimed. This is important: the thickness of the neutron fur coat is directly related to how matter compresses in neutron stars.

Such an approach—'theory first, then comparison'—resembles the work of a restorer who restores an old fresco not from photographs but by knowing the chemical composition of the paints and the artist's style. First-principles calculations are not fitted to the answer, and so their discrepancy with experiment is not an error but a signal: perhaps there are nuances in nuclear forces that we have not yet accounted for.