The term ‘magic number’ refers to the number of protons or neutrons corresponding to completely filled shells. Indeed, charge radii reflect various nuclear structure phenomena such as halo structures 6, shape staggering 7 and shape coexistence 8, pairing correlations 9, 10, neutron skins 11 and the occurrence of nuclear magic numbers 5, 12, 13. Although it globally scales with the nuclear mass as A 1/3, the nuclear charge radius also exhibits appreciable isotopic variations that are the result of complex interactions between protons and neutrons. The charge radius is a fundamental property of the atomic nucleus. These findings highlight our limited understanding of the nuclear size of neutron-rich systems, and expose problems that are present in some of the best current models of nuclear theory. This rise is well captured by Fayans nuclear density functional theory, which, however, overestimates the odd–even staggering effect in charge radii.

The coupled cluster theory reproduces the odd–even variations in charge radii but not the notable increase beyond N = 28. The results are interpreted with two state-of-the-art nuclear theories. It does not show a signature of magic behaviour at N = 32 in potassium. Here we provide a charge radius measurement of 52K. By combining the collinear resonance ionization spectroscopy method with β-decay detection, we were able to extend charge radii measurements of potassium isotopes beyond N = 32. 1, 2, 3) in the calcium region, whereas the unexpectedly large increases in the charge radii 4, 5 open new questions about the evolution of nuclear size in neutron-rich systems. Experimental evidence suggested a new magic neutron number at N = 32 (refs. Nuclear charge radii are sensitive probes of different aspects of the nucleon–nucleon interaction and the bulk properties of nuclear matter, providing a stringent test and challenge for nuclear theory. Nature Physics volume 17, pages 439–443 ( 2021) Cite this article Charge radii of exotic potassium isotopes challenge nuclear theory and the magic character of N = 32

Nuclear charge of calcium