Charge radii of exotic potassium isotopes challenge nuclear theory and the magic character of $N = 32$

TL;DR

This study extends charge radii measurements of potassium isotopes up to $^{52}$K, challenging the presumed magic nature of $N=32$ and revealing discrepancies between experimental data and current nuclear theories.

Contribution

It provides the first charge radii data beyond $N=32$ in potassium isotopes and compares these results with advanced nuclear models, highlighting their limitations.

Findings

No signature of magic character at $N=32$

Strong increase in charge radii beyond $N=28$ not captured by coupled-cluster calculations

Fayans functional reproduces radius increase but overestimates odd-even staggering

Abstract

Nuclear charge radii are sensitive probes of different aspects of the nucleon-nucleon interaction and the bulk properties of nuclear matter; thus, they provide a stringent test and challenge for nuclear theory. The calcium region has been of particular interest, as experimental evidence has suggested a new magic number at $N = 32$ [1-3], while the unexpectedly large increases in the charge radii [4,5] open new questions about the evolution of nuclear size in neutron-rich systems. By combining the collinear resonance ionization spectroscopy method with $\beta$-decay detection, we were able to extend the charge radii measurement of potassium ($Z =19$) isotopes up to the exotic $^{52}$K ($t_{1/2}$ = 110 ms), produced in minute quantities. Our work provides the first charge radii measurement beyond $N = 32$ in the region, revealing no signature of the magic character at this neutron number. The results are interpreted with two state-of-the-art nuclear theories. For the first time, a long sequence of isotopes could be calculated with coupled-cluster calculations based on newly developed nuclear interactions. The strong increase in the charge radii beyond $N = 28$ is not well captured by these calculations, but is well reproduced by Fayans nuclear density functional theory, which, however, overestimates the odd-even staggering effect. These findings highlight our limited understanding on the nuclear size of neutron-rich systems, and expose pressing problems that are present in some of the best current models of nuclear theory.