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The mesoscopic nature of the atomic nucleus gives rise to a wide array ofmacroscopic and microscopic phenomena. The size of the nucleus is a window intothis duality: while the charge radii globally scale as $A^{1/3}$, theirevolution across isotopic chains reveals unanticipated structural phenomena[1-3]. The most ubiquitous of these is perhaps the Odd-Even Staggering (OES)[4]: isotopes with an odd number of neutrons are usually smaller in size thanthe trend of their even-neutron neighbours suggests. This OES effect varieswith the number of protons and neutrons and poses a significant challenge fornuclear theory [5-7]. Here, we examine this problem with new measurements ofthe charge radii of short-lived copper isotopes up to the very exotic $^{78}$Cu$(Z=29, N=49)$, produced at only 20 ions/s, using the highly-sensitiveCollinear Resonance Ionisation Spectroscopy (CRIS) method at ISOLDE-CERN. Dueto the presence of a single proton outside of the closed Z=28 shell, thesemeasurements provide crucial insights into the single-particle proton structureand how this affects the charge radii. We observe an unexpected reduction inthe OES for isotopes approaching the $N=50$ shell gap. To describe the data, weapplied models based on nuclear Density Functional Theory [2,8] (DFT) andab-initio Valence-Space In-Medium Similarity Renormalization Group (VS-IMSRG)theory [9,10]. Through these comparisons, we demonstrate a relation between theglobal behavior of charge radii and the saturation density of nuclear matter,and show that the local charge radii variations, which reflect the many-bodypolarization effects due to the odd neutron, naturally emerge from the VS-IMSRGcalculations.

Measurement and microscopic description of odd-even staggering of charge radii of exotic copper isotopes