  The mesoscopic nature of the atomic nucleus gives rise to a wide array of
macroscopic and microscopic phenomena. The size of the nucleus is a window into
this duality: while the charge radii globally scale as $A^{1/3}$, their
evolution 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 than
the trend of their even-neutron neighbours suggests. This OES effect varies
with the number of protons and neutrons and poses a significant challenge for
nuclear theory [5-7]. Here, we examine this problem with new measurements of
the 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-sensitive
Collinear Resonance Ionisation Spectroscopy (CRIS) method at ISOLDE-CERN. Due
to the presence of a single proton outside of the closed Z=28 shell, these
measurements provide crucial insights into the single-particle proton structure
and how this affects the charge radii. We observe an unexpected reduction in
the OES for isotopes approaching the $N=50$ shell gap. To describe the data, we
applied models based on nuclear Density Functional Theory [2,8] (DFT) and
ab-initio Valence-Space In-Medium Similarity Renormalization Group (VS-IMSRG)
theory [9,10]. Through these comparisons, we demonstrate a relation between the
global behavior of charge radii and the saturation density of nuclear matter,
and show that the local charge radii variations, which reflect the many-body
polarization effects due to the odd neutron, naturally emerge from the VS-IMSRG
calculations.
