PACS numbers: to be definedMany properties of the atomic nucleus, such as vibrations, rotations and incompressibility can be interpreted as due to a two-component quantum liquid of protons and neutrons. Electron scattering measurements on stable nuclei demonstrate that their central densities are saturated, as for liquid drops. In exotic nuclei near the limits of mass and charge, with large imbalances in their proton and neutron numbers, the possibility of a depleted central density, or a "bubble" structure, was discussed in a recurrent manner since the seventies. Here we report first experimental evidence that points to a depletion of the central density of protons in the short-lived nucleus 34 Si. The proton-to-neutron density asymmetry in 34 Si offers the possibility to place constraints on the density and isospin dependence of the spin-orbit force -on which nuclear models have disagreed for decades-and on its stabilizing effect towards limits of nuclear existence.Microscopic systems composed of atoms or clusters can exhibit intrinsic structures that are bubble-like, with small or depleted central densities. For example, the fullerene molecules, composed of C atoms, are structures with extreme central depletion [1]. In nuclear physics, depletions also arise in nuclei with well-developed cluster structures when clusters are arranged in a triangle or ring-like structure -such as in the triple-α Hoyle state [2,3]. Unlike such a non-homogeneous, clustered system, central density depletions or bubble-like structures would be much more surprising in homogeneous systems, such as typical atomic nuclei with properties characteristic of a quantum liquid [4].This hindrance of bubble formation in atomic nuclei is inherent in the nature of the strong force between nucleons, which is strongly repulsive at short distances (below 0.7 fm), attractive at medium range (≈1.0 fm) and vanishes at distances beyond 2 fm. In a classical picture, the medium-ranged attraction of nuclear forces implies that nucleons interact strongly and attractively only with immediate neighbors, leading to a saturation of the nuclear central density, ρ 0 . Quantum mechanically, the delocalization of nucleons [5] leads to a further homogeneity of the density. Extensive precision electron scattering studies from stable nuclei [6] confirm that their central densities are essentially constant, with ρ 0 ≈ 0.16 fm −3 , independent of the number of nucleons A. As a consequence, like a liquid drop, the nuclear radii and volumes increase as A 1/3 and as A, respectively. Thus, a priori, bubble-like nuclei with depleted central densities are unexpected.Historically, the possibility of forming bubble nuclei was investigated theoretically in intermediate-mass [7][8][9][10], superheavy [11] and hyperheavy systems [12]. In general, central depletions will arise from a reduced occupation of single particle orbits with low angular momentum . These wave functions extend throughout the nuclear interior whereas those with high-are more excluded by centrifugal forces. For...

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