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...

The structure of 35 P was studied with a one-proton knockout reaction at 88 MeV/u from a 36 S projectile beam at NSCL. The γ rays from the depopulation of excited states in 35 P were detected with GRETINA, while the 35 P nuclei were identified event-by-event in the focal plane of the S800 spectrograph. The level scheme of 35 P was deduced up to 7.5 MeV using γ − γ coincidences. The observed levels were attributed to proton removals from the sd-shell and also from the deeply-bound p 1/2 orbital. The orbital angular momentum of each state was derived from the comparison between experimental and calculated shapes of individual (γ-gated) parallel momentum distributions. Despite the use of different reactions and their associate models, spectroscopic factors, C 2 S, derived from the 36 S (−1p) knockout reaction agree with those obtained earlier from 36 S(d, 3 He) transfer, if a reduction factor Rs, as deduced from inclusive one-nucleon removal cross sections, is applied to the knockout transitions. In addition to the expected proton-hole configurations, other states were observed with individual cross sections of the order of 0.5 mb. Based on their shifted parallel momentum distributions, their decay modes to negative parity states, their high excitation energy (around 4.7 MeV) and the fact that they were not observed in the (d, 3 He) reaction, we propose that they may result from a two-step mechanism or a nucleon-exchange reaction with subsequent neutron evaporation. Regardless of the mechanism, that could not yet be clarified, these states likely correspond to neutron core excitations in 35 P. This newly-identified pathway, although weak, offers the possibility to selectively populate certain intruder configurations that are otherwise hard to produce and identify.

Relativistic self-consistent mean-field (SCMF) models naturally account for the coupling of the nucleon spin to its orbital motion, whereas non-relativistic SCMF methods necessitate a phenomenological ansatz for the effective spin-orbit potential. Recent experimental studies aim to explore the isospin properties of the effective spin-orbit interaction in nuclei. SCMF models are very useful in the interpretation of the corresponding data, however standard relativistic mean-field and nonrelativistic Hartree-Fock models use effective spin-orbit potentials with different isovector properties, mainly because exchange contributions are not treated explicitly in the former. The impact of exchange terms on the effective spin-orbit potential in relativistic mean-field models is analysed, and it is shown that it leads to an isovector structure similar to the one used in standard non-relativistic Hartree-Fock. Data on the isospin dependence of spin-orbit splittings in spherical nuclei could be used to constrain the isovector-scalar channel of relativistic mean-field models. The reproduction of the empirical kink in the isotope shifts of even Pb nuclei by relativistic effective interactions points to the occurrence of pseudospin symmetry in the single-neutron spectra in these nuclei.

Spin-orbit coupling characterizes quantum systems such as atoms, nuclei, hypernuclei, quarkonia, etc., and is essential for understanding their spectroscopic properties. Depending on the system, the effect of spin-orbit coupling on shell structure is large in nuclei, small in quarkonia, perturbative in atoms. In the standard non-relativistic reduction of the single-particle Dirac equation, we derive a universal rule for the relative magnitude of the spin-orbit effect that applies to very different quantum systems, regardless of whether the spin-orbit coupling originates from the strong or electromagnetic interaction. It is shown that in nuclei the near equality of the mass of the nucleon and the difference between the large repulsive and attractive potentials explains the fact that spin-orbit splittings are comparable to the energy spacing between major shells. For a specific ratio between the particle mass and the effective potential whose gradient determines the spin-orbit force, we predict the occurrence of giant spin-orbit energy splittings that dominate the single-particle excitation spectrum.

Excited states in28 Na have been studied using the β-decay of implanted 28 Ne ions at GANIL/LISE as well as the in-beam γ-ray spectroscopy at the NSCL/S800 facility. New states of positive (J π =3,4 + ) and negative (J π =1-5 − ) parity are proposed. The former arise from the coupling between 0d 5/2 protons and a 0d 3/2 neutron, while the latter are due to couplings with 1p 3/2 or 0f 7/2 neutrons. While the relative energies between the J π =1-4 + states are well reproduced with the USDA interaction in the N=17 isotones, a progressive shift in the ground state binding energy (by about 500 keV) is observed between 26 F and 30 Al. This points to a possible change in the proton-neutron 0d 5/2 -0d 3/2 effective interaction when moving from stability to the drip line. The presence of J π =1-4 − negative parity states around 1.5 MeV as well as of a candidate for a J π =5 − state around 2.5 MeV give further support to the collapse of the N=20 gap and to the inversion between the 0f 7/2 and 1p 3/2 levels below Z=12. These features are discussed in the framework of Shell Model and EDF calculations, leading to predicted negative parity states in the low energy spectra of the 26 F and 25 O nuclei.

The structure of 33 Si was studied by a one-neutron knockout reaction from a 34 Si beam at 98.5 MeV/u incident on a 9 Be target. The prompt γ-rays following the de-excitation of 33 Si were detected using the GRETINA γ-ray tracking array while the reaction residues were identified on an eventby-event basis in the focal plane of the S800 spectrometer at NSCL (National Superconducting Cyclotron Laboratory). The presently derived spectroscopic factor values, C 2 S, for the 3/2 + and 1/2 + states, corresponding to a neutron removal from the 0d 3/2 and 1s 1/2 orbitals, agree with shell model calculations and point to a strong N = 20 shell closure. Three states arising from the more bound 0d 5/2 orbital are proposed, one of which is unbound by about 930 keV. The sensitivity of this experiment has also confirmed a weak population of 9/2 − and 11/2 − 1,2 final states, which originate from a higher-order process. This mechanism may also have populated, to some fraction, the 3/2 − and 7/2 − negative-parity states, which hinders a determination of the C 2 S values for knockout from the normally unoccupied 1p 3/2 and 0f 7/2 orbits.

The nuclear structure of 69 Cu has been investigated by means of the (d, 3 He) transfer reaction at the Orsay tandem in direct kinematics using a deuteron beam at E d = 27 MeV and a target of 70 Zn isotopically enriched to 95.4%. The 3 He of interest from the transfer reaction were detected with the split-pole spectrometer at different angles in the laboratory frame in order to perform angular distributions and assign the angular momentum for each populated state in 69 Cu. In this paper, the transferred angular momenta of the populated states will be presented.

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