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We studied the proton-rich $T_z=-1$ nucleus $^{70}$Kr through inelastic scattering at intermediate energies in order to extract the reduced transition probability, $B(E2;\;0^+ \rightarrow 2^+)$. Comparison with the other members of the $A=70$ isospin triplet, $^{70}$Br and $^{70}$Se, studied in the same experiment, shows a $3\sigma$ deviation from the expected linearity of the electromagnetic matrix elements as a function of $T_z$. At present, no established nuclear structure theory can describe this observed deviation quantitatively. This is the first violation of isospin symmetry at this level observed in the transition matrix elements. A heuristic approach may explain the anomaly by a shape change between the mirror nuclei $^{70}$Kr and $^{70}$Se contrary to the model predictions., Comment: accepted PRL

The $N=Z=36$ nucleus $^{72}$Kr has been studied by inelastic scattering at intermediate energies. Two targets, $^{9}$Be and $^{197}$Au, were used to extract the nuclear deformation length, $\delta_\text{N}$, and the reduced $E2$ transition probability, $B(E2)$. The previously unknown non-yrast $2^+$ and $4^+$ states as well as a new candidate for the octupole $3^-$ state have been observed in the scattering on the Be target and placed in the level scheme based on $\gamma-\gamma$ coincidences. The second $2^+$ state was also observed in the scattering on the Au target and the $B(E2;\;2^+_2 \rightarrow 0^+_1)$ value could be determined for the first time. Analyzing the results in terms of a two-band mixing model shows clear evidence for a oblate-prolate shape coexistence and can be explained by a shape change from an oblate ground state to prolate deformed yrast band from the first $2^+$ state. This interpretation is corroborated by beyond mean field calculations using the Gogny D1S interaction., Comment: 12 pages, 11 figures, accepted European Physical Journal A

When the density of a nuclear system is decreased, homogeneous states undergo the so-called Mott transition towards clusterised states, e.g. alpha clustering, both in nuclei and in nuclear matter. Here we investigate such a quantum phase transition (QPT) by using microscopic energy density functional (EDF) calculations both with the relativistic and the Gogny approaches on the diluted $^{16}$O nucleus. The evolution of the corresponding single-particle spectrum under dilution is studied, and a Mott-like transition is predicted at about 1/3 of the saturation density. Complementary approaches are used in order to understand this QPT. A study of spatial localisation properties as a function of the density allows to derive a value of the Mott density in agreement with the one obtained by fully microscopic calculations in $^{16}$O and in nuclear matter. Moreover a study of the spontaneous symmetry breaking of the rotational group in $^{16}$O, down to the discrete tetrahedral one, provides further insight on the features displayed by the single-particle spectrum obtained within the EDF approach.The content of the tetrahedrally deformed A-nucleon product state in terms of spherical particle-hole configurations is investigated. Finally a study of quartet condensation and the corresponding macroscopic QPT is undertaken in infinite matter., Comment: 13 pages, 13 figures

The lifetimes of first excited 2$^+$, 4$^+$ and 6$^+$ states in $^{98}$Zr were measured with the Recoil-Distance Doppler Shift method in an experiment performed at GANIL. Excited states in $^{98}$Zr were populated using the fission reaction between a 6.2 MeV/u $^{238}$U beam and a $^{9}$Be target. The $\gamma$ rays were detected with the EXOGAM array in correlation with the fission fragments identified in mass and atomic number in the VAMOS++ spectrometer. Our result shows very small B(E2;2$_1^+$ $\rightarrow$ 0$_1^+$) value in $^{98}$Zr thereby confirming the very sudden onset of collectivity at $N=60$. The experimental results are compared to large-scale Monte Carlo Shell model and beyond mean field calculations. The present results indicate coexistence of two additional deformed shapes in this nucleus along with the spherical ground state.

The electromagnetic structure of $^{140}$Sm was studied in a low-energy Coulomb excitation experiment with a radioactive ion beam from the REX-ISOLDE facility at CERN. The $2^+$ and $4^+$ states of the ground-state band and a second $2^+$ state were populated by multi-step excitation. The analysis of the differential Coulomb excitation cross sections yielded reduced transition probabilities between all observed states and the spectroscopic quadrupole moment for the $2_1^+$ state. The experimental results are compared to large-scale shell model calculations and beyond-mean-field calculations based on the Gogny D1S interaction with a five-dimensional collective Hamiltonian formalism. Simpler geometric and algebraic models are also employed to interpret the experimental data. The results indicate that $^{140}$Sm shows considerable $\gamma$ softness, but in contrast to earlier speculation no signs of shape coexistence at low excitation energy. This work sheds more light on the onset of deformation and collectivity in this mass region., Comment: 15 pages, 12 figures

$\alpha$ particle condensation is a novel state in nuclear systems. We briefly review the present status on the study of $\alpha$ particle condensation and address the open problems in this research field: $\alpha$ particle condensation in heavier systems other than the Hoyle state, linear chain and $\alpha$ particle rings, Hoyle-analogue states with extra neutrons, $\alpha$ particle condensation related to astrophysics, etc., Comment: 12 pages. To be published in J. of Phys. G special issue on Open Problems in Nuclear Structure (OPeNST)

A systematic study of low energy nuclear structure at normal deformation is carried out using the Hartree-Fock-Bogoliubov theory extended by the Generator Coordinate Method and mapped onto a 5-dimensional collective quadrupole Hamiltonian. Results obtained with the Gogny D1S interaction are presented from dripline to dripline for even-even nuclei with proton numbers Z=10 to Z=110 and neutron numbers N less than 200. The properties calculated for the ground states are their charge radii, 2-particle separation energies, correlation energies, and the intrinsic quadrupole shape parameters. For the excited spectroscopy, the observables calculated are the excitation energies and quadrupole as well as monopole transition matrix elements. We examine in this work the yrast levels up to J=6, the lowest excited 0^+ states, and the two next yrare 2^+ states. The theory is applicable to more than 90% of the nuclei which have tabulated measurements. The data set of the calculated properties of 1712 even-even nuclei, including spectroscopic properties for 1693 of them, are provided in CEA website and EPAPS repository with this article \cite{epaps}., Comment: 51 pages with 26 Figures and 4 internal tables; this version is accepted by Physical Review C

Microscopic optical model potential results for reaction cross sections of proton elastic scattering are presented. The applications cover the 10-1000 MeV energy range and consider both stable and unstable nuclei. The study is based on in-medium g-matrix full-folding optical model approach with the appropriate relativistic kinematic corrections needed for the higher energy applications. The effective interactions are based on realistic NN potentials supplemented with a separable non-Hermitian term to allow optimum agreement with current NN phase-shift analyzes, particularly the inelasticities above pion production threshold. The target ground-state densities are obtained from Hartree-Fock-Bogoliubov calculations based on the finite range, density dependent Gogny force. The evaluated reaction cross sections for proton scattering are compared with measurements and their systematics is analyzed. A simple function of the total cross sections in terms of the atomic mass number is observed at high energies. At low energies, however, discrepancies with the available data are observed, being more pronounced in the lighter systems., Comment: 11 pages, 4 figures, submitted to Phys. Rev. C

We examine the global performance of an extended self-consistent mean field theory of 2+ excitations in even-even nuclei. 518 nuclei are included in our survey, comprising all but 39 of the known nuclei tabulated by Raman et al. The theory is based on a quantal collective Hamiltonian in five dimensions in which the potential energy and the tensor of inertia are obtained from constrained triaxial Hartree-Fock-Bogoliubov calculations. The only parameters in theory are those of the finite-range, density-dependent Gogny D1S interaction. The following properties of the lowest 2+ excitations are calculated: excitation energy, reduced transition probability, and spectroscopic quadrupole moment. We find that the theory is very reliable to classify the nuclei by shape. Quantitatively the performance of the theory in deformed nuclei is excellent: average excitation energies and transition quadrupole moments are within 5% of the experimental values, and the dispersion about the averages are 20% and 10%, respectively. The performance is not as good on spherical and soft nuclei. Including all nuclei in the performance evaluation, the average transition quadrupole moment is 10% too high and the dispersion about the mean is 20%. For the energies, the average is 13% too high and the dispersion is 40%., Comment: 4 pages with 5 figures and 1 table; this version is a resubmission to Phys. Rev. Lett. including changes in response to referee comments

Structure properties of fifty five even-even actinides have been calculated using the Gogny D1S force and the Hartree-Fock-Bogoliubov approach as well as the configuration mixing method. Theoretical results are compared with experimental data., Comment: 5 pages, 5 figures, proceeding of FUSION06

Large scale Hartree-Fock-Bogoliubov (HFB) calculations with the finite-range Gogny force D1S have been performed in order to extract the corresponding theoretical average mass dependence of the nuclear gap values. Good agreement with experimental data from the three-point filter $\Delta^{(3)}$(N) with N odd has been found for both the neutron and proton gaps. The study confirms earlier findings [W. Satula, J. Dobaczewski, and W. Nazarewicz, Phys. Rev. Lett. 81 3599 (1998)] that the mass dependence of the gap is much weaker than the so far accepted 12/$\sqrtA$ MeV law.

Selfconsistent Hartree-Fock-Bogoliubov (HFB) calculations have been performed with the Gogny force for nuclei along several constant Z and constant N chains, with the purpose of extracting the macroscopic part of the binding energy using the Strutinsky prescription. The macroscopic energy obtained in this way is compared to current liquid drop formulas. The evolution of the single particle levels derived from the HFB calculations along the constant Z and constant N chains and the variations of the different kinds of nuclear radii are also analysed. Those radii are shown to follow isospin-dependent three parameter laws close to the phenomenological formulas which reproduce experimental data., Comment: 17 pages in LaTeX and 17 figures in eps. Phys. Rev. C, accepted for publication