The quadrupole deformation properties of the ground and low-lying excited states of the even-even Magnesium isotopes with N ranging from 8 to 28 have been studied in the framework of the angular momentum projected generator coordinate method with the Gogny force. It is shown that the N=8 neutron magic number is preserved (in a dynamical sense) in 20 Mg leading to a spherical ground state. For the magic numbers N=20 and N=28 this is not the case and prolate deformed ground states are obtained. The method yields values of the two neutron separation energies which are in much better agreement with experiment than those obtained at the mean field level. It is also obtained that 40 Mg is at the neutron dripline. Concerning the results for the excitation energies of the 2 + excited states and their transition probabilities to the ground state we observe a good agreement with the available experimental data. On the theoretical side, we also present a detailed justification of the prescription used for the density dependent part of the interaction in our beyond-mean-field calculations.

The particle number projection method is formulated for density dependent forces and in particular for the finite range Gogny force. Detailed formula for the projected energy and its gradient are provided. The problems arising from the neglection of any exchange term, which may lead to divergences, are thoroughly discussed and the possible inaccuracies estimated. Numerical results for the projection after variation method are shown for the nucleus 164 Er and for the projection before variation approach for the nuclei 48,50 Cr. We also confirm the Coulomb antipairing effect found in mean field theories.

We present the first implementation in the (β, γ) plane of the generator coordinate method with full triaxial angular momentum and particle number projected wave functions using the Gogny force. Technical details about the performance of the method and the convergence of the results both in the symmetry restoration and the configuration mixing parts are discussed in detail. We apply the method to the study of 24 Mg, the calculated energies of excited states as well as the transition probabilities are compared to the available experimental data showing a good overall agreement. In addition, we present the RVAMPIR approach which provides a good description of the ground and gamma bands in the absence of strong mixing.

The fission barriers of the nuclei 254 Fm, 256 Fm, 258 Fm, 258 No, and 260 Rf are investigated in a fully microscopic way up to the scission point. The analysis is based on the constrained Hartree-Fock-Bogoliubov theory and Gogny's D1S force. The quadrupole, octupole, and hexadecapole moments as well as the number of nucleons in the neck region are used as constraints. Two fission paths, corresponding to the bimodal fission, are found. The decrease with isotope mass of the half-life times of heavy Fm isotopes is also explained.

The collective yrast band of the nucleus 48 Cr is studied using the spherical shell model and the HFB method. Both approaches produce basically the same axially symmetric intrinsic state up to the -accurately reproduced -observed backbending. Agreement between both calculations extends to most observables. The only significant discrepancy comes from the static moments of inertia and can be attributed to the need of a more refined treatment of pairing correlations in the HFB calculation. 21.10.Re 21.10.KyThe study of the collective behavior of deformed nuclei is a classical problem in Nuclear Physics. Traditionally, mean field descriptions in the intrinsic frame have been favoured, as they take naturally advantage of the spontaneous breakdown of rotational symmetry. The price to pay for the gain in physical insight is the loss of angular momentum as good quantum number.In the laboratory frame description, as provided by spherical shell model calculations (SM), angular momentum is conserved but the physical insight, associated to the existence of an intrinsic state is lost, except in the very rare cases where Elliott's SU3 symmetry [1] operates. Furthermore, the approach suffers form numerical limitations. Hence, so far, it had been implemented mostly in regions such as the p and sd shells where the number of active particles is too small for collective features to become dominant. Nonetheless, there are a few nuclei -such as 20 Ne and 24 Mg -that are well reproduced by the SM calculations and do exhibit collective properties, whose origin can be traced to the approximate validity of the SU3 symmetry, for which the relationship between the intrinsic and laboratory frame descriptions is well understood.In regions where the SU3 symmetry is poorly respected, as in in the pf shell [2], the study of potentially good "rotors" was impaired by lack of experimental evidence, and by the difficulty of an exact SM treatment beyond 5 active particles. The situation has changed through recent measurements [3] demonstrating that 48 Cr is a good rotor up to spin J = 10 where the yrast band bends back. This behavior is reminiscent of the situation in much heavier deformed nuclei. Simultaneously, full pf calculations [4] have become available, that reproduce in detail the observed properties of A=48 isobars, and in particular those of 48 Cr. Therefore, this nucleus provides an unique testing ground to compare the SM (laboratory frame) description of permanent deformation with Cranked HartreeFock-Bogoliubov (CHFB) calculations [5] with the finite range density dependent Gogny force [6]; which represent the (self-consistent) state of the art formulation of the intrinsic frame approach.From the comparison it should be possible to obtain a better understanding of the intrinsic structure of the SM solutions, which in turn, may indicate in what sense the CHFB description falls short of an exact one. Computational procedures. In the Spherical Shell Model (SM)48 Cr is described in a 0hω space, i.e. eight particles are allowed to occupy al...

Nuclear matrix elements (NME) for the most promising candidates to detect neutrinoless double beta decay have been computed with energy density functional methods including deformation and pairing fluctuations explicitly on the same footing. The method preserves particle number and angular momentum symmetries and can be applied to any decay without additional fine tunings. The finite range density dependent Gogny force is used in the calculations. An increase of 10%-40% in the NME with respect to the ones found without the inclusion of pairing fluctuations is obtained, reducing the predicted half-lives of these isotopes. The possible detection of lepton number violating processes such as neutrinoless double beta decay (0νββ) is one of the current main goals for particle and nuclear physics research. In this process, an atomic nucleus decays into its neighbor with two neutron less and two proton more emitting only two electrons. Fundamental questions about the nature of the neutrino such as its Dirac or Majorana character, its absolute mass scale as well as its mass hierarchy can be determined if this process is eventually measured [1]. On the one hand, searching for 0νββ decays represents an extremely difficult experimental task because an ultra low background is required to distinguish the predicted scarce events from the noise. Recently, the controversial claim of detection in 76 Ge by the Heidelberg-Moscow (HdM) collaboration [2] has been overruled by the latest data released by . Nevertheless, these results are challenging the experiments that are already running or in an advanced stage of development to detect directly this process [3,[6][7][8][9][10][11][12][13][14]. On the other hand, in the most probable electroweak mechanism to produce 0νββ, namely, the exchange of light Majorana neutrinos [1,15], the half-life of this process is inversely proportional to the effective Majorana neutrino mass m ν , a kinematic phase space factor G 01 and the nuclear matrix elements M 0ν (NME):where m e is the electron mass and m ν = | k U 2 ek m k | is the combination of the neutrino masses m k provided by the neutrino mixing matrix U . The kinematic phase space factor can be determined precisely from the charge, mass and the energy available in the decay [16] while the nuclear matrix elements must be calculated using nuclear structure methods. The most commonly used ones are the quasiparticle random phase approximation [17][18][19][20][21] (QRPA), large scale shell model [22][23][24] (LSSM), interacting boson model [25,26] (IBM), projected HartreeFock-Bogoliubov [27] (PHFB) and energy density functional [28][29][30] (EDF). In recent years, most of the basic nuclear structure aspects of the NMEs have been understood within these different frameworks. In particular, the decay is favored when the initial and final nuclear states have similar intrinsic deformation [28,30,31]. Indications [18,21,23,28,30] about the strong sensitivity of the transition operator to pairing correlations suggest that fluctuations in this degree ...

A systematic study of 160 heavy and superheavy nuclei is performed in the Hartree-Fock-Bogoliubov (HFB) approach with the finite-range and density-dependent Gogny force with the D1S parameter set. We show calculations in several approximations: with axially symmetric and reflection-symmetric wave functions, with axially symmetric and non-reflection-symmetric wave functions, and finally with some representative triaxial wave functions. Relevant properties of the ground state and along the fission path are thoroughly analyzed. Fission barriers, Q α factors, and lifetimes with respect to fission and α decay as well as other observables are discussed. Larger configuration spaces and more general HFB wave functions as compared to previous studies provide a very good agreement with the experimental data.

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