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We present an approach for the calculation of odd-nuclei with exact self-consistent blocking and particle number and angular momentum projection with the finite range density dependent Gogny force. As an application we calculate the nucleus $^{31}$Mg at the border of the $N=20$ inversion island. We evaluate the ground state properties, the excited states and the transition probabilities. In general we obtain a good description of the measured observables., Comment: 8 pages, 4 figures, accepted for publication in Eur. Phys. J. A

A systematic study of 160 heavy and super-heavy nuclei is performed in the Hartree-Fock-Bogoliubov 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 reflexion symmetric wave functions, with axially symmetric and non-reflexion symmetric wave functions and finally some representative examples with triaxial wave functions are also discussed. Relevant properties of the ground state and along the fission path are thoroughly analyzed. Fission barriers, Q$_\alpha$-factors and lifetimes with respect to fission and $\alpha$-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., Comment: 26 pages, 15 figures

We study the spherical to prolate-deformed shape transition in $^{144-158}$Sm and $^{146-160}$Gd isotopes with modern calculations beyond the mean field with the Gogny D1S force. We compare the results with the shape-phase transition predicted by the collective hamiltonian model and with the experimental data. Our calculations do not support the existence of a first order phase transition in these isotopic chains in the viewpoint of the Bohr hamiltonian neither the interpretation of the nuclei N=90 as critical points., Comment: Proceeding of the XIII Conference on Capture Gamma-ray Spectroscopy and Related Topics, Cologne, 2008

We review the properties of nuclear halos and nuclear skins in drip line nuclei in the framework of the spherical Hartree-Fock-Bogoliubov theory with continuum effects and projection on good particle number with the Gogny force. We first establish the position of the un-projected HFB drip lines for the two most employed parametrizations of the Gogny force and show that the use of finite-range interactions leads almost always to small-sized halos, even in the least bound nuclei, which is in agreement with most mean-field predictions. We also discuss the size of the neutron skin at the drip line and its relation to neutron asymmetry. The impact of particle-number projection and its conceptual consequences near the drip line are analyzed in detail. In particular, we discuss the role of the chemical potential in a projected theory and the criteria required to define the drip line. We show that including particle number projection can shift the latter, in particular near closed shells. We notice that, as a result, the size of the halo can be increased due to larger pairing correlations. However, combining the most realistic pairing interaction, a proper treatment of the continuum and particle number projection does not permit to reproduce the very large halos observed in very light nuclei., Comment: Re-submitted to Phys. Rev. C after Referee's review. Layout of figures changed to cope with editor's requirements

The 1789 keV level in 30Mg was identified as the first excited 0^+ state by measuring its E0 transition to the ground state. The measured small value of rho^2(E0,0^+_2 --> 0^+_1) = 5.7(14) x 10^-3 implies a very small mixing of competing configurations with largely different intrinsic quadrupole deformation near N=20. Axially symmetric Beyond-Mean-Field configuration mixing calculations identify the ground state of 30Mg to be based on neutron configurations below the N=20 shell closure, while the excited 0^+ state mainly consists of a two neutrons excitated into the nu1 f_{7/2} orbital. Using a two-level model, a mixing amplitude of 0.08(4) can be derived., Comment: 4 pages, 4 figures, submitted to Physical Review Letters

We report the first calculations of nuclear properties near the drip-lines using the spherical Hartree-Fock-Bogoliubov mean-field theory with a finite-range force supplemented by continuum and particle number projection effects. Calculations were carried out in a basis made of the eigenstates of a Woods-Saxon potential computed in a box, thereby garanteeing that continuum effects were properly taken into account. Projection of the self-consistent solutions on good particle number was carried out after variation, and an approximation of the variation after projection result was used. We give the position of the drip-lines and examine neutron densities in neutron-rich nuclei. We discuss the sensitivity of nuclear observables upon continuum and particle-number restoration effects., Comment: 5 pages, 3 figures, Phys. Rev. C77, 011301(R) (2008)

The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the generator coordinate is analyzed performing numerical applications for the most relevant collective coordinates. The calculations reproduce the exact solution in the weak, crossover and strong pairing regimes. The physical insight of the Ansatz and its numerical simplicity make this theory an excellent tool to study pairing correlations in complex situations and/or involved Hamiltonians., Comment: Submitted to EPJB

The shape coexistence in the nuclei $^{182-192}$Pb is analyzed within the Hartree-Fock-Bogoliubov approach with the effective Gogny force. A good agreement with the experimental energies is found for the coexisting spherical, oblate and prolate states. Contrary to the established interpretation, it is found that the low-lying prolate and oblate $0^+$ states observed in this mass region are predominantly characterized by neutron correlations whereas the protons behave as spectators rather than playing an active role., Comment: 5 pages, 6 postscript figures

The superdeformed band of $^{36}$Ar is studied with the Gogny force D1S and the angular momentum projected generator coordinate method for the quadrupole moment. The band head excitation energy, moments of inertia, $B(E2)$ transition probabilities and stability against quadrupole fluctuations at low spin are studied. The Self Consistent Cranking method is also used to describe the superdeformed rotational band. In addition, properties of some normal deformed states are discussed., Comment: 8 pages, 3 figures, Talk given at 10th Nuclear Physics Workshop Marie and Pierre Curie, September 24-28, 2003, Kazimierz Dolny, Poland. To be published in IJMPE

The degrees of freedom associated with shape fluctuations and space orientation of atomic nuclei are analyzed with effective forces and large configuration spaces. A pedagogical theoretical introduction to the topic of symmetries restoration broken in the mean field approach as well as to the concept of generator coordinate is presented. We discuss global properties, like binding energies, two neutron separation energies and quadrupole moments, as well as spectroscopic ones like excitation energies or transition probabilities. The analysis covers selected examples of light and heavy nuclei, as well as some examples from the stability line to the drip lines., Comment: 34 pages, 13 figures, invited lecture at 307. WE-Heraeus-Seminar, "Relativistic Structure Models for the Physics of Radioactive Nuclear Beams," May 12-16, 2003, Bad Honnef, Germany

The behavior of several nuclear properties with temperature is analyzed within the framework of the Finite Temperature Hartree-Fock-Bogoliubov (FTHFB) theory with the Gogny force and large configuration spaces. Thermal shape fluctuations in the quadrupole degree of freedom, around the mean field solution, are taken into account with the Landau prescription. As representative examples the nuclei $^{164}$Er, $^{152}$Dy and $^{192}$Hg are studied. Numerical results for the superfluid to normal and deformed to spherical shape transitions are presented. We found a substantial effect of the fluctuations on the average value of several observables. In particular, we get a decrease in the critical temperature ($T_c$) for the shape transition as compared with the plain FTHFB prediction as well as a washing out of the shape transition signatures. The new values of $T_c$ are closer to the ones found in Strutinsky calculations and with the Pairing Plus Quadrupole model Hamiltonian., Comment: 17 pages, 8 Figures

The angular momentum projected Generator Coordinate Method, with the quadrupole moment as collective coordinate and the Gogny force (D1S) as the effective interaction, is used to describe the properties of the ground state and low-lying excited states of the even-even Neon isotopes $^{20-34}$Ne, that is, from the stability valley up to the drip-line. It is found that the ground state of the N=20 nucleus $^{30}$Ne is deformed but to a lesser extent than the N=20 isotope of the Magnesium. In the calculations, the isotope $^{32}$Ne is at the drip-line in good agreement with other theoretical predictions. On the other hand, rather good agreement with experimental data for many observables is obtained., Comment: 11 pages, 9 figures, accepted for publication in EPJA

The evolution of the pairing correlations from closed shell to middle shell nuclei is analyzed with a Finite Range Density Dependent interaction in the Sn isotopes. As theoretical approaches we use the Hartree-Fock-Bogoliubov, the Lipkin-Nogami, their particle number projected counterparts and the full variation after particle number projection method. We find that whereas all approaches succeed rather well in the description of the total energy they differ significantly in the pairing correlation content of the wave functions. The description of the evolution from the weak to the strong pairing regime is also approach dependent, specially at shell closure., Comment: 14 pages, 5 figures

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 \nuc{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 \nuc{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., Comment: 41 pages, 13 figures

The fission barriers of the nuclei 254Fm, 256Fm, 258Fm, 258No and 260Rf 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., Comment: 29 pages in LaTeX including 14 figures

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 throughly discussed and the possible inaccuracies estimated. Numericala results for the projection after variation method are shown for the nucleus 164Er and for the projection before variation approach for the nuclei 48-50Cr. We also confirm the Coulomb antipairing effect found in mean field theories., Comment: 33 pages, 8 figures. Submit to Nuc. Phys. A

The angular momentum projected Generator Coordinate Method using the quadrupole moment as collective coordinate and the Gogny force as the effective interaction is used to describe the properties of the ground state and low-lying excited states of the neutron rich light nuclei 32,34,36Si. It is found that the ground state of the nucleus 34Si is spherical. However, this is not only due to the N=20 shell closure as the ground state of 34Si contains a significant amount of the intruder f7/2 neutron orbital. On the other hand, rather good agreement with experimental data for many observables is obtained., Comment: Invited talk at "High Spin Physics 2001", see http://www.fuw.edu.pl/~hs2001/, to be published in Acta Physica Polonica B

A parameter free investigation of the moments of inertia of ground state rotational bands in well deformed rare-earth nuclei is carried out using Cranked Relativistic Hartree-Bogoliubov (CRHB) and non-relativistic Cranked Hartree-Fock-Bogoliubov (CHFB) theories. In CRHB theory, the relativistic fields are determined by the non-linear Lagrangian with the NL1 force and the pairing interaction by the central part of finite range Gogny D1S force. In CHFB theory, the properties in particle-hole and particle-particle channels are defined solely by Gogny D1S forces. Using an approximate particle number projection before variation by means of the Lipkin Nogami method improves the agreement with the experimental data, especially in CRHB theory. The effect of the particle number projection on the moments of inertia and pairing energies is larger in relativistic than in non-relativistic theory., Comment: 18 pages + 2 PostScript figures

We present exact Hartree-Fock-Bogoliubov calculations with the finite range density dependent Gogny force using a triaxial basis. For the first time, all contributions to the Pairing and Fock Fields arising from the Gogny and Coulomb interactions as well as the two-body correction of the kinetic energy have been calculated in this basis. We analyze the relevance of these terms in different regions of the periodic table at zero and high angular momentum. The validity of commonly used approximations that neglect different terms in the variational equations is also checked. We find a decrease of the proton pairing energies mainly due to a Coulomb antipairing effect., Comment: 32 pages, 12 figures. In press in Nucl. Physics A

Properties like the excitation energy with respect to the ground state, moments of inertia, B(E2) transition probabilities and stability against quadrupole fluctuations at low spin of the predicted superdeformed band of ^{32}S are studied with the Gogny force D1S using the angular momentum projected generator coordinate method for the axially symmetric quadrupole moment. The Self Consistent Cranking method is also used to describe the superdeformed rotational band. In addition, properties of some collective normal deformed states are discussed., Comment: 7 pages, 3 figures

Properties of the ground and several collective excited states of the light nuclei ^{30,32,34}Mg are described in the framework of the angular momentum projected Generator Coordinate Method using the quadrupole moment as collective coordinate and the Gogny force as the effective interaction. The calculated excitation energies and B(E2) transition probabilities agree reasonably well with experiment. The results clearly indicate that both the restoration of the rotational symmetry and the quadrupole dynamics are key ingredients for the description of the properties of the above mentioned nuclei., Comment: 15 pages, 4 figures, extended version

A microscopic angular momentum projection after variation is used to describe quadrupole collectivity in (^{30,32,34}Mg) and (^{32,34,36,38}Si). The Hartree-Fock-Bogoliubov states obtained in the quadrupole constrained mean field approach are taken as intrinsic states for the projection. Excitation energies of the first (2^{+}) states and the (B(E2,0^{+}\to 2^{+})) transition probabilities are given. A reasonable agreement with available experimental data is obtained. It is also shown that the mean field picture of those nuclei is strongly modified by the projection., Comment: 10 pages, 2 figures, to be published in Phys. Lett. B

Kamlah's second order method for approximate particle number projection is applied for the first time to variational calculations with effective forces. High spin states of normal and superdeformed nuclei have been calculated with the finite range density dependent Gogny force for several nuclei. Advantages and drawbacks of the Kamlah second order method as compared to the Lipkin-Nogami recipe are thoroughly discussed. We find that the Lipkin-Nogami prescription occasionally may fail to find the right energy minimum in the strong pairing regime and that Kamlah's second order approach, though providing better results than the LN one, may break down in some limiting situations., Comment: 16 pages, 8 figures

We derive the equations for approximate particle number projection based on mean field wave functions with finite range density dependent forces. As an application ground bands of even-A superdeformed nuclei in the A=150 and A=190 regions are calculated with the Gogny force. We discuss nuclear properties such as quadrupole moments, moments of inertia and quasiparticle spectra, among others, as a function of the angular momentum. We obtain a good overall description., Comment: 31 pages, 10 figures, 3 appendices. In press in Nucl. Phys

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., Comment: 4 pages, RevTeX 3.0 using psfig, 6 Postscript figures included using uufiles

The Lipkin-Nogami method is generalized to deal with finite range density dependent forces. New expressions are derived and realistic calculations with the Gogny force are performed for the nuclei $^{164}$Er and $^{168}$Er. The sharp phase transition predicted by the mean field approximation is washed out by the Lipkin-Nogami approach; a much better agreement with the experimental data is reached with the new approach than with the Hartree-Fock_Bogoliubov one, specially at high spins., Comment: 5 pages, RevTeX 3.0, 3 postscript figures included using uufiles. Submitted to Phys. Rev. Lett