Coulomb exchange and pairing contributions in nuclear Hartree-Fock-Bogoliubov calculations with the Gogny force

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

Thermal shape fluctuation effects in the description of hot nuclei

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 Figure

Mean-field Based Approaches to Pairing Correlations in Atomic Nuclei

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 figure

Particle number projection with effective forces

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.

Approximate particle number projection with density dependent forces: Superdeformed bands in the A=150 and A=190 regions

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. Phy

Approximate particle number projection for finite range density dependent forces

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. Let

Anatomy of nuclear shape transition in the relativistic mean field theory

A detailed microscopic study of the temperature dependence of the shapes of some rare-earth nuclei is made in the relativistic mean field theory. Analyses of the thermal evolution of the single-particle orbitals and their occupancies leading to the collapse of the deformation are presented. The role of the non-linear $\sigma-$field on the shape transition in different nuclei is also investigated; in its absence the shape transition is found to be sharper.Comment: REVTEX file (13pages), 12 figures, Phys. Rev. C(in press), \documentstyle[aps,preprint]{revtex

Approximate Particle Number Projection for Rotating Nuclei

Pairing correlations in rotating nuclei are discussed within the Lipkin-Nogami method. The accuracy of the method is tested for the Krumlinde-Szyma\'nski R(5) model. The results of calculations are compared with those obtained from the standard mean field theory and particle-number projection method, and with exact solutions.Comment: 15 pages, 6 figures available on request, REVTEX3.

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Nuclear Octupole Correlations and the Enhancement of Atomic Time-Reversal Violation

We examine the time-reversal-violating nuclear ``Schiff moment'' that induces electric dipole moments in atoms. After presenting a self-contained derivation of the form of the Schiff operator, we show that the distribution of Schiff strength, an important ingredient in the ground-state Schiff moment, is very different from the electric-dipole-strength distribution, with the Schiff moment receiving no strength from the giant dipole resonance in the Goldhaber-Teller model. We then present shell-model calculations in light nuclei that confirm the negligible role of the dipole resonance and show the Schiff strength to be strongly correlated with low-lying octupole strength. Next, we turn to heavy nuclei, examining recent arguments for the strong enhancement of Schiff moments in octupole-deformed nuclei over that of 199Hg, for example. We concur that there is a significant enhancement while pointing to effects neglected in previous work (both in the octupole-deformed nuclides and 199Hg) that may reduce it somewhat, and emphasizing the need for microscopic calculations to resolve the issue. Finally, we show that static octupole deformation is not essential for the development of collective Schiff moments; nuclei with strong octupole vibrations have them as well, and some could be exploited by experiment.Comment: 25 pages, 4 figures embedded in tex