Pairing gaps in Hartree-Fock Bogoliubov theory with the Gogny D1S interaction

As part of a program to study odd-A nuclei in the Hartree-Fock-Bogoliubov (HFB) theory, we have developed a new calculational tool to find the HFB minima of odd-A nuclei based on the gradient method and using interactions of Gogny's form. The HFB minimization includes both time-even and time-odd fields in the energy functional, avoiding the commonly used "filling approximation". Here we apply the method to calculate neutron pairing gaps in some representative isotope chains of spherical and deformed nuclei, namely the Z=8,50 and 82 spherical chains and the Z=62 and 92 deformed chains. We find that the gradient method is quite robust, permitting us to carry out systematic surveys involving many nuclei. We find that the time-odd field does not have large effect on the pairing gaps calculated with the Gogny D1S interaction. Typically, adding the T-odd field as a perturbation increases the pairing gap by ~100 keV, but the re-minimization brings the gap back down. This outcome is very similar to results reported for the Skyrme family of nuclear energy density functionals. Comparing the calculated gaps with the experimental ones, we find that the theoretical errors have both signs implying that the D1S interaction has a reasonable overall strength. However, we find some systematic deficiencies comparing spherical and deformed chains and comparing the lighter chains with the heavier ones. The gaps for heavy spherical nuclei are too high, while those for deformed nuclei tend to be too low. The calculated gaps of spherical nuclei show hardly any A-dependence, contrary to the data. Inclusion of the T-odd component of the interaction does not change these qualitative findings

Shape coexistence in Lead isotopes in the interacting boson model with Gogny energy density functional

We investigate the emergence and evolution of shape coexistence in the neutron-deficient Lead isotopes within the interacting boson model (IBM) plus configuration mixing with microscopic input based on the Gogny energy density functional (EDF). The microscopic potential energy surface obtained from the constrained self-consistent Hartree-Fock-Bogoliubov method employing the Gogny-D1M EDF is mapped onto the coherent-state expectation value of the configuration-mixing IBM Hamiltonian. In this way, the parameters of the IBM Hamiltonian are fixed for each of the three relevant configurations (spherical, prolate and oblate) associated to the mean field minima. Subsequent diagonalization of the Hamiltonian provides the excitation energy of the low-lying states and transition strengths among them. The model predictions for the $0^{+}$ level energies and evolving shape coexistence in the considered Lead chain are consistent both with experiment and with the indications of the Gogny-EDF energy surfaces.Comment: 12 pages, 6 figures, 1 tabl

Role of triaxiality in the ground state shape of neutron rich Yb, Hf, W, Os, and Pt isotopes

The evolution of the ground-state shape along the triaxial landscape of several isotopes of Yb, Hf, W, Os, and Pt is analyzed using the self-consistent Hartree-Fock-Bogoliubov approximation. Two well reputed interactions (Gogny D1S and Skyrme SLy4) have been used in the study in order to asses to which extent the results are independent of the details of the effective interaction. A large number of even-even nuclei, with neutron numbers from N=110 up to N=122 has been considered, covering in this way a vast extension of the nuclear landscape where signatures of oblate-prolate shape transitions have already manifested both theoretically and experimentally.Comment: 21 pages, 8 figure

Collective structural evolution in neutron-rich Yb, Hf, W, Os and Pt isotopes

An interacting boson model Hamiltonian determined from Hartree-Fock-Bogoliubov calculations with the new microscopic Gogny energy density functional D1M, is applied to the spectroscopic analysis of neutron-rich Yb, Hf, W, Os and Pt isotopes with mass $A\sim 180-200$. Excitation energies and transition rates for the relevant low-lying quadrupole collective states are calculated by this method. Transitions from prolate to oblate ground-state shapes are analyzed as a function of neutron number $N$ in a given isotopic chain by calculating excitation energies, $B$(E2) ratios, and correlation energies in the ground state. It is shown that such transitions tend to occur more rapidly for the isotopes with lower proton number $Z$, when departing from the proton shell closure Z=82. The triaxial degrees of freedom turn out to play an important role in describing the considered mass region. Predicted low-lying spectra for the neutron-rich exotic Hf and Yb isotopes are presented. The approximations used in the model and the possibilities to refine its predictive power are addressed.Comment: 12 pages, 7 figures, 1 table, accepted for publication in Phys. Rev.

Symmetry restoration in Hartree-Fock-Bogoliubov based theories

We present a pfaffian formula for projection and symmetry restoration for wave functions of the general Bogoliubov form, including quasiparticle excited states and linear combinations of them. This solves a long-standing problem in calculating states of good symmetry, arising from the sign ambiguity of the commonly used determinant formula. A simple example is given of projecting good particle number and angular momentum from a Bogoliubov wave function in the Fock space of a single j-shell.Comment: 5 pages and 1 table, revised version include more general result

Bismuth incorporation and the role of ordering in GaAsBi/GaAs structures

The structure and composition of single GaAsBi/GaAs epilayers grown by molecular beam epitaxy were investigated by optical and transmission electron microscopy techniques. Firstly, the GaAsBi layers exhibit two distinct regions and a varying Bi composition profile in the growth direction. In the lower (25 nm) region, the Bi content decays exponentially from an initial maximum value, while the upper region comprises an almost constant Bi content until the end of the layer. Secondly, despite the relatively low Bi content, CuPtB-type ordering was observed both in electron diffraction patterns and in fast Fourier transform reconstructions from high-resolution transmission electron microscopy images. The estimation of the long-range ordering parameter and the development of ordering maps by using geometrical phase algorithms indicate a direct connection between the solubility of Bi and the amount of ordering. The occurrence of both phase separation and atomic ordering has a significant effect on the optical properties of these layers

The parasitic turbellarian Urastoma cyprinae (Platyhelminthes: Urastomidae) from blue mussel Mytilus galloprovincialis in Spain: occurrence and pathology

8 pages, 8 figures, 2 tables.The turbellarian Urastoma cyprinae (Graff, 1882) Graff, 1903 was found inhabiting the mantle cavity between the lamellae of the demibranchs of mussels Mytilus galloprovincialis Lamarck cultured in Galicia (NW Spain). Heavily infested mussels were recognized by the presence of white spots in the gills. The affected area exhibited disarrangement of the gill filaments. The space between 2 lameliae was considerably reduced and the blood sinuses were wider in the unhealthy area than in the healthy area. The turbellarian also induced a heavy infiltration by blood cells and subsequent necrosis of the gill tissues. Routine parasitological studies showed that this parasite was first detected in the Galician region in early 1989. In 1993, U. cyprinae appeared to be present in the 3 main production rias in the Galician region, affecting both natural beds and rafted mussels. U. cyprinae could be considered a potential threat to mussel culture.J.A.F.R. acknowledges the Diputación de Pontevedra, Spain, and Xunta de Galicia, for his research fellowship in the IIM-CSIC. J.C.M. was supported by a grant of the CONACyT frorn Mexico.Peer reviewe

Nonadditive entropy and nonextensive statistical mechanics - Some central concepts and recent applications

We briefly review central concepts concerning nonextensive statistical mechanics, based on the nonadditive entropy $S_q=k\frac{1-\sum_{i}p_i^q}{q-1} (q \in {\cal R}; S_1=-k\sum_{i}p_i \ln p_i)$. Among others, we focus on possible realizations of the $q$-generalized Central Limit Theorem, including at the edge of chaos of the logistic map, and for quasi-stationary states of many-body long-range-interacting Hamiltonian systems.Comment: 15 pages, 9 figs., to appear in Journal of Physics: Conf.Series (IOP, 2010

Observational Constraints to the Evolution of Massive Stars

We consider some aspects of the evolution of massive stars which can only be elucidated by means of "indirect" observations, i.e. measurements of the effects of massive stars on their environments. We discuss in detail the early evolution of massive stars formed in high metallicity regions as inferred from studies of HII regions in external galaxies.Comment: 6 pages, 1 figure; Invited Paper presented at the Roma-Trieste Workshop 1999 "The Chemical Evolution of the Milky Way: Stars versus Clusters", Vulcano Island (ME, Italy), 20-24 September, 1999, eds. F. Giovannelli & F. Matteucci, Kluwer-Holland (in press

Structural evolution in Pt isotopes with the Interacting Boson Model Hamiltonian derived from the Gogny Energy Density Functional

Spectroscopic calculations are carried out, for the description of the shape/phase transition in Pt nuclei in terms of the Interacting Boson Model (IBM) Hamiltonian derived from (constrained) Hartree-Fock-Bogoliubov (HFB) calculations with the finite range and density dependent Gogny-D1S Energy Density Functional. Assuming that the many-nucleon driven dynamics of nuclear surface deformation can be simulated by effective bosonic degrees of freedom, the Gogny-D1S potential energy surface (PES) with quadrupole degrees of freedom is mapped onto the corresponding PES of the IBM. Using this mapping procedure, the parameters of the IBM Hamiltonian, relevant to the low-lying quadrupole collective states, are derived as functions of the number of valence nucleons. Merits of both Gogny-HFB and IBM approaches are utilized so that the spectra and the wave functions in the laboratory system are calculated precisely. The experimental low-lying spectra of both ground-state and side-band levels are well reproduced. From the systematics of the calculated spectra and the reduced E2 transition probabilities $B$(E2), the prolate-to-oblate shape/phase transition is shown to take place quite smoothly as a function of neutron number $N$ in the considered Pt isotopic chain, for which the $\gamma$-softness plays an essential role. All these spectroscopic observables behave consistently with the relevant PESs and the derived parameters of the IBM Hamiltonian as functions of $N$. Spectroscopic predictions are also made for those nuclei which do not have enough experimental E2 data.Comment: 11 pages, 5 figure