Pairing Correlations in Finite Systems: From the weak to the strong fluctuations regime

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 EPJ

Collective and Single-particle Motion in Beyond Mean Field Approaches

We present a novel nuclear energy density functional method to calculate spectroscopic properties of atomic nuclei. Intrinsic nuclear quadrupole deformations and rotational frequencies are considered simultaneously as the degrees of freedom within a symmetry conserving configuration mixing framework. The present method allows the study of nuclear states with collective and single-particle character. We calculate the fascinating structure of the semi-magic 44S nucleus as a first application of the method, obtaining an excellent quantitative agreement both with the available experimental data and with state-of-the-art shell model calculations.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Let

On the origin of the anomalous behaviour of 2+ excitation energies in the neutron-rich Cd isotopes

Recent experimental results obtained using $\beta$ decay and isomer spectroscopy indicate an unusual behaviour of the energies of the first excited 2$^{+}$ states in neutron-rich Cd isotopes approaching the N=82 shell closure. To explain the unexpected trend, changes of the nuclear structure far-off stability have been suggested, namely a quenching of the N=82 shell gap already in $^{130}$Cd, only two proton holes away from doubly magic $^{132}$Sn. We study the behaviour of the 2$^+$ energies in the Cd isotopes from N=50 to N=82, i.e. across the entire span of a major neutron shell using modern beyond mean field techniques and the Gogny force. We demonstrate that the observed low 2$^+$ excitation energy in $^{128}$Cd close to the N=82 shell closure is a consequence of the doubly magic character of this nucleus for oblate deformation favoring thereby prolate configurations rather than spherical ones.Comment: 10 pages, 4 figures, to be publised in Phys. Lett.

A variational approach to approximate particle number projection with effective forces

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 figure

Do Endowments Matter for Vertical Intra-Industry Trade with Emergent Countries? Empirical Evidence for Spain

In this paper, we study the nature of Spanish intra-industry trade and find that intra-industry trade with CEEC, Asian and Mediterranean countries has increased considerably since the middle of the Nineties. The second aim of the paper is to study if the comparative advantage argument also explains the vertical intra-industry trade between countries with different income levels. To this end we build physical, technological and human capital stocks for a large sample of countries. Results obtained with the panel techniques support the idea of a neo Ricardian explanation of vertical intra-industry trade rather than the neo-Hecksher-Ohlin explanation for intra-industry trade with emergent countries. Furthermore, our results suggest that the variables considered, mostly country-specific better explain vertical intra-industry trade than horizontal intra-industry trade. Results obtained with the Heckman method support the idea that intra-industry trade is more likely to occur with emergent countries with higher income per capita and with OECD countries that have a more similar level of income to that of Spain. Differences in endowments play an important role to determine the volume of intra-industry trade rather than the probability of intra-industry trade to occur. An additional contribution of this paper is to demonstrate that panel approach allows for more robust conclusions than OLS estimations when explaining intra-industry trade. The Heckman procedure to account for the zero flows also represents a major improvement respect to the standard approachIntra-industry trade; Comparative Advantage, Spain, Vertical Differentiation, Panel data, Truncated models.

Large amplitude pairing fluctuations in atomic nuclei

Pairing fluctuations are self-consistently incorporated on the same footing as the quadrupole deformations in present state of the art calculations including particle number and angular momentum conservation as well as configuration mixing. The approach is complemented by the use of the finite range density dependent Gogny force which, with a unique source for the particle-hole and particle-particle interactions, guarantees a self-consistent interplay in both channels. We have applied our formalism to study the role of the pairing degree of freedom in the description of the most relevant observables like spectra, transition probabilities, separation energies, etc. We find that the inclusion of pairing fluctuations mostly affects the description of excited states, depending on the excitation energy and the angular momentum. $E0$ transition probabilities experiment rather big changes while $E2$'s are less affected. Genuine pairing vibrations are thoroughly studied with the conclusion that deformations strongly inhibits their existence. These studies have been performed for a selection of nuclei: spherical, deformed and with different degree of collectivity.Comment: 23 pages, 23 Figures, To be published in Phys. Rev.

Breve reflexión ante una eventual constitución de la UE : de las soberanías nacionales al derecho comunitario

A finales del siglo XV, principio del XVI, se llevó a cabo en Europa la formación de los estados nacionales y apareció el Derecho internacional moderno. Dos fenómenos coexistentes, inseparables el uno del otro. Esta dualidad explica la doble legitimidad en la que se inserta el poder político estatal de los Estados nacionales. Cada uno establece el suyo propio aunque reconoce un orden superior que enlaza a todos los elementos nacionales. Pero en el caso de la UE, hay otra línea de legitimidad más clara y eficaz. Ha sido el genio creador de una generación de hombres clarividentes el que puso en marcha en Europa occidental hace medio siglo, un fenómeno de integración política que puede culminar en una Unión Política desde la diversidad de soberanías estatales insolidarias. Esta singularidad se manifiesta de modo multiforme: en los propios tratados comunitarios, en la naturaleza y características del Derecho comunitario y de modo muy especial en la relación entre el Derecho de la Unión y el particular de sus Estados miembros en la que prevalece el primero de ellos. Es así como la dinámica de integración y el correspondiente Derecho que las conduce han entrado en un proceso de aceleración que puede llevar lejos. ________________________________________At the end of the Fifteen century and beginning of the Sixteenth, national estates were created in Europe and modern International Law appeared. These are two coexisting and inseparable phenomena. This duality explains why the political power of national Estates is based on a double legitimacy: each Estate sets its own political power, but a the same time it recognises a higher system that binds all the national elements. Regarding the European Union, however, there is a clearer and more efficient legitimacy. Half a century ago, the creative talent of a generation of clear-sighted men was the driving force of the start in Western Europe of a political integration phenomenon that can culminate in a Political Union in spite of the differences between the several national estates. The singularity of this process becomes evident in different ways: in the community treaties, in the nature and features of Community Law and especially in the relationship between Community Law and the law of the different Member Estates. In this relationship is Community Law the one that prevails. Integration dynamics and its corresponding law have entered an acceleration process that may go far

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