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

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

Triaxial Angular Momentum Projection and Configuration Mixing calculations with the Gogny force

We present the first implementation in the $(\beta,\gamma)$ 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.Comment: 40 pages,14 figure

On the Solution of the Number-Projected Hartree-Fock-Bogoliubov Equations

The numerical solution of the recently formulated number-projected Hartree-Fock-Bogoliubov equations is studied in an exactly soluble cranked-deformed shell model Hamiltonian. It is found that the solution of these number-projected equations involve similar numerical effort as that of bare HFB. We consider that this is a significant progress in the mean-field studies of the quantum many-body systems. The results of the projected calculations are shown to be in almost complete agreement with the exact solutions of the model Hamiltonian. The phase transition obtained in the HFB theory as a function of the rotational frequency is shown to be smeared out with the projection.Comment: RevTeX, 11 pages, 3 figures. To be published in a special edition of Physics of Atomic Nuclei (former Sov. J. Nucl. Phys.) dedicated to the 90th birthday of A.B. Migda

Intrinsic vs. laboratory frame description of the deformed nucleus 48Cr

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 uufile

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

Moments of Inertia of Nuclei in the Rare Earth Region: A Relativistic versus Non-Relativistic Investigation

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 figure

Un modelo estadístico para la estimación cuantitativa de la precipitación en la provincia de Madrid

Utilizando cuatro variables geoclimáticas, características de los veinticuatro observatorios considerados de la provincia de Madrid, y aplicando un modelo estadístico de regresión múltiple, se ha obtenido una ecuación de estimación cuantitativa de la precipitación

Estimación de la precipitación en la cuenca del Duero en función de factor geo-meteorológicos generales

[ES]Se comprueba la importancia de factores geometeorológicos como latitud y longitud en la estimación de la precipitación en la Cuenca del río Duero, y se estudia la posibilidad de reducir a cuatro el número de los factores generales determinantes de dicha precipitación.[EN]The importance of geo-meteorological factors like latitude and longitude is verified in the valuation of the precipitation in the Duero River Basin, and the posibility of reducing to four the number of general determinative factors of this precipitation is studied