Multipair approach to pairing in nuclei

The ground state of a general pairing Hamiltonian for a finite nuclear system is constructed as a product of collective, real, distinct pairs. These are determined sequentially via an iterative variational procedure that resorts to diagonalizations of the Hamiltonian in restricted model spaces. Different applications of the method are provided that include comparisons with exact and projected BCS results. The quantities that are examined are correlation energies, occupation numbers and pair transfer matrix elements. In a first application within the picket-fence model, the method is seen to generate the exact ground state for pairing strengths confined in a given range. Further applications of the method concern pairing in spherically symmetric mean fields and include simple exactly solvable models as well as some realistic calculations for middle-shell Sn isotopes. In the latter applications, two different ways of defining the pairs are examined: either with J=0 or with no well-defined angular momentum. The second choice reveals to be more effective leading, under some circumstances, to solutions that are basically exact.Comment: To appear in Physical Review

A continuous rating method for preferential voting. The complete case

A method is given for quantitatively rating the social acceptance of different options which are the matter of a complete preferential vote. Completeness means that every voter expresses a comparison (a preference or a tie) about each pair of options. The proposed method is proved to have certain desirable properties, which include: the continuity of the rates with respect to the data, a decomposition property that characterizes certain situations opposite to a tie, the Condorcet-Smith principle, and a property of clone consistency. One can view this rating method as a complement for the ranking method introduced in 1997 by Markus Schulze. It is also related to certain methods of one-dimensional scaling or cluster analysis.Comment: This is part one of a revised version of arxiv:0810.2263. Version 3 is the result of certain modifications, both in the statement of the problem and in the concluding remarks, that enhance the results of the paper; the results themselves remain unchange

Projection and ground state correlations made simple

We develop and test efficient approximations to estimate ground state correlations associated with low- and zero-energy modes. The scheme is an extension of the generator-coordinate-method (GCM) within Gaussian overlap approximation (GOA). We show that GOA fails in non-Cartesian topologies and present a topologically correct generalization of GOA (topGOA). An RPA-like correction is derived as the small amplitude limit of topGOA, called topRPA. Using exactly solvable models, the topGOA and topRPA schemes are compared with conventional approaches (GCM-GOA, RPA, Lipkin-Nogami projection) for rotational-vibrational motion and for particle number projection. The results shows that the new schemes perform very well in all regimes of coupling.Comment: RevTex, 12 pages, 7 eps figure

Mean field theory for global binding systematics

We review some possible improvements of mean field theory for application to nuclear binding systematics. Up to now, microscopic theory has been less successful than models starting from the liquid drop in describing accurately the global binding systematics. We believe that there are good prospects to develop a better global theory, using modern forms of energy density functionals and treating correlation energies systematically by the RPA.Comment: RevTex, 17 pages, 5 eps figures. To be published in Yadernaya Fizika, special edition for the 90th birthday of Professor A.B. Migda

Self-Consistent Quasi-Particle RPA for the Description of Superfluid Fermi Systems

Self-Consistent Quasi-Particle RPA (SCQRPA) is for the first time applied to a more level pairing case. Various filling situations and values for the coupling constant are considered. Very encouraging results in comparison with the exact solution of the model are obtained. The nature of the low lying mode in SCQRPA is identified. The strong reduction of the number fluctuation in SCQRPA vs BCS is pointed out. The transition from superfluidity to the normal fluid case is carefully investigated.Comment: 23 pages, 18 figures and 1 table, submitted to Phys. Rev.

Nuclear pairing: new perspectives

Nuclear pairing correlations are known to play an important role in various single-particle and collective aspects of nuclear structure. After the first idea by A. Bohr, B. Mottelson and D. Pines on similarity of nuclear pairing to electron superconductivity, S.T. Belyaev gave a thorough analysis of the manifestations of pairing in complex nuclei. The current revival of interest in nuclear pairing is connected to the shift of modern nuclear physics towards nuclei far from stability; many loosely bound nuclei are particle-stable only due to the pairing. The theoretical methods borrowed from macroscopic superconductivity turn out to be insufficient for finite systems as nuclei, in particular for the cases of weak pairing and proximity of continuum states. We suggest a simple numerical procedure of exact solution of the nuclear pairing problem and discuss the physical features of this complete solution. We show also how the continuum states can be naturally included in the consideration bridging the gap between the structure and reactions. The path from coherent pairing to chaos and thermalization and perspectives of new theoretical approaches based on the full solution of pairing are discussed.Comment: 47 pages, 11 figure

Les équations de la superconductivité

The equations defining the Bogoliubov-Valatin transformation are studied. They present an interesting analogy with a problem in classical electrostatics. The existence and uniqueness of solutions are assured for the case of a separable pairing force. In the case of closed shells, and with a coupling constant whose absolute value is less than a certain critical value, the solution coïncides with the trivial solution, and therefore it is not possible to define a system of quasi-particles.On étudie les équations définissant la transformation de Bogoliubov-Valatin, qui présentent une analogie intéressante avec un problème d'électrostatique classique. L'existence et l'unicité des solutions sont assurées dans le cas d'une force d'Appariement séparable. Dans le cas des couches complètes, pour une constante de couplage inférieure, en valeur absolue, à une valeur critique, la solution se confond toutefois avec la solution triviale, et il n'est pas possible de définir un système de quasi-particules