S. Pittelª, G.G. Dusselb, J. Dukelskyc and P. Sarrigurenc
ª Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, DE19716 USA.
b Departamento de Fisica J.J. Giambiagi, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina.
c Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain.
Recibido el 7 de febrero de 2008
Aceptado el 15 de abril de 2008
Abstract
We describe recent efforts to study Cooper pairs in atomic nuclei. We consider a self–consistent Hartree Fock mean field for the even Sm isotopes and compare results based on three treatments of pairing correlations: a BCS treatment, a number–projected BCS treatment and an exact treatment using the Richardson ansatz. Significant differences are seen in the pairing correlation energies. Furthermore, because it does not average over the properties of the fermion pairs, the Richardson solution permits a more meaningful definition of the Cooper wave function and of the fraction of pairs that are collective. Our results confirm that only a few pairs near the Fermi surface in realistic atomic nuclei are collective.
Keywords: Nuclear structure; degenerate Fermi gases; integrable systems; BCS.
Resumen
Describimos los recientes esfuerzos en el estudio de pares de Cooper en el núcleo atómico. Consideramos un campo promedio autoconsistente Hartree Fock para los isótopos pares del Sm y comparamos los resultados de tres tratamientos de correlaciones de pairing: un tratamiento BCS, un tratamiento BCS con proyección de número, y un tratamiento exacto usando el ansatz de Richardson. Se encuentran diferencias significativas en las energías de correlación de pairing. Además, ya que la solución de Richardson no promedia sobre las propiedades de los pares de fermiones, permite una definición más significativa de la función de onda de Cooper y de la fracción de pares que son colectivos. Nuestros resultados confirman que solo unos pocos pares cerca de la superficie de Fermi en núcleos atómicos reales son colectivos.
Descriptores: Estructura nuclear; gases de Fermi degenerados; sistemas integrables; BCS.
PACS: 21.60.–n, 03.75.Ss, 02.30.Ik; 74.20.Fg
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Acknowledgements
This report was presented by one of the authors (S.P.) at the XXXIst International Symposium on Nuclear Physics in Cocoyoc, México, from 7–10 January 2008. The work was supported in part by the Spanish DGI under grants FIS2005–00640 and FIS2006–12783–C03–01, in part by the US National Science Foundation under grant #0553127, and in part by UBACYT X–053, Carrera del Investigador Científico and PIP–5287 (CONICET–Argentina).
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