Variation after Particle-Number Projection for the HFB Method with the Skyrme Energy Densit.pdf

a r X i v : n u c l - t h / 0 6 1 0 0 6 1 v 1 1 4 O c t 2 0 0 6 Variation after Particle-Number Projection for the HFB Method with the Skyrme Energy Density Functional M.V. Stoitsov,1, 2, 3, 4 J. Dobaczewski,5 R. Kirchner,6 W. Nazarewicz,1, 2, 3, 5 and J. Terasaki1, 2, 3 1Department of Physics Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA 2Physics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831, USA 3Joint Institute for Heavy-Ion Research, Oak Ridge, Tennessee 37831, USA 4Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia-1784, Bulgaria 5Institute of Theoretical Physics, Warsaw University, ul. Hoz?a 69, 00-681 Warsaw, Poland 6Technische Universita?t Wien, Karlsplatz 13, A-1040 Wien, Austria (Dated: February 9, 2008) Variation after particle-number restoration is incorporated for the first time into the Hartree-Fock- Bogoliubov framework employing the Skyrme energy density functional with zero-range pairing. The resulting projected HFB equations can be expressed in terms of the local gauge-angle-dependent densities. Results of projected calculations are compared with those obtained within the Lipkin- Nogami method in the standard version and with the Lipkin-Nogami method followed by exact particle-number projection. PACS numbers: 21.10.Dr, 21.30.Fe, 21.60.-n, 21.60.Jz I. INTRODUCTION Pairing correlations affect properties of atomic nuclei in a profound way [1, 2, 3, 4]. They impact nuclear bind- ing, properties of nuclear excitations and decays, and dramatically influence the nuclear collective motion. In particular, pairing plays a crucial role in exotic, weakly bound nuclei in which the magnitude of the chemical po- tential is close to that of the pairing gap. In such systems, a naive independent single-particle picture breaks down and the pair scattering, also involving the continuum part of the phase space, can determine the very nuclear exis- tence [5]. Many aspect