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Variational Multiparticle-Multihole Configuration Mixing Method with the D1S Gogny force

Variational Multiparticle-Multihole Configuration Mixing Method with the D1S Gogny force. Nathalie Pillet (CEA Bruyères-le-Châtel, France). Collaborators: J.-F. Berger, E. Caurier and H. Goutte. nathalie.pillet@cea.fr. INPC2007, Tokyo, 06/06/2007. Independent particles. Shell model

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Variational Multiparticle-Multihole Configuration Mixing Method with the D1S Gogny force

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  1. Variational Multiparticle-Multihole Configuration Mixing Methodwith the D1S Gogny force Nathalie Pillet (CEA Bruyères-le-Châtel, France) Collaborators: J.-F. Berger, E. Caurier and H. Goutte nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  2. Independent particles Shell model Mean field and beyond Nucleus = A interacting nucleons Many-body problem N-N interaction (QCD not yet usable) Numerical solution of exact equations A ≤ 12-14 Approximations Bare forces In medium forces (Phenomenology) nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  3. Variational mpmh configuration mixing Beyond mean field approach to the many-body problem Theoretical motivations • Unified description of correlations beyond the HF approximation • {mainly Pairing + RPA + particle vibration} • Conservation of particle numbers and respect of the Pauli principle • Treatement on the same footing of even-even, odd and odd-odd • nuclei • Description of both ground and excited states nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  4. Formalism Trial wave function: Superposition of Slater Determinants Variational parameters • Mixing coefficients • Single particle orbitals nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  5. One-body density matrix of the correlated state + Optimized single particle states Mixing coefficients Generalized HF equations Secular equation Variational principle • Functional • Determination of variational parameters => Simultaneous solution of both sets of equations (full self-consistency) => renormalization of HF field nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  6. Phenomenological effective D1S* Gogny force *J.-F. Berger, M. Girod and D. Gogny, Comput. Phys. Commun. 63 (1991) 365. Central Density-dependent Spin-orbit Coulomb • The two ranges simulate a “molecular potential” • Density dependence necessary for saturation in nuclear matter • Spin-orbit necessary for magic numbers • 14 parameters adjusted on nuclear matter properties and some stable nuclei nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  7. Residual interaction Study of “usual” Pairing correlations • No proton-neutron residual interaction A pair : two nucleons in time-reversed states • Correlated wave function • Spin-Isospin components of the D1S Gogny force “Usual” pairing S=0 T=1 nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  8. Example: 116Sn (non-selfconsistent mpmh calculations) Proton valence space: 286 levels -Ecorr (MeV) 1 pair 2 pairs BCS Number of neutron individual levels Usual Pairing in 116Sn, 106Sn and 100Sn ground states • 116Sn, 106Sn and 100Sn: spherical nuclei • Correlated wave function: up to 2 pair excitations (3 pair excitation negligibles) • Correlation energy: => Majority of correlations comes from single particle levels closest to the Fermi level => Majority of correlations comes from configurations associated to 1 pair excitations => Convergence of correlation energy (finite ranges of the central term) => More correlations than in the BCS approach nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  9. Usual Pairing in 116Sn, 106Sn and 100Sn ground states Without residual Coulomb interaction • Residual Coulomb: non-negligible effect • mpmh induced correlations: S=0 => dominant pairing correlations • S=1 => negligible contribution • BCS method is a better approximation in strong pairing regime (116Sn) • Conservation of particle numbers: very important in weak and medium pairing • regimes (100Sn and 106Sn) nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  10. 2pairs BCS Neutron occupation probabilities Neutron single particle states 2pairs Proton occupation probabilities BCS Proton single particle states 116Sn occupation probabilities Correlated wave function components (%) nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  11. Energy gain Self-consistency effect - 116SnPreliminar results ([h[ρ],ρ]=0) • Correlation energy • Correlated wave function components nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  12. Summary and Perpectives • Self-consistent mpmh approach (new in nuclear physics) • -unifies the description of important correlations beyond mean field in nuclei (Pairing, RPA, Particle vibration) • -now tractable for medium-heavy nuclei with present computers (pairing hamiltonian) • -still have to solve exactly the generalized HF equations • First applications to nuclear superfluidity quite encouraging • Future applications: collective vibrations, exotic light nuclei • Re-definition of effective N-N interaction needed in T=0 channel • (based on the PhD thesis work of F.Chappert -> Gogny force with a finite range density-dependent term) nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

  13. Single particle level spectrum nathalie.pillet@cea.fr INPC2007, Tokyo, 06/06/2007

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