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1.Description of correlations in mean-field and beyond mean-field methods. Variational multiparticle-multihole configuration mixing method N.Pillet (1) , J.-F.Berger (1) , E.Caurier (2) , H.Goutte (1) , N.Vinh Mau (3) , F.Chappert (1). Spatial structure of Cooper pairs in HFB approach
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1.Description of correlations in mean-field and beyond mean-field methods Variational multiparticle-multihole configuration mixing method N.Pillet(1), J.-F.Berger(1), E.Caurier(2), H.Goutte(1), N.Vinh Mau(3), F.Chappert(1) Spatial structure of Cooper pairs in HFB approach N.Pillet(1), N.Sandulescu(4), P.Schuck(3) 2.Nuclear excitations in plasmas G.Gosselin(1), V.Méot(1), N.Pillet(1) (1) SPN,CEA-Bruyères-le-Châtel (3) IPN, Orsay (2)IPHC, Strasbourg (4) IPNE, Bucharest nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing • Motivations: • Towards a unified description of correlations in the context of beyond mean- • field method {essentially Pairing + RPA + particle-vibration coupling} • Conservation of particle numbers + enforced Pauli principle • Description on the same footing of even-even, odd and odd-odd nuclei • Description of both ground states and excited states nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
with and + + + … Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing method Formalism: • Trial wave function:Superposition of Slater determinants corresponding to mpmh excitations built upon a given state of HF type nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Functional: Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing method • Variational principle with • Mixing coefficients: • Optimized single particle states: • Simultaneous solution of both equations (iterative): • self-consistent procedure and renormalization of the HF field nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing method Current study: Pairing correlations and link with projection on particle number methods-Applications to Sn isotope ground states(*) Correlation energy (MeV) Only configurations with excited pairs Structure of correlated wave functions D1S Gogny force (*) N.Pillet, J-F.Berger and E.Caurier, under submission to PRC. N.Pillet, N.Sandulescu, Nguyen Van Giai and J-F.Berger, Phys.Rev.C71, 044306 (2005). nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing method Effect of correlations on single particle spectra Charge radii nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing method • Future studies: • Link with RPA – How to simulate RPA calculation with mp-mh method? • Which one-body density should be used? • Description of light exotic nuclei (B, Li, Be, C, N, O, F) – PhD Proposal • Application of the mp-mh method to odd and odd-odd nuclei • Effect of general correlations on single particle spectra • Applications to island of inversion • Re-fit of Gogny interaction (D2)? • Need for experimental data on masses, spins, parities… towards drip lines nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Description of correlations in mean field and beyond mean field methods Spatial structure of Cooper pairs in HFB approach • Method:HFB with D1S Gogny interaction Two-body correlated wave function(J=0): Brody-Moshinsky transformation K(R,r) (R: center of mass, r: relative coordinates) and • Spherical nuclei:O, Ca, Ni, Sn, Pb isotopic chains (*) N. Pillet, N. Sandulescu and P. Schuck, Phys. Rev. C76, 024310 (2007). nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Description of correlations in mean field and beyond mean field methods Spatial structure of Cooper pairs in HFB approach Size of Cooper pairs: Strong coupling behavior of Cooper pairs on the surface of superfluid nuclei nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Description of correlations in mean field and beyond mean field methods Spatial structure of Cooper pairs in HFB approach Probability Distribution Future study: Generalization to deformed nuclei where the parity mixing is expected to be stronger + nucleon pair transfer nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Nuclear excitations in plasmas Main excitation processes Photon absorption Inelastic electron scattering NEET (nuclear excitation by electronic transition) NEEC (nuclear excitation by electron capture) Corresponding de-excitation processes BIC (bound internal conversion) IC (internal conversion) Photon emission spontaneous+ stimulated nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Nuclear excitations in plasmas Method for transition rate calculation: • Photon absorption, NEET and NEEC mechanisms (*): • First order perturbation theory Fermi golden rule • Inelastic electron scattering: (under development) • Second order perturbation theory • PWBA, WKB, DWBA (radial transition matrix element) (*) G. Gosselin, V. Méot and P. Morel, Phys.Rev.C76, 044611 (2007). (*) G. Gosselin, V. Méot and P. Morel, Phys.Rev.C70, 064603 (2004). (*) P.Morel, V.Méot, G.Gosselin, D.Gogny and W.Younes, Phys.Rev.A69, 063414 (2004). nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
26.27 keV 5/2- 630ps 1.56 keV 1/2- 81ns(*) 3/2- g.s. 0 keV 201Hg Nuclear excitations in plasmas Two level model Photon+NEEC/IC+NEET/BIC (thermodynamical equilibrium) Lifetime of first 201Hgm 201Hgm Future: inclusion of inelastic electron scattering (*) V.Méot, J.Aupiais, P.Morel, G.Gosselin, F.Gobet, J.N.Scheurer and M.Tarisien, Phys. Rev. C75, 064306 (2007). nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Future • Variational multiparticle-multihole configuration mixing method Link with RPA Study of light nuclei- PhD proposal Test and possible re-fit of Gogny interaction (D2) • Spatial structure ofCooper pairs Generalization to deformed nuclei + pair transfer • Nuclear excitations in plasmas Inclusion of inelastic electron scattering nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Description of correlations in mean field and beyond mean field methods Spatial structure of Cooper pairs in HFB approach Κ2(R,r) in Sn isotopes and Parity mixing effect Shell effects + Parity mixing effects nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay
Description of correlations in mean field and beyond mean field methods Spatial structure of Cooper pairs in HFB approach Probability Distribution Future study: Generalization to deformed nuclei where the parity mixing is expected to be stronger + nucleon pair transfer nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay