Nuclear structure far from stability Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February 4 – 6, 2008 Nuclear structure far from stability Marcella Grasso

General interest: Correlations in finite fermion many-body systems Adopted approaches: Microscopic mean field approaches and extensions

Extensions of RPA (avoiding the quasi-boson approximation) DIFFERENT TOPICS: Nuclear structure. Exotic nuclei (properties of exotic nuclei, pairing, continuum coupling, shell structure evolution along isotopic chains,…) Mean field, HF, HFB + QRPA Collaborations: Elias Khan, Jerome Margueron, Nguyen Van Giai, IPN-Orsay Nicu Sandulescu, Bucarest Nuclear astrophysics. Neutron star crusts (pairing, excitation modes, specific heat,…) Mean field, HFB + QRPA Collaborations: Elias Khan, Jerome Margueron, Nguyen Van Giai, IPN-Orsay Extensions of RPA (avoiding the quasi-boson approximation) Collaborations: Francesco Catara, Danilo Gambacurta, Michelangelo Sambataro, Catania Interdisciplinary activity: ultra-cold trapped Fermi gases Mean field, finite temperature HFB and QRPA Collaborations: Elias Khan, Michael Urban, IPN-Orsay

Second meeting: May 21 2007 Next meeting: to be fixed (2008)

Neutron drip line position? Two-neutron separation energy S2n(N,Z)=E(N,Z)-E(N-2,Z) Exp. values Isotopes of Ni S2n (MeV) Last observed isotope Drip line A Noyaux riches en neutrons – Approche self-consistante champ moyen + appariement Hartree – Fock – Bogoliubov (HFB) Etats du continuum: comportement asymptotique (états de diffusion) et largeur des résonances Microscopic mean field approach. Pairing is included in a self-consistent way (Bogoliubov quasiparticles): Hartree-Fock-Bogoliubov (HFB) Boundary conditions of scattering states for the wave functions of continuum states Grasso et al, PRC 64, 064321 (2001)

Pairing and continuum coupling in neutron-rich nuclei. What to look at? Direct reaction studies: pair transfer? (LoI GASPARD for Spiral2)

Reduction of spin-orbit splitting for neutron p states in 47Ar Transfer reaction 46Ar(d,p)47Ar: energies and spectroscopic factors of neutron states p3/2, p1/2 and f5/2 in 47Ar. Comparison with 49Ca: reduction the spin – orbit splitting for the f and p neutron states Gaudefroy, et al. PRL 97, 092501 (2006)

Energy difference between the states 2s1/2 and 1d3/2 Grasso, Ma, Khan, Margueron, Van Giai, PRC 76, 044319 (2007)

Effect due to the tensor contribution with SLy5 Grasso, Ma, Khan, Margueron, Van Giai, PRC 76, 044319 (2007)

HF proton density in 46Ar with SkI5 INVERSION Khan, Grasso, Margueron, Van Giai, NPA 800, 37 (2008)

Perspectives Particle-phonon coupling Extensions of RPA (to include correlations that are not present in a standard mean field approach). Applications to nuclei

B(E2;0+ g.s. -> 21+) (e2fm4) Inv. No inv. B (E2) (e2 fm4) 256 24 SkI5 SLy4 Inv. No inv. B (E2) (e2 fm4) 256 24 218  31 e2 fm4 Khan, Grasso, Margueron, Van Giai, NPA 800, 37 (2008) Riley, et al. PRC 72, 024311 (2005) Raman, et al., At. Data Nucl. Data Tables 36, 1 (2001)

Inversion of s and d proton states Theoretical analysis. Relativistic mean field (RMF). 48Ca et 46Ar Inversion of s and d proton states 48Ca Z=20 1d3/2 2s1/2 2s1/2 1d3/2 1d5/2 1d5/2 46Ar Z=18 1d3/2 2s1/2 2s1/2 1d3/2 1d5/2 1d5/2 Todd-Rutel, et al., PRC 69, 021301 (R) (2004)

Kinetic, central and spin – orbit contributions to the energy difference between the states 2s1/2 and 1d3/2 Grasso, Ma, Khan, Margueron, Van Giai, PRC 76, 044319 (2007)

Extension of RPA: starting from the Hamiltonian a boson image is introduced via a mapping procedure (Marumori type) Approximation: Degree of expansion of the boson Hamiltonian (quadratic -> standard RPA) If higher-order terms are introduced the RPA equations are non linear (the matrices A and B depend on the amplitudes X and Y) Grasso catara sambataro

Test on a 3-level Lipkin model Grasso et al. Diag. of HB in B RPA Extension

Spin – orbit potential Non relativistic case and standard Skyrme forces q, q’ -> proton or neutron Relativistic case The potential is proportional to

Hartree-Fock equations with the equivalent potential. Central term

Veqcentr

Kinetic contribution Central contribution Spin-orbit contribution

Important contributions of the HF potential Central term It favors the inversion Density-dependent term Against the inversion

…and the tensor contribution? Shell model : T. Otsuka, et al., PRL 95, 232502 (2005) Relativistic mean field: RHFB : W. Long, et al., PLB 640, 150 (2006) Non relativistic mean field: Skyrme : G. Colò, et al., PLB 646, 227 (2007) Gogny : T. Otsuka, et al., PRL 97, 162501 (2006)

Variation of the energy density (dependence on J) J -> spin density The spin – orbit potential is modified: