HIRFL -RIBLL 合作会议，上海， 2013.1

1. HIRFL -RIBLL 合作会议，上海， 2013.1

2. Contents • Motivation: physics of weakly bound deformed nuclei • Method: deformed coordinate-space HFB approach • Results: surface deformations and continuum effects • Summary HFB solvers and Continuum effects-------J.C. Pei

3. Motivation: Physics of drip-line nuclei RNB facilities offer unprecedented opportunities to access unstable nuclei Challenging theoretical approaches From B. Sherrill’s talk at NS2012 From J. Erler et al., Nature, 486, 509(2012) HFB solvers and Continuum effects-------J.C. Pei

4. Motivation: Physics of drip-line nuclei • Weakly-bound quantum systems: density diffuse, halo structures • Pairing induced continuum couplings become important; BEC and BCS pairing coexisted • Novel collective excitation modes: pygmy modes andetc. • Nuclear astrophysics: e.g., neutron stars, symmetry energy • Testing ground for new effective interactions: UNEDF, 3-body forces HFB solvers and Continuum effects-------J.C. Pei

5. Motivation: Physics of deformed halos • New insights from spherical halo core-halo decoupling I. Tanihata, J. Phys. G 22, 157(1996) pairing anti-halo K. Bennaceur et al., PLB 2000 continuum coupling M. Yamagami, PRC 72, 064308 (2005). shell quenching J. Dobaczewskiet al., PRL, 1994 BEC-BCS pairing K. Hagino et al., PRL 99, 022506 (2007). • Expected new insights from deformed halo/skin core-halo deformation decoupling: exotic structures neutron-proton isovector deformation: isovectorquadrupole modes deformation of pairing densities: ?by pair transfer experiments Mechanism of deformed halos: low Ω states with negative parity T. Misu, W. Nazarewicz, S. Aberg, NPA (1997) S.G. Zhou, PRC 82, 011301(R)(2010). HFB solvers and Continuum effects-------J.C. Pei

6. HFBG.S.: BCS G.S.: Continuum coupling in HFB theory Hartree-Fock-Bogoliubovincludes generalized quasi-particle correlations; while BCS is a specialquasiparticle transformation only on conjugate states. • The general HFB equation(or BdG) HFB is superior to BCS for describing weakly-bound systems where continuum coupling becomes essential One visible difference: deep bound single-particle states become HFB resonances JP et al. PRC, 2011 HFB solvers and Continuum effects-------J.C. Pei

7. HFB solving approaches • The difficulty: HFB resonances are embedded in the continuum • Coordinate-space HFB takes an unique opportunity for describing weakly-bound systems and large deformations • Diagonalization on single-particle basis • Direct diagonalization on coordinate-space lattice • Outgoing boundary condition: difficult for deformed cases • ※H. Oba, M. Matsuo, PRC, 2009, made progress in deformed Green function HFB approach, but self-consistent calculations are still missing • The HO basis has a Gaussian form exp(-ar2) that decays too fast, while the density distribution decays exponentially exp(-kr). • Bound states, continuum and embedded resonances are treated on an equal footing; L2 discretization leads to a very large configuration space • Providing better inputs for QRPA, for describing excited states • Computing resources and capabilities are increasing exponentially HFB solvers and Continuum effects-------J.C. Pei

8. Deformed coordinate-space HFB • Development issues: very expensive, therefore parallel is essential • 2D HFB based on B-splines, finite-difference method • 3D MADNESS-HFB with Multi-wavelets techniques and sophisticated parallel techniques • V. E. Oberacker, A. S. Umar, E. Terán, and A. Blazkiewicz, PRC, 2003 • J. P., M. V. Stoitsov, G. I. Fann, W. Nazarewicz, N. Schunck, and F. R. Xu, PRC, 2008 • (HFB-AX: Much faster and be able to calculate heavy nuclei and cold atoms) • H. Oba, M. Masto, Prog.Theor.Phys., 2008 • J.P., G.I. Fann, R.J. Harrison, W. Nazarewicz, J. Hill, D. Galindo, J. Jia, JPCS, 2012 HFB solvers and Continuum effects-------J.C. Pei

9. Hybrid parallel calculations for large boxes • MPI+OpenMP (400 cores for one nucleus takes 1 hour) Computing different blocks on different nodes (MPI) Multi-thread computing within a node(OpenMP) • Works well in Tianhe-1A and Cray systems Large boxes calculations are crucial for describing density diffuseness and discretized continuum J.P. et al., JPCS 402, 012035(2012) From 20 fm to 30 fm, the estimated computing cost increased by 40 times. HFB solvers and Continuum effects-------J.C. Pei

10. Deformations of drip-line nuclei Extensive studies on light drip-line nuclei Controversial about spherical halos in heavy nuclei, giant or collective halo? N/Z=2.3 J. Erleret al., Nature, 486, 509(2012) HFB solvers and Continuum effects-------J.C. Pei

11. Systematics of deformed neutron halo/skin • New exotic “egg”-like halo structure • Halo hindered by deformed cores? F.M. Nunes, NPA, 2005 J.C. Pei, Y.N. Zhang, F.R. Xu, arXiv:1301.1461, 2013 HFB solvers and Continuum effects-------J.C. Pei

12. Development of resonances in light nuclei • Levels near Fermi surface are sparse in light nuclei • Near threshold quasiparticleresonances (especially negative parity states) below 2 MeV are mainly responsible for the halo structures and surface deformations • No halo is obtained since pairing is missed in Mg40 Smoothed neutron quasiparticle spectrum Ω=1/2 HFB solvers and Continuum effects-------J.C. Pei

13. Development of resonances in heavy nuclei • Low- halo resonances gradually grows and decouples in heavy nuclei • Bound states move away from the Fermi surface collectively; larger level density • Density distribution decoupling is related to the phase space decoupling HFB solvers and Continuum effects-------J.C. Pei

14. Isovector deformations • Neutron skin/halo: pygmy dipole resonances (two humps) • Isovector deformations: pygmy quardpole resonances From J. Erler et al., Nature, 486, 509(2012) HFB solvers and Continuum effects-------J.C. Pei

15. Development of surface deformations • Slightly largerisovector deformations obtained, except for the egg-like structure • Deformation of pairing density are very sensitive to pairing Hamiltonian; non-resonant continuum plays an important role Abnormal isovector deformation of 0.24 in the egg-like structure! HFB solvers and Continuum effects-------J.C. Pei

16. Continuum effects in excited states • It will be more interesting, however, it is not easy for deformed nuclei. • Finite-amplitude-method QRPA is a promising solution to avoid computing tremendously large QRPA matrix In progress: monopole strength calculated by FAM-QRPA with SLy4 and mixed pairing HFB solvers and Continuum effects-------J.C. Pei

17. Summary • Coordinate-space HFB takes an unique opportunity for describing weakly bound nuclei in large boxes by using hybrid parallel computing. • Deformed coordinate-space HFB is accurate not only for density diffuse structures but also for continuum effects • Newexotic deformed halo structure of spherical core plus deformed halo is found • Surface deformations of pairing densities also shows decoupling effects To be done: • It will be interesting to looking for continuum effects in excited states, such as Pygmy dipole and quardpole resonances based on deformed coordinate-space QRPA, and its in progress Collaborators: F.R. Xu, Y.N. Zhang, W. Nazarewicz HFB solvers and Continuum effects-------J.C. Pei

18. Thanks for your attention! HFB solvers and Continuum effects-------J.C. Pei