1. Insights into continuum effects in deformed drip-line nuclei Junchen Pei ( 裴俊琛 ) School of Physics, Peking University 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 -2-

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

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 and etc. 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-4--4-

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. Dobaczewski et 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: isovector quadrupole 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 -5-

6. Continuum coupling in HFB theory HFB solvers and Continuum effects-------J.C. Pei-6--6- 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 HFB G.S.:BCS G.S.:  The general HFB equation(or BdG) Hartree-Fock-Bogoliubov includes generalized quasi-particle correlations; while BCS is a special quasiparticle transformation only on conjugate states. JP et al. PRC, 2011

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 HFB solvers and Continuum effects-------J.C. Pei-7--7-  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(-ar 2 ) that decays too fast, while the density distribution decays exponentially exp(-kr).  Bound states, continuum and embedded resonances are treated on an equal footing; L 2 discretization leads to a very large configuration space  Providing better inputs for QRPA, for describing excited states  Computing resources and capabilities are increasing exponentially

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 HFB solvers and Continuum effects-------J.C. Pei-8--8-  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

9. Hybrid parallel calculations for large boxes HFB solvers and Continuum effects-------J.C. Pei -9- -9- 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 J.P. et al., JPCS 402, 012035(2012) Large boxes calculations are crucial for describing density diffuseness and discretized continuum From 20 fm to 30 fm, the estimated computing cost increased by 40 times.

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

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

12. Development of resonances in light nuclei Levels near Fermi surface are sparse in light nuclei Near threshold quasiparticle resonances (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 HFB solvers and Continuum effects-------J.C. Pei -12- Smoothed neutron quasiparticle spectrum Ω=1/2

13. Development of resonances in heavy nuclei HFB solvers and Continuum effects-------J.C. Pei -13-

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

15. Development of surface deformations Slightly larger isovector 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 HFB solvers and Continuum effects-------J.C. Pei -15- Abnormal isovector deformation of 0.24 in the egg-like structure!

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 HFB solvers and Continuum effects-------J.C. Pei -16- In progress: monopole strength calculated by FAM-QRPA with SLy4 and mixed pairing

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 New exotic 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 HFB solvers and Continuum effects-------J.C. Pei-17- Collaborators: F.R. Xu, Y.N. Zhang, W. Nazarewicz

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