RIBLL1 合作会议 , 兰州， 2013.8

1. RIBLL1合作会议, 兰州， 2013.8

2. Contents • Recent progress: weakly-bound deformed nuclei • Method progress: deformed coordinate-space HFB approach • Results: Exotic shapes and continuum effects and MADNESS • Summary HFB solvers and Continuum effects-------J.C. Pei

3. Principles of theory progress • The descriptive precision of theoretical approaches depends very much the degrees of freedom we assumed in solving nuclear many-body problems • The history we observed is that in what perspective to chose the degree of freedom in developing theoretical tools is a topic closely related to the development of computing capabilities. • For example: • abinitono-core full configuration (A~14) • For heavier nuclei, we have to freeze out more degrees of freedom: HFB • Progress: • the continuum degree of freedom; • from 2D to 3D without restriction on symmetries • from single configuration to configuration mixing HFB solvers and Continuum effects-------J.C. Pei

4. Expected exotic structures • Exotic nuclear structures appear as a threshold effect: halo and cluster • Pairing anti-halo versus continuum coupling effect • Continuum resulted in phase-space decoupling in quasiparticlespectrum • 2-n halos still have puzzles due to 3-body and continuum effects Spherical halo extensive studies pygmy dipole res. Pei, Zhang, Xu, 2013 Not likely exist Molecular-like Prof. Ye’s group Rotational band F. Nunes, NPA, 2005 Egg-like Halo recently predicted dipole, quardpole res. Misu, Nazarewicz, NPA, 1997 Zhou SG et al, PRC(R)2010 Various core-halo deformation decoupling situations HFB solvers and Continuum effects-------J.C. Pei

5. Continuum effects • Continuum coupling: pairing induced; depend on different angular-momentum • Weakly-bound states coupled with continuum: resonances • Near-threshold non-resonant continuum is important for halos • High energy continuum: Thomas-Fermi approximation (Pei et al. 2011) • Enhance stability; enhance halo HFB solvers and Continuum effects-------J.C. Pei

6. Continuum effects • 6He: momentum distribution with continuum • Breakup, elastic scattering, transfer… S.N. Ershov, et al, PRL 1998 J. Al-Khalili & F. Nunes, JPG 2003 HFB solvers and Continuum effects-------J.C. Pei

7. 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-DFT equation (or BdG) is the theoretical tool of choice for describing medium-mass and heavier nuclei and also for cold atomic gases. (abinitofor A≤14) HFB is superior to BCS for describing weakly-bound systems where continuum coupling becomes essential Pei et al. PRC, 2011 HFB solvers and Continuum effects-------J.C. Pei

8. Continuum coupling in HFB theory • Current progress: particularly difficult for deformed nuclei • Coordinate-space HFB takes an advantage 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, self-consistent calculations are still missing • Bound states, continuum and embedded resonances are treated on an equal footing; L2 discretization leads to a very large configuration space • Computing resources and capabilities are increasing exponentially HFB solvers and Continuum effects-------J.C. Pei

9. Deformed coordinate-space HFB approach • Breaking geometric symmetry is very expensive: parallel calculations • 2D axial symmetric HFB based on B-splines, finite-difference method • 3D MADNESS-HFB with Multi-wavelets techniques and sophisticated parallel techniques • J.C.Pei., 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) • J.C.Pei, G.I. Fann, R.J. Harrison, W. Nazarewicz, J. Hill, D. Galindo, J. Phys. Conf. Ser., 2012 HFB solvers and Continuum effects-------J.C. Pei

10. Hybrid parallel calculations for large boxes • MPI+OpenMP hybrid parallel calculations • Works well in Tianhe-1A; Tianhe-2 is coming next year! Large boxes calculations are crucial for describing density diffuseness, large deformation and discretized continuum From 20 fm to 30 fm, the estimated computing cost increased by 40 times. J.C. Pei et al., JPCS 402, 012035(2012) HFB solvers and Continuum effects-------J.C. Pei

11. Egg-like halo structure • 38Ne, (a) neutron density; (b) neutron pairing density • About 2 neutrons in the halo • beta2 = 0.24, beta2_pair=0.48 • Mainly contributed by near-threshold continuum Isovector deformation: pygmy quardpoleresonances New exotic “egg”-like halo structure found; accurate approach is essential J.C. Pei, Y.N. Zhang, F.R. Xu, PRC (rapid communications) 87, 051302(2013) HFB solvers and Continuum effects-------J.C. Pei

12. Near-Threshold Continuum • Different box calculations to distinguish resonances and continuum states • Near threshold non-resonant continuum is responsible for halo and surface deformations • No halo in 40Mg since no near-threshold continuum contributions (N=28) Smoothed neutron quasiparticle spectrum of Ω=1/2 HFB solvers and Continuum effects-------J.C. Pei

13. Phase-space decoupling • Non-resonant continuum states gradually grows and decouples in heavy nuclei • sparse negative-parity level density is crucial; deformed halos in medium-mass nuclei is possible, e.g. in 110Ge • Core-halo decoupling is related to the phase space decoupling in quasiptaricle spectrum HFB solvers and Continuum effects-------J.C. Pei

14. Coordinate-space vs. Basis calculations • Surface asympotics; energy spectrum Basis HFB has problem in broad resonances Y.N. Zhang, J.C. Pei, F.R. Xu, in preparation, 2013 HFB solvers and Continuum effects-------J.C. Pei

15. Density and pairing density 38Ne HFB solvers and Continuum effects-------J.C. Pei

16. Quasiparticle spectrum near thershold particle pairing HFB solvers and Continuum effects-------J.C. Pei

17. Box size dependence of energies • Total energy is not sensitive to box size, however…. Y.N. Zhang, J.C. Pei, F.R. Xu, in preparation, 2013 HFB solvers and Continuum effects-------J.C. Pei

18. Stability Peninsula (continuum and deformation) • Interesting! Y.N. Zhang, J.C. Pei, F.R. Xu, in preparation, 2013 HFB solvers and Continuum effects-------J.C. Pei

19. Main • MPI 3D MADNESS-HFB Multi-resolution ADaptive Numerical Scientific Simulation • Multi-resolution: • CS infrastructure: Task-oriented: MPI, Global arrays, multi-threaded, futures (asynchronous computation), loadbalance 1. do A 2. do B if A 3. do C 4. do D if A • ThreadPool • WorldTaskQueue • 1. • 3. • 2. • 4. • Task dependencies: managed by Futures • API HFB solvers and Continuum effects-------J.C. Pei

20. Multi-Wavelets • Decomposition Wavelet space at level n Scaling function expansion: expensive • Transformation • Truncation HFB solvers and Continuum effects-------J.C. Pei

21. MADNESS-HFB strategy Step-1: Step-2: HFB solvers and Continuum effects-------J.C. Pei

22. MADNESS-HFB performance J.C. Pei et al, JPCS, 2012 S. Bonger et al., CPC, 2013 HFB solvers and Continuum effects-------J.C. Pei

23. MADNESS-SHF+BCS solver • Benchmark for the triaxial deformed nucleus Mo110: • Next step: HFB calculations is very expensive. J.C. Pei, G. Fann, W. Nazarewicz, et al. in preparation, 2013 HFB solvers and Continuum effects-------J.C. Pei

24. Summary • Coordinate-space HFB has a very good opportunity to explore new exotic structures and continuum effects, with the development of supercomputing facilities To be done: • It will be interesting to look for continuum effects in excited states, such as Pygmy dipole and quardpole resonances based on deformed coordinate-space QRPA, and it is on track. • MADNESS-HFB for nuclear calculations HFB solvers and Continuum effects-------J.C. Pei