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RIBLL1 合作会议 , 兰州, 2013.8. Contents. Recent progress: weakly-bound deformed nuclei Method progress: deformed coordinate-space HFB approach R esults: Exotic shapes and continuum effects and MADNESS Summary. Principles of theory progress.

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contents
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

principles of theory progress
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

expected exotic structures
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

continuum effects
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

continuum effects1
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

continuum coupling in hfb t heory
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

continuum coupling in hfb theory
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

deformed coordinate space hfb approach
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

hybrid parallel calculations for large boxes
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

egg like halo structure
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

near threshold continuum
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

phase space decoupling
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

coordinate space vs basis calculations
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

density and pairing density
Density and pairing density

38Ne

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

quasiparticle spectrum near thershold
Quasiparticle spectrum near thershold

particle

pairing

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

box size dependence of energies
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

stability peninsula continuum and deformation
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

3d madness hfb

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

multi wavelets
Multi-Wavelets
  • Decomposition

Wavelet space at level n

Scaling function expansion: expensive

  • Transformation
  • Truncation

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

madness hfb strategy
MADNESS-HFB strategy

Step-1:

Step-2:

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

madness hfb performance
MADNESS-HFB performance

J.C. Pei et al, JPCS, 2012

S. Bonger et al., CPC, 2013

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

madness shf bcs solver
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

summary
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