RIBLL1 合作会议 , 兰州， 2013.8

形变弱束缚核的理论进展

Junchen Pei ( 裴俊琛 ) School of Physics, Peking University State Key Laboratory of Nuclear Physics and Technology

RIBLL1 合作会议 , 兰州， 2013.8

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 -2-

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.

HFB solvers and Continuum effects-------J.C. Pei -3-

For example: ab inito no-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

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 quasiparticle spectrum 2-n halos still have puzzles due to 3-body and continuum effects

HFB solvers and Continuum effects-------J.C. Pei -4-

Molecular-likeProf. Ye’s groupRotational band

Spherical haloextensive studiespygmy dipole res.

Egg-like Halo recently predicteddipole, quardpole res.

Not likely exist

Various core-halo deformation decoupling situations

F. Nunes, NPA, 2005

Pei, Zhang, Xu, 2013

Misu, Nazarewicz, NPA, 1997Zhou SG et al, PRC(R)2010

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 -5-

Continuum effects 6He: momentum distribution with continuum Breakup, elastic scattering, transfer…

HFB solvers and Continuum effects-------J.C. Pei -6-

S.N. Ershov, et al, PRL 1998J. Al-Khalili & F. Nunes, JPG 2003

Continuum coupling in HFB theory

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HFB is superior to BCS for describing weakly-bound systems where continuum coupling becomes essential

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. (ab inito for A≤14)

Hartree-Fock-Bogoliubov includes generalized quasi-particle correlations; while BCS is a special quasiparticle transformation only on conjugate states.

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

Pei et al. PRC, 2011

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

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

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

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

-9-

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

-10-

MPI+OpenMP hybrid parallel calculations

Works well in Tianhe-1A; Tianhe-2 is coming next year!J.C. Pei et al., JPCS 402, 012035(2012)

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.

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

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

HFB solvers and Continuum effects-------J.C. Pei -11-

0 5 10 15 20 250

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z

r

-8.0

-6.0

-5.0

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-2.0

-1.0-0.90

38Ne (a)

0 5 10 15 20 250

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25(b)

zr

New exotic “egg”-like halo structure found; accurate approach is essentialJ.C. Pei, Y.N. Zhang, F.R. Xu, PRC (rapid communications) 87, 051302(2013)

Isovector deformation: pygmy quardpole resonances

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)

HFB solvers and Continuum effects-------J.C. Pei -12-

Smoothed neutron quasiparticle spectrum of Ω=1/2

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 -13-

Coordinate-space vs. Basis calculations

Surface asympotics; energy spectrum

HFB solvers and Continuum effects-------J.C. Pei -14-

Basis HFB has problem in broad resonancesY.N. Zhang, J.C. Pei, F.R. Xu, in preparation, 2013

Density and pairing density

HFB solvers and Continuum effects-------J.C. Pei -15-

38Ne

Quasiparticle spectrum near thershold

HFB solvers and Continuum effects-------J.C. Pei -16-

pairingparticle

Box size dependence of energies

Total energy is not sensitive to box size, however….

HFB solvers and Continuum effects-------J.C. Pei -17-

Y.N. Zhang, J.C. Pei, F.R. Xu, in preparation, 2013

Stability Peninsula (continuum and deformation)

Interesting!

HFB solvers and Continuum effects-------J.C. Pei -18-

Y.N. Zhang, J.C. Pei, F.R. Xu, in preparation, 2013

3D MADNESS-HFB

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API 1. do A2. do B if A3. do C 4. do D if A

WorldTaskQueue ThreadPoolTask dependencies: m

anaged by Futures1.3.2.4.

Main MPI

Multi-resolution ADaptive Numerical Scientific Simulation

CS infrastructure:

Task-oriented: MPI, Global arrays, multi-threaded, futures (asynchronous computation), loadbalance

• Multi-resolution:

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

Multi-Wavelets

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Truncation

Decomposition

Wavelet space at level n

Scaling function expansion: expensive

Transformation

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

MADNESS-HFB strategy

HFB solvers and Continuum effects-------J.C. Pei -21-

Step-1:

Step-2:

MADNESS-HFB performance

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S. Bonger et al., CPC, 2013

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

J.C. Pei et al, JPCS, 2012

MADNESS-SHF+BCS solver Benchmark for the triaxial deformed nucleus Mo110:

Next step: HFB calculations is very expensive.

HFB solvers and Continuum effects-------J.C. Pei -23-

J.C. Pei, G. Fann, W. Nazarewicz, et al. in preparation, 2013

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

-24- HFB solvers and Continuum effects-------J.C. Pei