Exotic nuclear structures and dynamics in HFB theory The 9 th Japan-China Joint Nuclear Physics...

Exotic nuclear structures and dynamics in HFB theory

The 9th Japan-China Joint Nuclear Physics Symposium, Osaka University, 2015

Junchen Pei (School of Physics, Peking University)Collaborators: F.R. Xu, W. Nazarewicz, G. Fann,

Y.N. Zhang, Y. Zhu, X.Y. Xiong, N. Fei, Y. Shi, M. Kortelainen, P. Schuck

superheavies

Contents

Stable nuclei

Weakly bound nuclei

Nuclear Landscape

Developments of coordinate-space HFB approach

Studies of weakly bound nuclear structures and collective excitations

2nd-order superfluid Thomas-Fermi method

Developments of new Skyrme forces

Weakly bound nuclei

Weakly bound effects ： halo/deformed halo, soft modes, Borromean, BEC-BCS pairing ， shell evolution ， clustering, continuum coupling,

Thomas-Ehrman shift, other threshold effects…

Deformed coordinate-space Hartree-Fock-BogoliubovTo solve the self-consistency problem, simultaneously describe the deformations, pairing, halo, continuum together

Problems ： HO basis has been widely used in nuclear physics, it is efficient and has excellent mathematical properties, but insufficient for weakly bound systems

2D-Coordinate-space HFB

2D coordinate-space HFB with axial-symmetry: HFB-AX

Continuum discretization—Dense quasiparticle spectrum(high resolution)

Lattice space flexible—not limited by deformation Hybrid parallel(Tianhe)—Large space

Pei et al. PRC 78, 064306 (2008)Pei et al. PRL 102, 192501(2009)Pei et al. PRA 82, 021603(R)2010Pei et al. PRC 84, 024311(2011)Pei et al. PRC 87, 051302(R)2013

Methods ：2D B-spline Galerkin

operators;

Lattice direct

diagonalization;

Broyden optimized

iteration;

MPI+OpenMP Hybrid

parallel

Quasiparticle continuum and resonances

Dense quasiparticle spectrum∝ L3

Based on stabilization method ， we obtain the widths of quasiparticle resonances

Stabilization has been widely applied in atomic physics and chemistry; has been used for nuclear single-particle resonances. S.G. Zhou, J. Meng, and E.G Zhao , JPB 2009

Change the box size resonance widths

Pei et al., PRC 84, 024311(2011)


Toward the 3D coordinate-space HFB ： a big challenge

Conventional methods such as finite-difference, B-splines, are too expensive

Collaborate with applied math, comput. chemists to apply the multi-wavelets techniques, with multi-resolutions, and it is very efficient 2 1 1

0 0

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Scaling wavelets at Vn

Multi-wavelets

https://github.com/m-a-d-n-e-s-s

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quality=1027KB

quality=2041KB

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Multi-wavelets

Wavelets

𝑊𝑛−1=𝑉 𝑛−𝑉 𝑛− 1

Representation of wavefunctions


3D coordinates-space HFB: MADNESS-HFB

Benchmark

Trapped Cold Fermi gasesHO basis compare

MADNESS-HFB potential applications to complex superfluid systems includes: weakly-bound nuclei, fission, cold atoms, neutron stars

No good quantum numbers, fully broken symmetries

3D-HFB solver

Diagonalization with initial wfs

Updating basis

• This procedure is independent of basis choices and the number of eigen-functions to be solved are reduced.

• This is very flexible to study two-body terms, state-dependent Hamiltonian, non-local potential.

Poisson equation are solved by direct integral

MADNESS applications in nuclear structures

Parallel computing strategy

MPI: node to node communication Distributed arrays and FUTURES POSIX threads: multi-threading within one node

threads per node: 10+main+MPI server = 12 Load-balance: map tree to parallel hash table

Main MPI

Threading Pool

API 1.2.3.4. ……

WorldTaskQueue ThreadPool

Task dependencies: m

anaged by Futures

1.

3.

2……

Globally distributed wfs

Remarks of Coordinate-space HFB

Advantages: Results are independent of basis (basis numbers, deformations,

frequency) (an issue also in ab initio calculations) Can describe densities at large distances with halo asympotics Exotic shapes and large deformations can be described. Continuum can be accurately discretized (for broad resonances) Adapted to other physical systems: cold atomic condensates… Can be extended to describe dynamics

Computing issues

Parallel calculations are necessary for non-spherical cases

• 2D: Distribution MPI scheme with good quantum numbers

• 3D: Global distribution of wavefunctions on all nodes: complicated

Future computers: increase the local capability with accelerators

Coordinate-space HFB describe weakly bound nuclei

Deformed halo ： core-halo deformation decoupling ， in principle various structures exist

Expt. deformed halos ： 11Be, 31Ne, 37Mg, but 2n deformed halos not found yet

Need self-consistent description ： decoupling ， halo orbital components ， continuum enhancement ， pairing anti-halo

Spherical halo Various deformed halos

S.G. Zhou, J. Meng, P. Ring, and E.G. Zhao, PRC(R)(2010)


“egg-like deformed halo”

Systematic calculations ： not completely decoupling ； egg-like halo mostly significant ； deformation and high level density suppress halo

Based on Tianhe-1 calculations 。 Precise HFB solutions are essential

"Evolution of surface deformations of weakly bound nuclei in the continuum" Pei*, Zhang, and Xu, PRC 87, 051302(2013)(R)

Odd-A weakly bound nuclei

Xiong, Pei, Zhang, Zhu, 2015(accepted by Chin.Phys.C)

Possible Larkin-Ovchinnikov pairing


neutron emission rates

Bohr-Wheeler statistical model

continuum

Neutron emission rates with finite-temperature deformed coordinate-space HFB

Different Picture ： Evaporation equilibrium due to neutron gas in FT-HFB; statistical models depends a level density parameter

Our approach

"Microscopic description of neutron emission rates in compound nuclei", Yi Zhu ( 朱怡 ) and J. C. Pei ( 裴俊琛 )*, Phys. Rev. C 90, 054316(2014).

Only in coordinate-space HFB

Exotic excitations in weakly bound nuclei

New excitation modes and dynamics ： core-halo motion ， new physics of soft modes

Continuum Pairing

Deformation Colle

ctiv

e

Excita

tion

Halo

Challenge ： self-consistency （ spherical available ） Aim ： fully self-consistent deformed continuum QRPA

PygmySoft modes

Giant resonance

Collective excitation descriptions

Collective excitation based on coordinate space HFB+ FAM-QRPA

Fully self-consistent deformed continuum QRPA

Conventional QRPA matrix form

FAM-QRPA iterative solution

Need calculate (Aklmn,

Bklmn),Too costly, can not treat large deformed coordinate space

Tianhe-1A hybrid parallel calculation different excitation frequency: MPI ； on each node: OpenMP

Need calculate( , ), Computation reduced, can calculate weakly bound deformed nucleiT. Nakatsukasa, PRC 2007

P. Avogadro and T. Nakatsukasa, PRC 2011


dipole modes has been studied extensively soft monopole modes(less incompressibility of halo)issues ： collective coherence of halo excitation ， the role of continuum in excitation

Breath modes of halo nuclei

impressibilityKhan, et al, PRL 2012

Vandebrouck, et al, PRL 2014

Emergent soft monopole modes in weakly bound deformed nuclei,J.C.Pei, M, Kortelainen, Y.N.Zhang, F.R.Xu, PRC 90,051304(2014)(R)

68Ni

Self-consistent Deformed Continuum-FQRPA

Transform from B-spline to Gauss-Legendre lattice Solve the complex Poisson equation Time-odd terms are included Be careful of spurious states Large coordinate space is essential

Zr100 (mix pairing , surface pairing) FAM-QRPA test of 40Mg


Non-resonant continuum; sensitive to pairing interaction Not so collective

Further studies of multipole modes are in progress

Coordinate-space HFB development

High-Energy spectrum

(Thomas-Fermi) Demonstrate the coordinate-space HFB treatment of

continuum is accurate Hybrid-HFB is very useful: coordinate-space HFB+Thomas-

Fermi

3D-HFB too costly ？ the Hybrid-HFB

2nd-Thomas-Fermi(2015)

"Quasiparticle continuum and resonances in the Hartree-Fock-Bogoliubov theory", J. C. Pei, A. T. Kruppa, and W. Nazarewicz, Phys. Rev. C 84, 024311(2011).

Hybrid-HFB

2nd-order superfluid Thomas-Fermi

2nd Thomas-Fermi is very complex for superfluid systems We derived the terms with effective mass and spin-orbit, based on Green

function method, could be used for general superfluid systems

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Some results of non-sc calculations

J.C. Pei, Na Fei, Y.N. Zhang, P. Schuck, arXiv: 1509.02616

Different contribution terms

0TF underestimate pairing at surface

Hybrid self-consistent HFB calculations

Hybrid HFB iterations with: 2nd-order TF for continuum, low-energy HFB solutions, and deep-hole states

• Hybrid HFB can reduce HFB computing costs and still maintain the accuracy• 2nd-TF will be more useful in cold atomic gases and neutron star crusts, which

have large pairing fields.

J.C. Pei, Na Fei, Y.N. Zhang, P. Schuck, arXiv: 1509.02616

New parameterization of Skyrme force

kjiji

kjivjivV ),,(),(

termorbitspin])([

termslocalnon)()1(

])()()[1(2

1

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'0

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PrrPPxt

rPxtrrV

)()(3)3(

kjjiijk rrrrtv

)2

()()1(6

1'~ 3

)2()3( jijiijijk

rrrrPtvv

Skyrme interaction (1956) can be seen as a very low-momentum effective potential with a two-body part vij and three-body part vijk.

3-body term in Skyrme force:γ)()()1(

61

'～ 3)2()3( rrrPtvv jiijijk

Density dependency is an open question

γ ranges from 1/6 to 1 γ=1/6 in SLy4, SkM*, SkP; 0.25 in SkIx γ=1/3 in Gogny, Bsk1 UNEDF0=0.32, UNEDF1=0.27

Important for saturation properties

Present work - high-order terms

)()]()][1()]()[1(61

[ 31

4433’12

rRPxtRPxtv

Arguments:

A single density dependence might be too simplistic;

Consider the higher order density-dependent terms and correlations

Impact on high-density region and isovector properties

3/83/103/532

3/73/23/422

22

3/53/222

2

378.0

)2ln211(35

32)3(

10

3

m

a

m

a

m

a

m

Lee-Yang, 1957 : Fermi systems with repulsive cores

New fittings of Skyrme force

Fitting binding energies, charge radii, EOS in the s-wave channel

Simulated annealing method for parameter fitting

X.Y. Xiong, J.C. Pei, and W.J. Chen, arXiv:1509.07633∗

Effects of higher-order terms

X.Y. Xiong, J.C. Pei, and W.J. Chen, arXiv:1509.07633∗

Summary

Coordinate-space HFB for deformed weakly bound systems

have a lot of advantages and extensions. However the

computation is still very costly.

2nd superfluid TF has been extended to general systems.

Hybrid HFB is useful for large systems to reduce computing cost

High-order density dependencies can impact dense nuclear

matter properties

Thank you for your attention!

Exotic nuclear structures and dynamics in HFB theory The 9 th Japan-China Joint Nuclear Physics...

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