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HIRFL -RIBLL 合作会议,上海, 2013.1. Contents. Motivation: physics of weakly bound deformed nuclei Method: deformed coordinate-space HFB approach Results: surface deformations and continuum effects Summary. Motivation: Physics of d rip-line nuclei.

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contents
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

motivation physics of d rip line nuclei
Motivation: Physics of drip-line nuclei

RNB facilities offer unprecedented opportunities to access unstable nuclei

Challenging theoretical approaches

From B. Sherrill’s talk at NS2012

From J. Erler et al., Nature, 486, 509(2012)

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

motivation physics of drip line nuclei
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 andetc.
  • 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

motivation physics of deformed halos
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. Dobaczewskiet 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: isovectorquadrupole 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

continuum coupling in hfb t heory

HFBG.S.:

BCS

G.S.:

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 equation(or BdG)

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

JP et al. PRC, 2011

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

hfb solving approaches
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
  • 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(-ar2) that decays too fast, while the density distribution decays exponentially exp(-kr).
  • Bound states, continuum and embedded resonances are treated on an equal footing; L2 discretization leads to a very large configuration space
  • Providing better inputs for QRPA, for describing excited states
  • Computing resources and capabilities are increasing exponentially

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

deformed coordinate space hfb
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

  • 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

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

hybrid parallel calculations for large boxes
Hybrid parallel calculations for large boxes
  • 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

Large boxes calculations are crucial for describing density diffuseness and discretized continuum

J.P. et al., JPCS 402, 012035(2012)

From 20 fm to 30 fm, the estimated computing cost increased by 40 times.

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

deformations of drip line nuclei
Deformations of drip-line nuclei

Extensive studies on light drip-line nuclei

Controversial about spherical halos in heavy nuclei, giant or collective halo?

N/Z=2.3

J. Erleret al., Nature, 486, 509(2012)

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

systematics of deformed neutron h alo skin
Systematics of deformed neutron halo/skin
  • New exotic “egg”-like halo structure
  • Halo hindered by deformed cores? F.M. Nunes, NPA, 2005

J.C. Pei, Y.N. Zhang, F.R. Xu, arXiv:1301.1461, 2013

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

development of resonances in light nuclei
Development of resonances in light nuclei
  • Levels near Fermi surface are sparse in light nuclei
  • Near threshold quasiparticleresonances (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

Smoothed neutron quasiparticle spectrum Ω=1/2

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

development of resonances in heavy nuclei
Development of resonances in heavy nuclei
  • Low- halo resonances gradually grows and decouples in heavy nuclei
  • Bound states move away from the Fermi surface collectively; larger level density
  • Density distribution decoupling is related to the phase space decoupling

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

isovector deformations
Isovector deformations
  • Neutron skin/halo: pygmy dipole resonances (two humps)
  • Isovector deformations: pygmy quardpole resonances

From J. Erler et al., Nature, 486, 509(2012)

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

development of surface deformations
Development of surface deformations
  • Slightly largerisovector 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

Abnormal isovector deformation of 0.24 in the

egg-like structure!

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

continuum effects in excited states
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

In progress: monopole strength calculated by FAM-QRPA with SLy4 and mixed pairing

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

summary
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
  • Newexotic 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

Collaborators: F.R. Xu, Y.N. Zhang, W. Nazarewicz

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

thanks for your attention
Thanks for your attention!

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