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Properties of hypernuclei in the Skyrme Hartree-Fock method

Xian-Rong Zhou

Department of physics, Xiamen University,

Xiamen, China

Present Status of the Nuclear Interaction Theory , 08/25 -09/19,2014, Beijing, China

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Outline

Introduction

Extended Skyrme Hartree-Fock

Properties of hypernuclei shapes of hypernuclei effects of hyperon enegery spetrum

Summary

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N

Z , Hypernuclei, Hypernuclei

Str

an

ge

ne

ss

0

-1

-2

3-D nuclear chart

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Multistrange system: Neutron star, …

Why to study hypernuclei?

Nucleon-nucleon interaction

Hyperon-nucleon interaction

Impurity of nuclear system

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Theoretical studies about hypernuclei

Energy spectrum

Decay properties

The effect of hyperon(s)

Shapes

…….

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Studies based on spherical

symmetry:

1. Relativistic mean-field model (RMF)

2. Skyrme Hartree-Fock model (SHF)

3. Woods-Saxon potential + YN interaction

4. Few-body theory

Theoretical studies about the shapes of hypernuclei

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Deformed HF with nonrealistic YN interaction:

T. H. Ho and A.Volkov, Phys. Lett. B30, 303, 1969.

W. H. Bassichis, A. Gal, Phys. Rev. C1, 28, 1970.

J. Zofka, Czech, J. Phys. B30, 95, 1980.

Nilsson Model:

assume the same deformation for core and hypernuclei: K. Hagino, Phys. Rev. C63, 044318, 2001

Calculations considering deformation:

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Deformed SHF with Microscopic YN int. X.-R. Zhou, H.-J. Schulze, H. Sagawa,et al., Phys. Rev. C76, 034312(2007)

Relativistic mean-field model (RMF):Myaing Thi Win, H. Hagino, et al., Phys. Rev. C 78, 054311 (2008)

Triaxial SHF with Skyrme-like YN interaction:Myaing Thi Win, H. Hagino, et al., Phys. Rev. C 83, 014301 (2011)

Antisymmetrized molecular dynamics (AMD):M. Isaka,, et al., Phys. Rev. C 83, 044323 (2011)

Triaxial RMF:Bing-Nan Lu (吕炳楠 ), S.-G.Zhou, Phys. Rev. C 84, 014328 (2011)

Considering deformation self-consistently:

9Bing-Nan Lu, E. Hiyama, H. Sagawa, and S.-G. Zhou, Phys. Rev. C 89, 044307 (2014)

Superdeformation in hypernuclei

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Why to study deformations of hypernuclei

Many p-shell and sd-shell nuclei are deformed.

For example, experimentally, 10B and 11C have large quadrupole moments.

F. Ajzenberg-Selove, Nucl. Phys. A490, 1 (1988); A506, 1(1990).

Also, 8Be is known to be strongly deformed due to its double-α structure.

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Several models for deformed nuclei

Alpha-model

Projected shell model (PSM)

Deformed Skyrme Hartree-Fock (DSHF)

Relativistic mean-field model (RMF)

Antisymmetrized molecular dynamics (AMD)

……

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Microscopic hyperon-nucleon interaction

for deformed hypernuclei

BY, Hypernuclear Structure

Effective YN interaction

BHF cal. for asymmetric

matter

Free YN interaction

MF cal.

YN: Nijmegen soft-core hyperon-nucleon potential NSC89,NSC97a,NSC97f,ESC08

NN: Argonne v18 nucleon-nucleon interaction

Comparison of different hyperon-nucleon potential

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Extended DSHF including hyperon-nucleon interaction

Total energy of a hypernucleus in extended DSHF:

where the energy density

SHF

Due to the YN force,

DSHF + YN interaction:

The energy density functional εNΛ is obtained from a fit to the binding energy per baryon, B/A(ρn, ρp, ρ), of asymmetric hypermatter, as generated by BHF calculations.

Effective mass of hyperon

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In practice we use the following parametrizations:

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Extended SHF equation

Minimizing the total energy of the hypernucleus, one arriveswith extended SHF equation

with the modified mean field by hyperon:

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For light nuclei,

For medium-mass and heavy nuclei,

Pairing interaction

Nucl. Phys. A722, c183, 2003

Euro. Phys. J. A8, 59, 2000

We take a density-dependent delta pairing

Nucl. Phys. A551, 434 (1993)

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1. Hypernuclei is deformed or not?

2020

0.65

0.63

0.63

0.55

0.52

0.55

X.-R. Zhou, H.-J. Schulze, H. sagawa et.al, PRC76, 034312(2007)

Binding energies vs deformations

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Binding energies vs deformations

X.-R. Zhou, H.-J. Schulze, H. sagawa et.al, PRC76, 034312(2007)

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2. The effect of hyperon on nuclear structure?

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The effect of hyperon in neutron-rich nuclei

X.-R. Zhou,A.Polls,H.-J.Schulze, et al.,PRC78,054306(2008)

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The Oxygen isotopes

exp.

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3. Energy spectrum of hypernulcei

The SHF models can just give the single-particle energies and ground state of Λ hypernuclei in intrinsic frame of reference.

The conservation of particle number is destroyed by BCS method.

The study of the gamma spectra and electromagnetic transitions needs symmetry restoration.

Limitations of extended SHF+BCS method:

Angular momentum and particle-number projection (AMP&PNP) are needed !

Projected SHF+BCS Model

The projected mean-field state

The projection operator

Energies with angular momentum and E2 transitions

, J N ZMKJMK P P P

Energy potential surface of 12C and

Ji-Wei Cui, X.-R. Zhou, in preparation

Energy potential surface of 20 Ne and

Energy potential surface of 24Mg and

Energy potential surface of 26Mg and

Energy potential surface of 26Si and

Energy potential surface of 28Si and

Comparison of NSC89(upper) and Skyrme-type(lower) ΛN Interactions

Comparison of different Skyrme parameters

Energy spectrum of 12C and

cal1 and cal2 label energy levels with or without the Λ spin-orbit term.

cal1 and cal2 label energy levels with or without the Λ spin-orbit term.

Energy spectrum of 20Ne and

cal1 and cal2 label energy levels with or without the Λ spin-orbit term.

Energy spectrum of 24Mg and

Energy spectrum of 28Si and

cal1 and cal2 label energy levels with or without the Λ spin-orbit term.

Exp data in W.u. from:http://www.nndc.bnl.gov The B(E2) transitions of hypernuclei become a little

smaller due to the shrinkage of the quadruple shape.

B(E2) transition probabilities

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Summary

1.The DSHF was extended to hypernuclei by including a microscopically derived hyperon- nucleon interaction.

3. Due to the effect of hyperons, the nuclei close to the drip line are stabilized and new isotopes are potentially made available.

2.The calculated core nuclei and the corresponding hypernuclei have similar deformations with the same sign when the core nuclei are well deformed.

4. The projected SHF+BCS model gives reasonable initial results of energy spectra and E2 transition rates for well-deformed sd-shell nuclei and hypernuclei .

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Cooperators

H. SagawaUniversity of Aizu, Japan

H.-J. Schulze,University of Catania, Italy

En-Guang ZhaoInstitute of Theoretical Physics, CAS, China

Ji-Wei Cui Xiamen University, China

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Thank you for your attention!

Furong Lake Xiamen Univ.