1 properties of hypernuclei in the skyrme hartree-fock method xian-rong zhou department of physics,...
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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.