1
Deformed hypernuclei with the Skyrme-Hartree-Fock approach
Xian-Rong Zhou
Department of physics, Xiamen University,
Xiamen, China
9th, Feb. 2012, Tokai
2
Outline
Introduction
Extended deformed Skyrme-
Hartree-Fock (DSHF)
Results
Summary
3
Why do we study hypernuclei?
Multistrange systemNeutron star
IntroductionIntroduction
Nucleon-nucleon interaction
Hyperon-nucleon interaction
4
Present Status of Hypernuclear Spectroscopy
O. Hashimoto and H. Tamura, Prog. Part. Nucl. Phys. 57 (2006) 564.
(2006)
5
Theoretical studies
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
6
Theoretical studies
Deformed calculations:Deformed HF with nonrealistic 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
Deformed SHF with Microscopic YN int. (self-consistent) X.-R. Zhou, et al., Phys. Rev. C 76, 034312 (2007)
7
Theoretical studies
Relativistic mean-field model (RMF):Myaing Thi Win et al., Phys. Rev. C 78, 054311 (2008)
Triaxial SHF with Skyrme-like YN interaction:Myaing Thi Win, 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 ), Phys. Rev. C 84, 014328 (2011)
8
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.
9
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)
10
Microscopic hyperon-nucleon interaction
for deformed hypernuclei
BY, Hypernuclear Structure
Effective YN interaction
BHF cal. for asymmetric
matter
Free YN interaction
DSHF MF cal.
YN: Nijmegen soft-core hyperon-nucleon potential NSC89
NN: Argonne v18 nucleon-nucleon interaction
11
Extended DSHF including hyperon-nucleon interaction
Total energy of a hypernucleus in extended DSHF
where the energy density
SHF
Due to the YN force,
12
Energy density due to hyperons
where the last term corresponds to the kinetic energy contribution of the Λ’s.
The hyperon effective mass extracted from the BHF single-particle potential,
It can be constructed from BHF energy density,
13
Finally, the energy density is written as
The parameterizations of numerical results:
Parameterizations
14
Extended SHF equation
Minimizing the total energy of the hypernucleus, one arriveswith extended SHF equation
15
For light nuclei,
For medium-mass and heavy nuclei,
Pairing interaction
Nucl. Phys. A722, c183, 2003
Euro. Phys. J. A8, 59, 2000
The pairing interaction is taken to be a density-dependent delta force
Nucl. Phys. A551, 434 (1993)
16
Results
Self-consistent DSHF calculations forexperimentally studied hypernuclei including light, medium-mass and heavy hypernuclei.
Hypernuclei is deformed or not?
17
Binding energies vs deformations
0.65
0.63
0.63
0.55
0.52
0.55
18
X.-R. Zhou, et.al, PRC76, 034312(2007)
Binding energies vs deformations
19
Deformations, Energies, and B Λ
20
Binding energies vs deformations
X.-R. Zhou, H.-J. Schulze, et.al, PRC76, 034312(2007)
21
Binding energies vs deformations
X.-R. Zhou, H.-J.Schulze, et.al, PRC76, 034312(2007)
22
Shrinking effect of hyperons
B(E2) |<f| e r∝ 2 Y2 |i>|2
∝R4 or (<r2>)2
R <r2>
similar to Q-moment
Motoba, Bando, Ikeda Prog.Theor.Phys. 70 (1983) 189. 4He + d + model ~ 20% shrinkage
23
The effect of hyperon in neutron-rich nuclei
X.-R. Zhou, H.-J. Schlze, et.al, PRC78, 054306 (2008)
24
The Oxygen isotopes X.-R. Zhou, et.al, PRC78, 054306 (2008)
exp.
25
Summary
1.The DSHF was extended to hypernuclei by including a microscopically derived hyperon- nucleon interaction.
3. The main qualitative effect of added hyperons is demonstrated: 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.
26
Prospect
DSHF + Nucleon-kaon interaction
1. Kaonic nuclei
2. η nuclei?
DSHF + η-nucleon interaction
27
Cooperators
H. SagawaUniversity of Aizu, Japan
H.-J. Schulze,University of Catania, Italy
En-Guang ZhaoInstitute of Theoretical Physics, CAS, China
28
Thank you!
Welcome to Xiamen University, China!
Furong Lake Xiamen Univ.