structure of be hyper-isotopes
DESCRIPTION
Structure of Be hyper-isotopes. Masahiro ISAKA (RIKEN) Collaborators: H. Homma and M. Kimura (Hokkaido University). Structure study of L hypernuclei. Knowledge of L N effective interaction Through studies of s-p shell L hypernuclei Accurate solution of few-body problems [1] - PowerPoint PPT PresentationTRANSCRIPT
Structure of Be hyper-isotopes
Masahiro ISAKA (RIKEN)
Collaborators: H. Homma and M. Kimura (Hokkaido University)
Structure study of L hypernucleiKnowledge of LN effective interaction Through studies of s-p shell L hypernuclei
– Accurate solution of few-body problems [1]
– LN G-matrix effective interactions [2]
– Increases of experimental information [3]
Developments of theoretical modelsBy structure studies of unstable nuclei
Ex.: Antisymmetrized Molecular Dynamics (AMD)[4]
• AMD describes dynamical changes of various structure • No assumption on clustering and deformation
[1] E. Hiyama, NPA 805 (2008), 190c, [2] Y. Yamamoto, et al., PTP Suppl. 117 (1994), 361., [3] O. Hashimoto and H. Tamura, PPNP 57 (2006), 564., [4] Y. Kanada-En’yo et al., PTP 93 (1995), 115.
Systematic (theoretical) study of L hypernuclear structure“Structure changes by hyperon as an impurity”
Structure of Be isotopes
Be isotopes have a 2a cluster structure– 2a cluster structure is changed depending on the neutron number
p2 config. s2 config.
ps config.
ps config.
p-orbit
s-orbit
“molecular-orbit”
Y. Kanada-En’yo, et al., PRC60, 064304(1999) N. Itagaki, et al., PRC62 034301, (2000).
Structure of 9Be 9Be has a 2a + n structureThe difference of the orbit of the last neutron leads to the difference of
deformation
8Be(0+) + n(s-orbit)
Large deformationNo barrier
1/2+
b = 1.02
8Be(0+) + n(p-orbit)
Small deformation
Centrifugal barrier due to L=1
3/2-
b = 0.73
(compact)
Exotic structure of 11Be Parity inversion of the 11Be7 ground stateThe ground state of 11Be is 1/2+
One of the reasons of the parity inversion is the molecular orbit structure of the 1/2+ and 1/2- states.
Vanishing of the magic number N=8
411Be 1/2-
Extra neutrons in p orbit[1]
(small deformation)
11Be 1/2+
Extra neutrons in s orbit[1]
(large deformation)
[1] Y. Kanada-En’yo and H. Horiuchi, PRC 66 (2002), 024305.
Difference of deformation
inversion
L binding energy as a function of bL in s-orbit is deeply bound with smaller deformation
Example: 13LC Binding energy of L
12C(Pos)⊗L(p)
12C(Pos.)⊗L(s)12C(Neg)⊗L(s)
L b
indi
ng e
nerg
y [M
eV]
Bing-Nan Lu, et al., PRC 84, 014328 (2011)M. T. Win and K. Hagino, PRC78, 054311(2008)
M. Isaka, et. al., PRC 83 (2011), 044323.
12C Pos.
12C(Pos)⊗L(p)
12C(Pos)⊗L(s) + 8.0MeV
E en
ergy
(MeV
)
Energy curves of 13LC
Spherical2
1
Purpose of this study Purpose of this studyTo reveal how L hyperon affects and modifies the low-lying states of Be
isotopes with different deformation Examples
10LBe: ground and 1/2+ resonance states of 9Be
12LBe: abnormal parity ground state of 11Be
MethodHyperAMD (Antisymmetrized Molecular Dynamics for hypernuclei)
– No assumption on 2a cluster structure– AMD has succeeded in the structure studies of Be isotopes
YNG-interaction (NSC97f, NF)
(Produced by JLab experiments)
(It will be possible to produce 12LBe at J-PARC)
Theoretical framework: HyperAMDWe extended the AMD to hypernuclei
NNNN VTVTH LL +++= ˆˆˆˆˆ
Wave function Nucleon part: Slater determinant
Spatial part of single particle w.f. is described as Gaussian packet
Single particle w.f. of L hyperon: Superposition of Gaussian packets
Total w.f.:
[1] Y. Yamamoto, T. Motoba, H. Himeno, K. Ikeda and S. Nagata, Prog. Theor. Phys. Suppl. 117 (1994), 361.[2] E. Hiyama, M. Kamimura, T. Motoba, T. Yamada and Y. Yamamoto, Prog. Theor. Phys. 97 (1997), 881.
LN: YNG interaction (NSC97f, NF[ 1 ])
NN: Gogny D1S
HamiltonianHyperAMD (Antisymmetrized Molecular Dynamics for hypernuclei)
=Lm
mm rcr
mzyx
mm zrr s
ss
--
= ,,
2exp += mmm ba
+= ba iii iizyx
ii Zrr s
ss
--
= ,,
2exp
jiN rA
r
det!
1=
jim
mm rA
rcr det!
1 = L
Theoretical Framework (AMD[1],[2]) Procedure of the calculation
Variational Calculation • Imaginary time development method• Variational parameters:
Angular Momentum Projection
Generator Coordinate Method(GCM)•Superposition of the w.f. with different configuration•Diagonalization of and
*i
i
XH
dtdX
=
0
+= sJMK
sK RDdJM *;
MJHMJH sK
sK
JKssK
= ;ˆ;,
MJMJN sK
sK
JKssK
= ;;,
=sK
sKsK
MJ MJg ;
[1] Y. Kanada-En’yo, H. Horiuchi and A. Ono, Phys. Rev. C 52 (1995), 628.[2] H. Matsumiya, K. Tsubakihara, M. Kimura, A. Doté and A. Ohnishi, To be submitted
iiiiiiiii cbazZX ,,,,,,, ba=
JKssKH ,
JKssKN ,
Application to 9LBe hypernucleus
[1] Bando et al., PTP 66 (1981) 2118.[2] M. May et al., PRL 51 (1983) 2085; H. Akikawa et al., PRL 88 (2002) 082501.
[3] O. Hashimoto et al., NPA 639 (1998) 93c
[1] [2] [3]
Level structure of 10LBe
Structure of 9Be 9Be has 2a + n structureThe difference of the orbit of the last neutron leads to the difference of
deformation
8Be(0+) + n(p-orbit)
Small deformation
Centrifugal barrier due to L=1
3/2-
b = 0.73
8Be(0+) + n(s-orbit)
Large deformationNo barrier
1/2+
b = 1.02
How does L hyperon modify the level structure with different deformation?
Excitation spectra of 10LBe
Four-body cluster model
Excitation spectra of 10LBe
Y. Zhang, E. Hiyama, Y. Yamamoto, NPA 881, 288 (2012).
Positive parity states in 10LBe are shifted up by L hyperon
Four-body cluster model
Shift up of the positive parity states
L hyperon coupled to the 3/2- state is more deeply bound due to the smaller deformation.
L hyperon in s-orbit is deeply bound with small nuclear deformation
Binding energy of L hyperon
J p Etot TL VLN Enucl2- - 68.60 7.23 -16.63 -59.200+ - 65.87 6.45 -15.04 -57.28
BL= 8.9 MeV
b = 0.70
BL= 8.2 MeVb = 0.92
2.0 MeV
2.7 MeV
0+ 1/2+⊗Ls
1- 3/2-⊗Ls3/2-
1/2+
b = 0.73
b = 1.02
9Be 10BeL
r = 2.55fm
r = 2.46fm
r = 2.94fm
r = 2.82fm
Ground state parity of 12LBe
Exotic structure of 11Be Parity inversion of the 11Be7 ground stateThe ground state of 11Be is 1/2+
One of the reasons of the parity inversion is the molecular orbit structure of the 1/2+ and 1/2- states.
Vanishing of the magic number N=8
411Be 1/2-
Extra neutrons in p orbit[1]
(small deformation)
11Be 1/2+
Extra neutrons in s orbit[1]
(large deformation)
[1] Y. Kanada-En’yo and H. Horiuchi, PRC 66 (2002), 024305.
Difference of deformation
inversion
How does the L hyperon affect the parity-inverted ground state?
Excitation spectra of 11Be
b=0.52
b=0.72
11Be 1/2-
11Be 1/2+
Parity reversion of the 12LBe ground state may occur by L in s orbit
Deformation of the 1/2- state is smaller than that of the 1/2+ state L hyperon in s orbit is deeply bound at smaller deformation
11Be(AMD)
11Be(Exp)
13C(Exp)
Excitation spectra of 11Be
b=0.52
b=0.72
11Be 1/2-
11Be 1/2+
Parity reversion of the 12LBe ground state may occur by L in s orbit
Deformation of the 1/2- state is smaller than that of the 1/2+ state L hyperon in s orbit is deeply bound with smaller deformation
BLBL
Reversion?12LB
e
11Be(AMD)
11Be(Exp)
13C(Exp)
Results: Parity reversion of 12LBe
Ground state of 12LBe
The parity reversion of the 12LBe g.s. occurs by the L hyperon
0.0
1.0
2.0
3.0
Exci
tatio
n En
ergy
(MeV
)
13C7(Exp.)11Be7
(Exp.)11Be7
(AMD)12
LBe(HyperAMD)
Deformation and L binding energy
L hyperon coupled to the 1/2- state is more deeply bound than that coupled to the 1/2+ state
– Due to the difference of the deformation between the1/2- and 1/2+ states
BL = 10.24 MeV
BL = 9.67 MeV
0.32 MeV
0.25 MeV
1/2+
b=0.72
1/2-
b=0.52
b=0.47
b=0.70
0+ 1/2+⊗Ls
0- 1/2-⊗Ls
11Be(Calc.)
12Be(Calc.)L
J p Etot TL VLN Enucl0-(GS) - 74.69 6.71 -16.93 -64.470+ - 74.44 6.68 -16.42 -64.70
r = 2.53 fm
r = 2.69 fm
r = 2.67 fm
r = 2.51 fm
Glue-like role in 10LBe
Glue-like role of L hyperon in 10LBe
Y. Zhang, E. Hiyama, Y. Yamamoto, NPA 881, 288 (2012).
The resonance (virtual) state 1/2+ will bound by adding L hyperon
Glue-like role of L hyperon in 10LBe
Y. Zhang, E. Hiyama, Y. Yamamoto, NPA 881, 288 (2012).
The resonance (virtual) state 1/2+ will bound by adding L hyperon
Summary SummaryTo reveal how L hyperon affects and modifies the low-lying states of Be isotopes
with different deformation, we applied the HyperAMD to 10LBe and 12
LBe.
We focus on the positive and negative parity states in 10LBe and 12
LBeL hyperon coupled to compact state is more deeply bound
– 10LBe: pos. parity states are shifted up by L hyperon
– 12LBe: the parity reversion of the ground state will occur.
In 10LBe, the resonance state 1/2+ in 9Be will be bound by L hyperon
Future plansTo reveal how L hyperon affects the 2a clustering and orbit of extra neutrons
To predict production cross section of 10LBe, 12
LBe etc.
Systematic structure study of Be hyper isotopes
Consistent with the prediction of 10LBe and 13
LC by Hiyama et al.
Backup: Density distribution of 12LBe
Excitation spectra
Improved YNG-NF[2] YNG-NF[1] YNG-ND[1]
[1] Y. Yamamoto, et al., PTPS 117 (1994), 361. [2] E. Hiyama, et al.,PTP 97 (1997), 881.
The 1/2-⊗Ls state always becomes the ground state of 12LBe
Parity reversion will occur with all of these 3 kinds of LN interactions
Excitation spectra
[1] E. Hiyama, et al., PTP 97, 881 (1997).[2] Y. Yamamoto, et al., PTPS 117 (1994), 361.
[3] E. Hiyama, et al., PTP 185, 106 (2010)
[1] [2] [2][3]
Backup: LS interaction between L and N
Backup: Transition density Transition densityTransition density is an input to perform DWIA calculationTransition density will be calculated based on the AMD wave function
Structure described by AMD wave function
Ex.) 9LBe production reaction
Ex.) 10LBe production reaction
Deformation change by L in s-orbit From changes of energy curves
9LBe
20LNe
21LNe
CL13
adding L in s-orbit
12C (Pos)
b = 0.27
quadrupole deformation b
b = 0.00
12C (Pos)⊗L(s)
Spherical 11.5
L in s-orbit reduces the nuclear deformation
12C(Pos)⊗L(s) + 8.0MeV
12C Pos.
Deformation change by L in p-orbit From changes of energy curves
9LBe
20LNe
21LNe
CL13
12C (Pos)
b = 0.27
b = 0.30
12C(Pos)⊗L(p)
quadrupole deformation b
adding L in p orbit
Spherical 11.5
L in p-orbit enhances the nuclear deformationOpposite trend to L in s-orbit
12C Pos.
12C(Pos)⊗L(p)
L binding energy Variation of the L binding EnergyL in s-orbit is deeply bound at smaller deformationL in p-orbit is deeply bound at larger deformation
13LC Binding energy of L 13
LC Energy curves
12C Pos.
12C(Pos)⊗L(p)
12C(Pos)⊗L(s) + 8.0MeVE en
ergy
(MeV
)
12C(Pos)⊗L(p)
12C(Pos.)⊗L(s)12C(Neg)⊗L(s)
L b
indi
ng e
nerg
y [M
eV]
Variation of the L binding energies causes the deformation change (reduction or enhancement)