structure of l hypernuclei with the antisymmetrized molecular dynamics method
DESCRIPTION
Structure of L hypernuclei with the antisymmetrized molecular dynamics method. Masahiro Isaka (RIKEN). Grand challenges of hypernuclear physics. 2 body interaction between baryons (nucleon, hyperon) hyperon-nucleon (YN) hyperon-hyperon (YY) - PowerPoint PPT PresentationTRANSCRIPT
Structure of L hypernuclei with the antisymmetrized molecular dynamics
method
Masahiro Isaka (RIKEN)
Grand challenges of hypernuclear physics
2 body interaction between baryons (nucleon, hyperon)– hyperon-nucleon (YN)– hyperon-hyperon (YY)
Addition of hyperon(s) shows us new features of nuclear structure Ex.) Structure change by hyperon(s)
– No Pauli exclusion between N and Y– YN interaction is different from NN
A major issue in hypernuclear physics
“Hyperon as an impurity in nuclei”
L hypernucleus Normal nucleus As an impurity
+
Interaction: To understand baryon-baryon interaction
Structure: To understand many-body system of nucleons and hyperon
Today’s talk: “Structure change by a L particle”
Recent achievements in (hyper)nuclear physicsKnowledge of LN interactionStudy of light (s, p-shell) L hypernuclei
– Accurate solution of few-body problems [1]
– LN G-matrix effective interactions [2]
– Increases of experimental information [3]
Development of theoretical modelsThrough the study of unstable nuclei
Ex.: Antisymmetrized Molecular Dynamics (AMD)[4]
• AMD can describe 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.
Recent developments enable us to study structure of L hypernuclei
Structure of L hypernucleiL hypernuclei observed so farConcentrated in light L hypernucleiMost of them have well pronounced cluster structure
Taken from O. Hashimoto and H. Tamura, PPNP 57(2006),564.
Developed clusterLight L hypernuclei
Structure of L hypernucleiL hypernuclei observed so farConcentrated in light L hypernucleiMost of them have well pronounced cluster structure
Taken from O. Hashimoto and H. Tamura, PPNP 57(2006),564.
Developed clusterLight L hypernuclei
Changes of cluster structure
6Li LiL7
Adding L
Example: LiL7
L reduces inter-cluster distance between a + d
T. Motoba, et al., PTP 70,189 (1983)E. Hiyama, et al., PRC 59 (1999), 2351.K. Tanida, et al., PRL 86 (2001), 1982.
ad
Toward heavier and exotic L hypernucleiExperiments at J-PARC, JLab and Mainz etc.Heavier and neutron-rich L hypernuclei can be producedVarious structures will appear in hypernuclei
Taken from O. Hashimoto and H. Tamura, PPNP 57(2006),564.
Developed clusterLight L hypernuclei
Coexistence of structures
sd shell nuclei
Ex.: 21LNe
n-rich region
n-rich nucleiExotic cluster
Ex.: 12LBe
p-sd sh
ell regio
n
Stricture of p-sd shell nucleiEx.) 20Ne Mean-field like and a + 16O cluster structures coexist
within the small excitation energy
0+(g.s.)
1- 2-
20Nea + 16O Mean-field
What is difference in structure changes by adding a L particle ?
cf. 7LLi (a + d + L)
6Li 7LLi
Adding L
L reduces the a + d distancea
dMean-field structure also contributes
Structure of neutron-rich nuclei
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).
Ex.) Be isotopes Exotic cluster structure exists in the ground state regionsBe isotopes have a 2a cluster structure
‒ 2a cluster structure is changed depending on the neutron number
What is happen by adding a L to these exotic cluster structure ?
L Hypernuclei chart will be extended
Hypernuclear chart: O. Hashimoto and H. Tamura, PPNP 57(2006),564.
Developed clusterLight L hypernuclei
Coexistence of structures
sd shell nuclei
Ex.: 21LNe
n-rich region
n-rich nucleiExotic cluster
Ex.: 12LBe
p-sd sh
ell regio
n
“Structure of L hypernuclei”How does a L particle modify structures of p-sd shell/n-rich nuclei ?
Our method: antisymmetrized molecular dynamics (AMD)
Theoretical Framework: HyperAMDWe extended the AMD to hypernuclei
gNNNN TVTVTH ˆˆˆˆˆˆ -+++ LL
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.:
LN: YNG interactions (NF, NSC97f)NN: Gogny D1S
HamiltonianHyperAMD (Antisymmetrized Molecular Dynamics for hypernuclei)
Lm
mm rcr
mzyx
mm zrr s
ss
--
,,
2exp + mmm ba
+ a iii iizyx
ii Zrr s
ss
--
,,
2exp
jiN rA
r
det!
1
jim
mm rA
rcr det
!1 L
M.Isaka, et al., PRC83(2011) 044323M. Isaka, et al., PRC83(2011) 054304
Theoretical Framework: HyperAMD Procedure of the calculation
Variational Calculation • Imaginary time development method• Variational parameters:
*i
i
XH
dtdX
0
iiiiiiiii cbazZX ,,,,,,, a
M.Isaka, et al., PRC83(2011) 044323M. Isaka, et al., PRC83(2011) 054304
Energy variation
Initial w.f.: randomly generated
Various deformationsand/or cluster structure
L
L L
Theoretical Framework: HyperAMD 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 ;
iiiiiiiii cbazZX ,,,,,,, a
JKssKH ,
JKssKN ,
M.Isaka, et al., PRC83(2011) 044323M. Isaka, et al., PRC83(2011) 054304
1. Heavier (sd-shell) L hypernuclei
Based onM. Isaka, M. Kimura, A. Dote, and A. Ohnishi, PRC83, 054304(2011)
Examples: 21LNe (Theoretical prediction)
What is the difference of structure changes ?
Mean field like state a + 16O cluster state
Stricture of p-sd shell nucleiEx.) 20Ne Mean-field like and a + 16O cluster structures coexist
within the small excitation energy
0+(g.s.)
1-
2-
20Nea + 16O
Mean-fieldMean-field
What is difference in structure changes by adding a L particle ?
“Shrinkage effect” of cluster structure by L
6Li: a + d cluster structureL hyperon penetrates into the nuclear interiorL hyperon reduces a + d distance B(E2) reduction (Observable)
B(E2) = 3.6±0.5 e2fm4+0.5+0.4B(E2) = 10.9±0.9 e2fm4
Shrinkage effect: L hyperon makes nucleus compact
Example: LLi7
2
22 ˆ)2( if rYrEB
4/1
6
7
6
7
);2();2(
LL
LiEBLiEB
LirLir
T. Motoba, et al., PTP 70,189 (1983)E. Hiyama, et al., PRC 59 (1999), 2351.K. Tanida, et al., PRL 86 (2001), 1982.
Adding L
ad
Structure of 20Ne Various structure coexist near the ground state
20Ne(AMD)
0+(g.s.)
Ground band(mean-field like)
1-
Kp=0- band(a + 16O clustering)
What is difference in structure change between two bands?Difference in shrinkage effects?
Structure study of 21LNe hypernucleus
a + 16O + L cluster model
“shrinkage effect” by LL reduce the RMS radii in both ground and Kp = 0+ bands
Preceding Study of 21LNe: cluster model calculation
T. Yamada, K. Ikeda, H. Bandō and T. Motoba, Prog. Theor. Phys. 71 (1984), 985.
Similar B(E2) reduction in both bands(Both 20 % reduction)
MeV
Energy Spectra of 21LNe
Results: Excitation spectra of 21LNe
a +16O threshold
a +17LO
threshold
a+O cluster
Mean-field like
a+O cluster
Mean-field like
21LNe (AMD)20Ne (AMD)
Energy Spectra of 21LNe
Results: Excitation spectra of 21LNe
a+O cluster
Mean-field like
a+O cluster
Mean-field like
Kp = 0- band Kp = 0- ⊗ L
Ground⊗ L 21LNe (AMD)20Ne (AMD)
Ground band
L reduces nuclear matter RMS radiiReduction of the RMS radii is larger in the Kp = 0- (a + 16O + L)
than in the ground band
Results: Shrinkage effect
Ground band (intermediate structure)
Kp=0+ rRMS(fm) 0+×Ls rRMS(fm)DrRMS(fm)0+ 2.97 (1/ 2)+ 2.92 -0.05
(3/ 2)+ 2.91 -0.05(5/ 2)+ 2.91 -0.05(7/ 2)+ 2.87 -0.06(9/ 2)+ 2.88 -0.04(11/ 2)+ 2.81 -0.05(13/ 2)+ 2.83 -0.04(15/ 2)+ 2.77 -0.04(17/ 2)+ 2.77 -0.05
2.93
2.96
8+
6+
4+
2+
21LNe20Ne
2.82
2.87
0+(g.s.) (1/2)+20Ne 21
LNe
Kp=0- band (a + 16O cluster)
Kp=0- rRMS(fm) 0-×Ls rRMS(fm) DrRMS(fm)(1/ 2)- 3.15 -0.11(3/ 2)- 3.15 -0.11(5/ 2)- 3.13 -0.11(7/ 2)- 3.14 -0.10(9/ 2)- 3.11 -0.12(11/2)- 3.11 -0.13(13/2)- 3.06 -0.17(15/2)- 3.05 -0.187- 3.23
20Ne 21LNe
3.27
3.24
3.235-
3-
1-
1- (1/2)-20Ne 21
LNe
Large shrinkage mainly comes from the reduction of a + 16O distance
Results: B(E2) reduction Intra-band B(E2) values
Larger B(E2) reduction in the Kp=0- band
Ground band(Intermediate)
Kp=0- band(Pronounced a + 16O)
2. neutron-rich L hypernuclei
H. Homma, M. Isaka and M. Kimura
Examples: 12LBe (Theoretical prediction)
How does L modify exotic cluster structure ?
Molecular orbit structure of Be isotopes
Exotic structure of 11Be Parity inverted ground state of the 11Be7The ground state of 11Be is the 1/2+,
while ordinary nuclei have a 1/2- state as the ground state
1/2- state
1/2+ state
Vanishing of the magic number N=8
4
1/2- state
1/2+ state
Inversion
Exotic structure of 11Be Parity inversion of the 11Be7 ground stateThe ground state of 11Be is 1/2+
Main reason of the parity inversion: molecular orbit structure11Be has 2a clusters with 3 surrounding neutrons
4
[1] Y. Kanada-En’yo and H. Horiuchi, PRC 66 (2002), 024305.
inversion
11Be 1/2-
Extra neutrons in p orbit[1]
11Be 1/2+
Extra neutrons in s orbit[1]
Extra neutrons occupy molecular orbits around the 2a cluster
Excitation spectra of 11Be
=0.52
=0.72
11Be 1/2-
11Be 1/2+
11Be(AMD)
11Be(Exp)
13C(Exp)
Deformation of the 1/2- state is smaller than that of the 1/2+ state
Excitation spectra of 11Be11Be 1/2-
11Be 1/2+
Parity reversion of the 12LBe ground state may occur by L in s orbit
Extra neutrons in p orbit[1]
(small deformation)
Extra neutrons in s orbit[1]
(large deformation)
[1] Y. Kanada-En’yo and H. Horiuchi, PRC 66 (2002), 024305.
Difference in the orbits of extra neutrons
Deformation of the 1/2- state is smaller than that of the 1/2+ state
11Be(AMD)
11Be(Exp)
13C(Exp)
Structure change in 12LBe
Deformations are reduced?Parity-inverted ground state changes?
11Be 1/2-
Extra neutrons in p orbit(small deformation)
11Be 1/2+
Extra neutrons in s orbit(large deformation)
1/2+ 1/2-
11Be
What is happen by L in these states with different deformations?
Parity inverted
Results: Parity reversion of 12LBe
Ground state of 12LBe
0.0
1.0
2.0
3.0
Exci
tatio
n En
ergy
(MeV
)
13C7(Exp.)11Be7
(Exp.)11Be7
(AMD)=0.52
=0.72
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 slightly reduces deformations, but the deformation is still different 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+
0.72
1/2-
0.52
0.47
0.70
0+ 1/2+⊗Ls
0- 1/2-⊗Ls
11Be(Calc.)
12Be(Calc.)L
r = 2.53 fm
r = 2.69 fm
r = 2.67 fm
r = 2.51 fm
Summary SummaryTo study structure change by L, we applied an extended
version of AMD to 21LNe and 12
LBe .
Coexistence of structures in sd-shell nuclei– Shrinkage effect is larger in a + 16O + L band than the ground band
Exotic cluster structure of n-rich nuclei– The abnormal parity of 11Be ground state is reverted in 12
LBe
Future works: “Structure changes”Be hyper isotopes: L modifies 2a clustering and extra neutrons?Coexistence structures: 13
LC, 20LNe, etc.
Predictions of the production cross sections
Large reduction of the B(E2) values in a + 16O + L band
The L hyperon coupled to the intermediate state is more deeply bound than that coupled to the well developed a + 16O state
The L hyperon stays around O cluster in the a + O cluster state.
Backup: L binding energy in 21LNe
shallow binding in the a + O state
BL=16.9 MeV
Kp=0I+ band
(1/2)+
0+
Kp=0- band
BL=15.9 MeV
1-
(1/2)-
20Ne
21LNe
Backup: Parity Coupling Contribution of L hyperon in p orbitThe L(s) hyperon in the “Kp=0-⊗L(s) ” stays around the 16O cluster
Kp=0I+⊗L(p) : about 10 %
Kp=0-⊗L(s) : about 90 %
it is not eigen state of parityL(p) component should contribute to the “Kp=0-⊗L(s) ” state
(Parity Coupling)
(1/2)-
21LNe: Kp=1-⊗Ls state
Backup: L hyperon in a + 16O cluster structure
(1/2)-
Quadruple deformation parameter
Ener
gy (M
eV)
Deformation change by L in p-orbit From changes of energy curves
9LBe
20LNe
21LNe
CL13
12C (Pos)
= 0.27
= 0.30
12C(Pos)⊗L(p)
quadrupole deformation
adding L in p orbit
Spherical 11.5
L in p-orbit enhances the nuclear deformationOpposite trend to L in s-orbit
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)