Three-body cluster state in 11 B Center for Nuclear Study, University of Tokyo KAWABATA Takahiro RCNP, Osaka University H. Fujimura, H. Fujita, M. Fujiwara, K. Hara, K. Hatanaka, M. Itoh, K. N akanishi, Y. Shimbara, A. Tamii, M. Uchida, H.P. Yoshida, M. Yosoi Department of Physics, Kyoto University S. Kishi, M. Nakamura, H. Sakaguchi, H. Takeda, S. Terashima, Y. Yasu da Department of Physics, Konan University H. Akimune Department of Physics, Kyushu University T. Wakasa Department of Physics, Osaka University Y. Fujita Yukawa Institute for Theoretical Physics, Kyoto University Y. Kanada-En’yo
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Three-body cluster state in 11 B Center for Nuclear Study, University of Tokyo KAWABATA Takahiro RCNP, Osaka University H. Fujimura, H. Fujita, M. Fujiwara,
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Three-body cluster state in 11B
Center for Nuclear Study, University of Tokyo KAWABATA Takahiro
RCNP, Osaka UniversityH. Fujimura, H. Fujita, M. Fujiwara, K. Hara, K. Hatanaka, M. Itoh, K. Nak
anishi, Y. Shimbara, A. Tamii, M. Uchida, H.P. Yoshida, M. Yosoi
Department of Physics, Kyoto UniversityS. Kishi, M. Nakamura, H. Sakaguchi, H. Takeda, S. Terashima, Y. Yasuda
Department of Physics, Konan UniversityH. Akimune
Department of Physics, Kyushu UniversityT. Wakasa
Department of Physics, Osaka UniversityY. Fujita
Yukawa Institute for Theoretical Physics, Kyoto UniversityY. Kanada-En’yo
IntroductionAlpha particle clustering is an important concept in nuclear physics for light
nuclei. Alpha cluster structure is expected to appear near the -decay threshold energy.
The 02 state at Ex = 7.65 MeV in 12C
Famous 3alpha cluster state.Condensed state where three alpha particles occupy the lowest s-orbit.Dilute-gas state of alpha clusters.
Similar dilute-gas-like states have been predicted in self-conjugate N = 4n nuclei.
Does such a dilute cluster state exists in the other N≠4n nuclei ?
T.Yamada and P. Schuck, Euro. Phys. J. A 26, 185 (2005).
12C0
1
02
GT strengths in 11B
Ex (MeV)B(GT)
Experiment Shell Model
0.000 (3/2) 0.345±0.008 0.588
2.125 (1/2) 0.401±0.032 0.782
4.445 (5/2) 0.453±0.029 0.616
5.020 (3/2) 0.487±0.029 0.745
8.104 (3/2) 0.003
8.420 (5/2) 0.398±0.031 0.483
GT Strengths have been measured by the (3He,t) reaction.
The 3/23 state has exotic characters.
Suppressed GT strengthNot predicted by the shell-model calculationLocate 100-keV below the -decay threshold.
It is interesting to study the 3/23 state
from view of the cluster model.
T. Kawabata et al., Phys. Rev. C 70, 034318 (2004).
Transition Strengths
2 22
1 1
ˆ ˆ( 0) , ( 2)Z Z
k kk k
O E r O E r Y
The IS excitation strengths should be determined by the different measurement.
Nuclear transition strengths provide structural information.
Alpha cluster states are mainly excited by natural-parity isoscalar transitions.
Monopole (E0) and Quadrupole (E2) operators
(e,e’) and -decay measurements were extensively performed, but those are sensitive to proton parts only.
21( ; ) ( ; ) ( ; )
2 1i
B E IS M E p M E nJ
1 1ˆ ˆ( ; ) 1 ( ) , ( ) 1 ( ) .2 2z zM E p f O E i M n f O E i
2 21( ) ( ; )
2 1i
B E M E p eJ
IS strengths are different from the EM transition strengths in N≠Z nuclei.
Hadron ScatteringHadron scattering is a good probe for nuclear excitation strengths.
We measured the (d,d’) reactionsto investigate the cluster structure in 11B.
Simple reaction mechanism - Good linearity between d/d and B(ô).
Selectivity for the T = 1 and T = 0 components.
Multiple decomposition analysis is useful to separate J.
(3He,t) … T = 1 only (Tz = 1)(d,d’) … T=0 only (Tz =0)(p,p’) … T = 1 and T = 0 (Tz = 0)
expcalc( ) ( )
J
d dA J J
d d
2( ) ( ) ( )
dJ KN J q B O
d
ExperimentExperiment was performed at RCNP, Osaka University.
The previous (e,e’) data do not contradict the present experimental and theoretical results.
Large E0 and negligibly small M1 and E2 stregths !!
Analogies to the 02 state in 12C
The 3/23 state is inferred to be a 2+t cluster state with the dilute density.
• Analogies between the 3/23 state and the 0+
2 state in 12C (dilute-gas-like 3 cluster state) has been observed.Located near the -decay threshold.Similar monopole strengths.Not predicted in SM calculations.
• Analogies suggests a dilute structure of the 3/23.
Large RMS radius is predicted.
13 2 (g.s.)
r21/2 = 2.5 fm33 2
r21/2 = 3.0 fmAMD (VAP) Calculation by Y. Kanada-En’yo
11B, 13C(,’) Experiment
• Radius of the 3/23 state should be experimentally determined.
• Analogue state for the 0+3 state in 12C as well as the 0+
2 state might exist.• Similar analog states are also expected in 13C.
Recently, the 11B and 13C(,’) reactions have been measured for further clarification.
Y. Sasamoto et al.
Summary
• Isoscalar excitation strengths in 11B are measured via the 11B(d,d’) reaction.
• Experimental results are compared with the SM and AMD (VAP) calculations.
– AMD (VAP) successfully predicts the 3/23 state
with a 2 + t configuration.
– Strong E0 transition for the 3/23 state should be an evidence of
the 2 + t cluster structure.
• Analogous relation between 11B and 12C is speculated.
– 3/23 state in 11B is inferred to be a dilute cluster state in similar
to the 0+2 state in 12C.
Dilute Character of 3/23
To evaluate the dilution of the 3/23 state, new quantity D is introduced.
AMD (VAP) RGMr21/2 D r21/2 D
11B 3/21 2.5 0.29
11B 3/22 3.0 0.42
12C 01 2.5 0.21 2.4 0.17
12C 02 0.42 3.5 0.57
0
3
1 5
1D r d r
A
D: Fraction of nucleon numbers in low density region with /0 1/5.
Rrms and D for 3/23 are ...
Extraordinary larger than those for the ground state,As large as those for the 0+
2 state in 12C . Dilute structure of the 3/2
3 state.
RGM: M. Kamimura, Nucl. Phys. A351, 456 (1981).
Excitation Modes in 11B
. . 3 2 1 2
. .
1 , 2
0 ,1 , 2 , 3
1
3 2 3 2
. . 3 2 5 2
0,1
0,1
0,, 3 1, 2 , 4
g s J
J
J
g
T
Ts
g s T
G.S. of 11B is J=3/2 and T=1/2.
Excitation modes in 11B are complex.
To extract the IS transition strengths....
• Each J transition must be isolated.• Isoscalar and isovector transitions must be separated.
,L
J L S
Macroscopic analysis for the 12C(d,d’) reaction12C(d,d’) can be a reference for the J decomposition.
• 0+ and 2+ transitions are parameterized in terms of DP model.
• Fit the 1+ transition by the spherical Bessel function.
2 2
0 0 2 2(1 ) ( ) ( )d d j qR j qR
0
2
3 ( )
( )5
J
J
dU r U r
drR r d
U U rR dr
Transition form factors in 12C and 11B are expected to be similar.
Measured Spectra(3He,t)V is strong.
Spin-flip transitions are dominant.
(d,d’)V0 is strong.
Non-spin-flip transitions are dominant.
M1 transitions are dominant.
Unpredicted by SM calculation.Non-spin-flip transition is dominant.Expected to be a cluster state.
E2 transitions are dominant.
1 1 2 21 2 , 5 2 , 3 2 , and 5 2
1 15 2 and 7 2
33 2
Proton and Neutron Quadrupole Strengths
2 2 21 1( 2; ) ( ) ( ) , ( 2) ( ) .
2 1 2 1i i
B E IS M p M n B E M p eJ J
2 22 2
1 1( ) 1 , ( ) 1 .
2 2z zM p f r Y i M n f r Y i
Quadruple proton and neutron transition strengths are defined by
B(GT) from (3He,t) reactions
Ex (MeV)B(GT)Exp
Present (p,n)
0.000 (3/2) 0.345±0.008
2.125 (1/2) 0.401±0.032 0.399±0.032
4.445 (5/2) 0.453±0.029
0.961±0.0605.020 (3/2
) 0.487±0.029
8.104 (3/2) 0.003
0.444±0.0108.420 (5/2
) 0.398±0.031
B(GT) for excited states were obtained from DWBA analysis.
Present results are consistent with previous (p,n) result.
Eff. Int. for DWIA were adjusted for ground-state transitions.B(GT)=0.345±0.008, B(F)=NZ=1
DWBA
exp SM
( ) ( )
(GT) ( 1 ) (GT)J
d dA J J
d dB A J B
Proton Inelastic Scattering
DWIA calculation- Franey-Love NN interaction- H.O. single-particle w.f. - Strengths from (d,d’) and (3He,t)
No parameters adjusted.
8.92-MeV state- DWIA underestimates 50%.- Problem on linearity between B(GT) and d/d.- Interference between IS and IV parts??- The reason is still unclear.