Weak Isoscalar Response of 11B

1
Three-body cluster state in 11B
Center for Nuclear Study, University of Tokyo
KAWABATA Takahiro
2
Introduction
Alpha particle clustering is an important concept
in nuclear physics for light nuclei.
Alpha cluster structure is expected to appear
near the a-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 ?
3
GT strengths in 11B
GT Strengths have been measured by the (3He,t)
reaction.
T. Kawabata et al., Phys. Rev. C 70, 034318
(2004).
The 3/2-3 state has exotic characters. Suppressed
GT strength Not predicted by the shell-model
calculation Locate 100-keV below the a-decay
threshold.
It is interesting to study the 3/2-3 state
from view of the cluster model.
4
Transition Strengths
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 g-decay measurements were extensively
performed, but those are sensitive to proton
parts only.
IS strengths are different from the EM transition
strengths in N?Z nuclei.
The IS excitation strengths should be determined
by the different measurement.
5
Hadron Scattering
Hadron scattering is a good probe for nuclear
excitation strengths.
Simple reaction mechanism - Good linearity
between ds/dW and B(ô). Selectivity for
the DT 1 and DT 0 components. Multiple
decomposition analysis is useful to separate DJp.
(3He,t) DT 1 only (DTz -1) (d,d) DT0
only (DTz 0) (p,p) DT 1 and DT 0 (DTz 0)
We measured the (d,d) reactionsto investigate
the cluster structure in 11B.
6
Experiment

• Experiment was performed at RCNP, Osaka
  University.

11B(d,d) RCNP-E207E 200 MeV, qlab 025-
ds/dW, Ay, Ayy
B(E0 IS) and B(E2 IS) have been
determined as well as B(s).
7
Isoscalar strengths from 11B(d,d)
Deformed potential model were used to analyze the
(d,d) data.
DP model well-explains the 12C(d,d) result.
12C(d,d) is used as a reference
for DJ decomposition.

• B(s) for 4.44 MeV was not reliably determined.
• 8.56 MeV is strongly excited by the monopole
  transition.

8
Comparison with Shell model
Measured strengths are compared with SM
calculation by SFO.
epeff 1.24, eneff 0.23.

• Reasonably well-reproduced except ....
• M1 and GT strengths are overestimated by 20-50.
• 3/2-3 state is not predicted. 3/2-3 state is
  inferred to be a cluster state.

9
AMD (VAP) Calculation
Y. Kanada-Enyo

• AMD (VAP) calculation successfully predict the
  3/2-3 state with the 2a t structure.
• The 5/2-2 and 5/2-3 states were described as a
  mixture of the SM and cluster components.
• Lower states have shell-like structures.

10
Comparison with AMD (VAP)
AMD (VAP) successfully predicts the experimental
data. E2 strength for the 5/2-2 state implies
coexistence of the SM and CM wave functions. E0
and M1 strengths for the 3/2-3 states are well
described by a 2a t cluster w.f.
11
Comparison with AMD (VAP)
Large B(E2) value reported from the (e,e)
experiment contradicts the AMD result.
E0, M1, and E2 are allowed, nevertheless,
previous analysis takes only M1 and E2 into
account.
Re-analyze the (e,e) data by taking E0 and M1
into account, and neglecting E2.
B(E0) 18.7 /- 0.7 e2fm4
If Mn (N/Z)Mp, B(E0IS) 90 /- 3 fm4.
Large E0 and negligibly small M1 and E2 stregths
!!
The previous (e,e) data do not contradict
the present experimental
and theoretical results.
AMD (VAP) nicely predicts the excitation
strengths for the 3/2-3 state. ? Evidence for
the 2a t cluster structure.
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Analogies to the 02 state in 12C

• Analogies between the 3/2-3 state and the 02
  state in 12C (dilute-gas-like 3a cluster state)
  has been observed.
• Located near the a-decay threshold.
• Similar monopole strengths.
• Not predicted in SM calculations.
• Analogies suggests a dilute structure of the
  3/2-3.
• Large RMS radius is predicted.

The 3/2-3 state is inferred to be a 2at cluster
state with the dilute density.
13
11B, 13C(a,a) Experiment
Recently, the 11B and 13C(a,a) reactions have
been measured for further clarification.
Y. Sasamoto et al.

• Radius of the 3/2-3 state should be
  experimentally determined.
• Analogue state for the 03 state in 12C as well
  as the 02 state might exist.
• Similar analog states are also expected in 13C.

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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 3/2-3 state
  with a 2a t configuration.
• Strong E0 transition for the 3/2-3 state should
  be an evidence of the 2a t cluster structure.
• Analogous relation between 11B and 12C is
  speculated.
• 3/2-3 state in 11B is inferred to be a dilute
  cluster state in similar to the 02 state in 12C.

15
Dilute Character of 3/2-3
To evaluate the dilution of the 3/2-3 state, new
quantity D is introduced.
D Fraction of nucleon numbers in low density
region with r/r0 lt 1/5.
RGM M. Kamimura, Nucl. Phys. A351, 456 (1981).
Rrms and D for 3/2-3 are ... Extraordinary larger
than those for the ground state, As large as
those for the 02 state in 12C . -gt Dilute
structure of the 3/2-3 state.
16
Excitation Modes in 11B
G.S. of 11B is Jp3/2- and T1/2.
Excitation modes in 11B are complex.

• To extract the IS transition strengths....
• Each DJp transition must be isolated.
• Isoscalar and isovector transitions
  must be separated.

17
Macroscopic analysis for the 12C(d,d) reaction
12C(d,d) can be a reference for the DJp
decomposition.
Transition form factors in 12C and 11B are
expected to be similar.
18
Measured Spectra
(3He,t) Vst is strong. Spin-flip transitions are
dominant. (d,d) V0 is strong. Non-spin-flip
transitions are dominant.
M1 transitions are dominant.
E2 transitions are dominant.
Unpredicted by SM calculation. Non-spin-flip
transition is dominant. Expected to be a cluster
state.
19
Proton and Neutron Quadrupole Strengths
Quadruple proton and neutron transition strengths
are defined by
20
B(GT) from (3He,t) reactions
B(GT) for excited states were obtained from DWBA
analysis.
Eff. Int. for DWIA were adjusted
for ground-state transitions.B(GT)0.3450.008,
B(F)N-Z1
Present results are consistent with previous
(p,n) result.
21
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
  ds/dW.- Interference between IS and IV
  parts??- The reason is still unclear.

Describe experimental results except 8.92-MeV
state.
22
Inelastic Alpha Scattering

• Alpha scattering is suitable to investigate
  molecular states.
• Simple reaction mechanism.
• Only central interaction V0 contributes.
• Extract transition densities in the surface
  region for discrete states.
• Search for analog states of 03 in continuum
  region by means of MDA.
• Precise measurement of B(E2IS) for the 5/2-2
  state.

M. Itoh et al.
M. Itoh et al.
Beam time is scheduled in October.
23
Transition Strengths
Alpha cluster states are mainly excited by
isoscalar transitions.
IS transition strengths are important to study
the cluster structures.
g-decay measurements were extensively
performed, but world is not enough...
M1 IV parts are dominant (gIVs/gISs)228.6.
E0, E2 Sensitive to proton parts only.
For light NZ nuclei, mirror symmetry gives
missing parts, but for the other nuclei .....