Low-lying states in 11 B

Low-lying states in 11BCenter for Nuclear Study, University of Tokyo

KAWABATA TakahiroRCNP, Osaka University H. Fujimura, M. Fujiwara, K. Hara, K. Hatanaka,

M. Itoh, J. Kamiya, A. Tamii, M. Uchida, H.P. Yoshida

Department of Physics, Kyoto University

T. Ishikawa, M.. Nakamura, H. Sakaguchi, H. Takeda, Y. Yasuda, M. Yosoi

Department of Physics, Konan University

H. Akimune, K. Y. Hara

Department of Physics, Kyushu University

T. Noro, T. Wakasa

SPring-8 H. Toyokawa

Department of Physics, Osaka University

H. Fujita, Y. Fujita, Y. Shimbara, H. Ueno

Introduction

• A=11 mirror system.- M1 and GT transitions.

• Non-zero g.s. isospin.- Both T=1 and T=0 exist.

• Promising neutrino detection material.

- Selectivity for eand x.- Detection by one setup at one time. R.S. Raghavan et al., Phys. Rev. Lett. 57, 1801 (1989).

11 11

11 11

(C.C.(N

)B C B B C . . )

e

x x

e

Isovector (T=1) transitions were extensively studied,but there are few data on isoscalar (T=0) component.

M1 (GT) strengths provide important information on the nuclear structure.

Hadron ScatteringHadron scattering is a good measure for nuclear matrix elements.

(3He, t) … T = 1 only (Tz = 1)(d, d’) … T=0 only (Tz =0)(p, p’) … T = 1 and T = 0 (Tz = 0)

Simple reaction mechanism - Good linearity between d/d and B(ô).

Selectivity for the T = 1 and T = 0 components.

Spin observables give a good measure to separate J and T.

. . 3 2 1 2

. .

1 , 2

1 , 2 , 3 , 4

0

3 2 5 2

. . 3 2 3 2

0,1

0,1

0,, 2 1,1 , 3

g s J

J

J

g

T

Ts

g s T

We measured the three reactions to decompose the excitation modes.

ExperimentExperiment was performed at RCNP, Osaka University.

11B(3He, t) RCNP-E114 E= 450 MeV, lab= 0˚~14˚ - d/d

11B(d,d’) RCNP-E200E= 200 MeV, lab= 0˚~25˚- d/d, Ay, Ayy

11B(p, p’) RCNP-E137E=392 MeV, lab= 2˚~14˚- d/d, Ay, P, DNN

Charge Exchange ReactionsCharge exchange reaction provides B(GT) values.

22

( , ): Kinematic Factor , : Effective Interaction , : Distortion Factor from -decay strength, (IAS( )( ) 0.345 0.008 )1.0

g.s. g.s. ( ( )), ) (

BK E V V N N

BG F ZT N

V V BBd K E V N Nd

GT F

R2= |V/V|2 is a key ingredient for B(GT) determination.R2=8.24 (11) is widely used for (3He,t) reaction at 450 MeV.

FL int. suggests a smaller value R2=5.24 for A=11 system.

B(GT) from (3He,t) reactions

Ex (MeV)B(GT)Exp

(R2=8.24)B(GT)Exp

(R2=5.24)

0.000 (3/2) 0.345±0.008 0.345±0.008

2.125 (1/2) 0.401±0.032 0.461±0.026

4.445 (5/2) 0.453±0.029 0.521±0.031

5.020 (3/2) 0.487±0.029 0.551±0.036

8.104 (3/2) 0.003 0.004

8.420 (5/2) 0.398±0.031 0.466±0.045

B(GT) for excited states were obtained from DWBA analysis.

Choice of the R2 value changes 15% normalization.

Elastic and inelastic deuteron scattering

• Optical model parameters were determined for the macroscopic analysis.

- Modify the optical potential to obtain a reasonable description on the 2+ transition.

- Replace q by 0.78q for the 0+ transition.

• Fit the 1+ transition by the spherical Bessel function.

2 2

0 0 2 2(1 ) ( ) ( )d d j qR j qR

Deuteron Inelastic Scattering12C(d, d’) is used as a reference for J decomposition.

Ex (MeV) B()Exp

2.12 0.040±0.006

4.44 --------

5.02 0.043±0.008

8.92 0.016±0.004

• B()s for 2.12 and 5.02-MeV states were successfully extracted.

• B(E2) for 4.44-MeV state is strong and obscures the M1 strength.

• 8.56 MeV seems to be a cluster state.

Proton Inelastic ScatteringDWBA calculation

- Franey-Love - H.O. single particle state - Strengths from (d,d’) and (3He,t)

Blue … No parameters adjusted.

Describe experimental results except DNN

1 sin cosm mM IS IV

- and are from SM calcSearch and .

ulation.- m

IS IV

Red … Best fit.

DNN is sensitive to the mixing angle m.

Comparison with Shell model

B(): no problem.

(3He, t) and (d,d’) results are consistent with -decay result.

B() for 2.12 and 5.02 strongly suppressed in the (p, p’) result.. - uncertainty in the DWIA calculation ??

Experiment Yellow .. From (3He, t) and (d, d’)

Red .. From (p, p’) with Franey-Love

Gray .. From -decay width(-MeV state only)

Shell modelBlack .. Cohen-Kurath (CKPOT, 0ħ)Red .. Fujimoto-Otsuka (2ħ)

Measured B() and B() are compared with SM calculation.

Test of DWBA calculation

Black … Franey-Love 425 MeV

Blue … Franey-Love-Tamii 425 MeV (Modify Vand V using 12C(p,p’) data.)

Red … Melbourne (Density dependent)

• FL and FLT provide good description.

• ML is less reliable.

Summary

• M1 transition strengths in 11B are studied by measuring the 11B(3He,t), 11B(d, d’), and 11B(p, p’) reactions.

• B(GT) is obtained from the 11B(3He, t) cross section.

• B() for 2.12 and 5.02-MeV states were successfully obtained from the 11B(d, d’) data. - (3He, t) and (d, d’) are consistent with -decay results

• B() from (p, p’) is good, but B() ….. - Systematic uncertainty on B() is very large.