H. Sakurai, S. Takeuchi, N. Aoi, H. Baba, S. Bishop, M. Ishihara, T. Kubo, T. Motobayashi, Y. YanagisawaN. Imai D. Suzuki, T. Nakao, H. Iwasaki, T. K. Onishi, M. K. Suzuki, Y. IchikawaS. OtaY. Togano, K. KuritaY. Kondo, T. Nakamura, T. Okumura

RIKENKEKTokyo U.CNS, Tokyo U.Rikkyo U.Titech

In collaboration with

Anomalously Hindered E2 Strengths in C16,18H. J. Ong

Upgraded Recoil Shadow Method

377 cm514 cm

HodoscopeNaI(Tl) ArrayBeam-line DetectorsEΔ E

F3PLF2PLPPAC

SecondaryBeam

Pb shield + Be target

16,18C Ejectiles

(x13)(x16)(x130)

5 mmt 60 mmt

1 mmt1 mmt

Experimental Setup @ RIPS (RIKEN)

L1 L2 L3 L4 L5 L6L7 L8 L9

L10

Pb

Be target

16,18C

NaI(Tl)

0 5cm

16,18 CBe

target

Measurements with/without Pb

Betarget

Measurements with/without Pb

Target at “Center”

Target at “Upstream”

◎

◎

Variety of measurements

◎ 130 NaI(Tl) detectors were used to compensate for the lower beam intensity.◎ Lifetime was determined by comparing the measured with the simulated , which is free of uncertainty in the angular distribution of γ rays.

iN Pbwo−

)exp(iDε

∑=

−=

N

i i

ii DD1

2

22 ))exp()sim((

σχ εε

FittingiN Pb-w

sim;τ( )iDε

Experiment

Simulation

Generation and detection of γ rays generated isotropically in CM frame Lorentz boost “detected” by NaI(Tl)

Number of full-energy peak

Beam info position on target, θ energy

Scattered particle info scattered θ energy

Responsefunction

+Ejectiles

( or )18CStep 1

Step 2

(72/79 AMeV)

ii NN /≡

Nw-Pb

Number of γ rays detected in i-th layer

i

γ γ

Deficiency:D (exp)iε

D (sim;τ)iε

Determination of mean lifetime

0

2

4

6

8

10

Ener

gy [M

eV]

14C 16C 18C 20C

(2 )+

0+ 0+ 0+ 0 +

(0 )+

2+ (2 )+

2+

3(+)4+2

1−0+3−

2−

0−

Sn

Sn

Sn

Sn

22C0 +Sn

Level schemes of even-even C isotopes

N. Imai et al, PRL 92, 062501 (2004)Recoil Shadow Method

SimulationExperiment

Data R

eduction & Results

Disc

ussio

n

R1/

R2

◎ 32 NaI(Tl) detectors were used.◎ Lifetime was determined by comparing the measured R1/R2(exp) with the simulated R1/R2(sim;τ), for which an angular distribution of the γ rays was assumed in the simulation.

D (exp)iε w-Pb wo-Pb

Mot

ivat

ion

Method & Experiment

Possible proton-shell

closure in C 14,16,18

B(E

2) [W

.U.]

Mass number

B(E

2) /

B(E

2)sy

s

Mass number

◎ Lifetime measurement of the 2 state in C

◎ Combined with the results from the inelastic proton scattering

See also

161+

Anomalously hindered E2 strength in C (as shown by in Fig. 1) 16

N. Imai et al, PRL 92, 062501 (2004)

Probing the quadrupole collectivity... Lifetime measurement Coulomb excitation

(model-dependent for Z<10)

Inelastic proton scattering

B(E2)

βpp’

βC

β n

+

DWBA

Fig. 2

H. J. Ong et al, PRC 73, 024610 (2006)

Neutron-dominant quadrupole collectivity in C (see Fig. 2) 16

Z. Elekes et al, PLB 586, 34 (2004)

S. Raman et al, ADNDT 78, 1 (2001)‡

While the significantdrops in E(2 ) from C to

C and C seem to suggest enhanced quadrupole collectivity,

we show that (i) the protons hardly contribute

to the E2 strength, and (ii) the excitations are (or very likely for the C case)

a neutron-dominant one(s).

QUESTION:

1+ 14

16 18

18

+

To determine the mean lifetime, we performed Monte Carlo simulationsusing the GEANT3(1) to determine , and(2) to generate response functions for use in fitting to deduce

D (exp)iε

D (sim;τ)iε

τ = 0,5, ... ,40 [ps]

Procedures for simulations:

Fig. 3

Fig. 4

RESULTS

Comparison with microscopic theoretical predictions:◎ Shell Model predicts proton-closed shell in C◎ AMD predicts opposite deformations in C◎ “No-core” Shell Model reproduces B(E2) values for the neutron-rich C quite well, when a small neutron effective charge en = 0.164e is assumed.Both SM and AMD look promisingin explaining the small B(E2) values;but which picture is correct? Moreexperimental data are necessary.For the immediate future, it will be interesting to see whether theB(E2) value for C increasesas predicted.

R. Fujimoto, Ph.D Thesis, UT (2003)H. Sagawa et al, PRC 70, 054316 (2004)Y. Kanada-En’yo, PRC 71, 014310 (2005)G. Thiamova et al, EPJA 22, 461 (2004)S. Fujii et al, PLB 650, 9 (2007)

J. K. Jewell et al, PLB 454, 181 (1999);E. Khan et al, PLB 490, 45 (2000)

16,18

16,18

14,16,18

The low E(2 ) and small B(E2) valueobserved for C, a trend observed alsoin C and O , indicate a possible neutron-dominant quadrupole collectivityin C.

18

18

16 20 ‡

‡

Determine the B(E2)

1+

RCNP, Osaka Univ.

16C

[W.u.][e2fm4][ps]1.5(1)(4)4.3(2)(10)18.9(9)(44)18C

B(E2)τ (21+)

0.26(5)(6)0.63(11)(15)77(14)(19)16Cd

0.6(2)(2)1.4(6)(4)34(14)(9)16Cc

1.0(2)(2)2.4(4)(6)19.6(30)(45)16Cb

1.1(1)(3)2.7(2)(7)17.7(16)(46)16Ca

Besides C, the mean lifetime τ( ) for C was also remeasured withtwo reaction channels. Moreover, angular distribution of γ rays, which was not determined in the previous work (PRL 92, 062501(2004)), was also measured and incorporated into an improved reanalysis of the previous data.(See Fig.5)

N. Imai et al, PRL 92, 062501 (2004)*

18 21+ 16

previous

C.-C Sahm et al, PRC 34, 2165(1986)M. E. Brandan, PRL 60, 784(1988)

Fig. 5a: inelastic channel @ 72 MeV/nucleonb: breakup channel @ 79 MeV/nucleonc: inelastic channel @ 40 MeV/nucleond: inelastic channel @ 40 MeV/nucleon; previous result *

e: LBL data; M. Wieldeking et al, PRL 100, 152501 (2008)

‡global systematics

4.3(2)(10) This Work

2.6(2)(7)

Fig. 7

Fig. 6

20

Small B(E2) values!!(See Fig.1)

SMDSHFAMD1AMD2NCSM 1.7(3)4.1(7)11.7(20)16Ce

Now available: Physical Review C 78, 014308 (2008)

mean lifetime, τ

Fig. 1

N. Imai et al, PRL 92, 062501 (2004)