Paul Fallon

Lawrence Berkeley National Laboratory

Measurements of B(E2) transition rates in neutron rich carbon isotopes, 16C-20C.

EFES-NSCL Workshop on

Perspectives on the modern shell model and related experimental topics.

MSU Feb 4-6, 2010

Marina Petri, R. M. Clark, M. Cromaz, S. Gros, H. B. Jeppesen,

I-Y. Lee, A. O. Macchiavelli, S. Paschalis

LBNL

K. Starosta, T. Baugher, D. Bazin, H. Crawford, A. Gade, Grinyer, S. McDaniel,

D. Miller, A. Ratkiewicz, P. Voss, K. Walsh, D. Weisshaar

NSCL/MSU

M. Wiedeking

LLNL

A. Dewald, M. Hackstein, W. Rother

Cologne

Energy Levels in a Woods Saxon Potential

A second distinct effect is due to

weakly bound levels

• low l levels (s, p) extended

wavefunctions (“halos”)

• Spatially extended valence particles

can have less influence on the core

(“decoupled”)

• Coupling to continuum statesA.Bohr and B.R. Mottelson, Nuclear Structure, vol. 1

In a well bound nucleus

• steady evolution of energy levels in a

1 body potential

• modified by 2-body NN interaction

(s.t, Tensor)

PHYSICAL REVIEW C 76, 054319 (2007)

Nilsson diagrams for light neutron-rich nuclei with weakly-bound neutrons

Ikuko Hamamoto

PHYSICAL REVIEW C 76, 054319 (2007)

Nilsson diagrams for light neutron-rich nuclei with weakly-bound neutrons

Ikuko Hamamoto

Carbon Nuclei

• N=8 closed p-shell (14C)

• N=16 dripline 22C (cf 24O)

• Occupation of n(s1/2) (A≥15)

• Weak binding (15,17,19C)

N > 8

g.s. large ns1/2 component

2+ dominant neutron excitation

B(E2) wavefunction; charge distribution; en(eff)

F.Rintaro. PhD Thesis (U.Tokyo 2002)Data from A. Ozawa, et al., NPA691, 599 (2001).

8 neutrons

Interaction cross sections for

carbon isotopes.

Oxygen Carbon

M.Staniou et al., PHYSICAL REVIEW C 78, 034315 (2008)

Disappearance of the N = 14 shell gap in the carbon isotopic chain

TBME Vpn

pp1/2 - nd5/2 attracts

pp1/2 - ns1/2 repels

Constant 2+

16C and 18O 2+ state - dominant neutron excitation

18O: B(E2) = 9.5(3) e2fm4

= 3.2 W.u.

16C: B(E2) = 4.15(73) e2fm4

= 1.73 W.u.

Core polarization ~ Z

B(E2)18O *(6/8)2 = 1.8 W.u

~ B(E2) 16C

N=10: 2n valence nuclei 16C and 18O

( ( 22

12 pds pn

Interaction matrix element V

in β between proton holes

and neutrons is ~ 1 MeV.

→ Consistent with p-1 and

(sd)4 value in 19F

Arima and Hamamoto, Ann.

Rev. Nucl. Sci. 21 (1971).

222 22)2( pEpUSDEUSDEB

3 e2fm4 from USD model 3.7 e2fm4 from 14C4.15 e2fm4 from 16C

( ( 2216

1 24.097.0;2 pdsC pn

94% 6%

15C d5/2s1/2 transition; derive en ~ 0.4

(assume “neutrons” only)

en ~ 0.4 16C B(E2;USD) ~ 3 e2fm4

proton admixture

The 16C B(E2) – “components”

Vint

2+

2+

( 2dsn

( 2pp

0+

B(E2) = 1/(2Ji+1) * | Mn*en + Mp*ep |2

B(E2)

…. from M.Wiedeking et al., PRL 100, 152501 (2008)

Effective Charges

• 16,18C B(E2) strong dependence on en(eff)

neutron excitation

• 14C B(E2) weak dependence on en(eff)

proton excitation

B(E2) “constrains” e(eff)n,p

S. Fujii et al. Phys. Lett. B 650 (2007) 9–14

14C expt 3.74(50)

B(E2) = 1/(2Ji+1) * | Mn*en + Mp*ep |2

• Effective charge – a measure of

coupling between valence particles

and core (binding)

• Model-space dependent

Isospin Dependence of Effective Charges(Bohr Mottelson Vol 2)

Carbon Isotopes (A)

en

Epol ~ Z/A

Sagawa et al PRC 70 (2004) 054316

16C: B(E2, 2+ → 0+)

16C Wiedeking et al16C Ong et al

16C Imai et al

B(E

2)

[e2fm

4]

12C 14C 16C 18C 20C

Ong

Wiedeking

Ong

Shell Model

H. Sagawa

Carbon Isotopes B(E2) Systematics

B(E2) = 1/(2Ji+1) * | Mn*en + Mp*ep |2

Elekes

Inelastic scattering on C, Pb

Lifetime measurement

B(E2) = 1/(2Ji+1) * | Mn*en + Mp*ep |2

Z. Elekes et al. PHYSICAL REVIEW C 79, 011302(R) (2009)

Carbon Isotopes (A)

en

A campaign of experiments (Feb 2009) to measure the lifetime of the

2+ state in 16,18,20C was carried out at the NSCL

Lifetimes were measured using the Recoil Distance Method with fast

RI beams (v ~0.4c)

2+ states were populated using the knockout reactions

Preliminary 16C 2+ Tau = 11.9 (1) ps

16C 2+ State Mean Lifetime

a)b)c)

C C C C C C

Carbon B(E2: 2+→ 0+) Systematics

(1)

(2)

(1) This work – M.Petri (LBNL)

(2) This Work – P.Voss (MSU)

20C Simulation Spectra: 22O-2p removal, 2+ lifetimes 10,15, 20 ps

10 ps

15 ps

20 ps

1620 keV

20C Spectra: 22O-2p

t = 10(3) ps (preliminary)

B(E2) ~ 7.2 +3.1/-1.7 e2fm4

Lifetime (ps)

2 for 30 and 140 degree detectors

30 degree detectors

140 degree detectors

20C 2+ State Mean Lifetime

data6ps

15ps10ps

a)b)c)

Carbon B(E2: 2+→ 0+) Systematics

x

xx

Shell Model: B.A.Brown

WBP interaction

“A-dependent” e(p,n)(1)

(2)

(1) This work – M.Petri (LBNL)

(2) This Work – P.Voss (MSU)

(3) This work – M.Petri (LBNL)

(3)

B(E2) = 1/(2Ji+1) * | Mn*en + Mp*ep |2

Z. Elekes et al. PHYSICAL REVIEW C 79, 011302(R) (2009)

This work

e(p)

15C (expt)

16C

18C

20C

B(E2) = |Mpep + Mnen|2 /(2Ji+1)

e(n) smooth dependence on A

16C (expt)

20C(Elekes)

18C (expt)

20C “expected”

p-sd shell model H.O wavefunctions WBP interaction (Alex Brown)

Sagawa PRC 70, 054316 (2004)

20C (LBL/MSU)

B(E

2)

[e2fm

4]

12C 14C 16C 18C 20C

Shell Model

H. Sagawa

Carbon Isotopes B(E2) Systematics

“↑ proton” “neutron” “↑ proton”

2+ state component

Proton ESPE (Z=6)

F.Rintaro. PhD Thesis (U.Tokyo 2002)

• Reduced p3/2-p1/2 gap

1-Proton Knockout Spectroscopic FactorsA+1N AC

Calculated

s (0+/2+

13% 21% 57%

Measured

s (0+/2+

10% 20%

( ( 22

12 pds pn

In 1-p knockout population of 2+

proceeds through the proton component

SF (2+/0+ = s (2+/0+ ~ 2* 5/2

Calculated amplitudes and occupations

(16C) ~ 0.2 ~5% proton occ.

( 18C ) ~ 0.3 ~8% proton occ.

( 20C ) ~ 0.5 ~23% proton occ.

20C 2+ is a mixed state

Neutron Contribution

Shell Model (A. Brown)M_p M_n

16C 1.54 9.2218C 1.9 11.1120C 3.33 11.65

( ( 22

12 pds pn

Seniority Scheme B(E2, n) = [n (2j+1-n)/(2(2j-1)]* B(E2, n=2)

Neutron shell closed at 14C (N=8) and 22C (N=16) 2j+1=8 (ns1/2+nd5/2)

16C M(E2, n=2) ~ 20C M(E2, n=6)

22C M(E2, n=8) ~ 0 (if N=16 closed) 0 (if N=16 broken)

20C M_n remains high

Oxygen Carbon

• Experiments with Fast beams

- most neutron-rich

• RDDS (DSAM lineshape?) lifetimes

• good energy resolution

• efficiency

GRETINA has efficiency and resolution

to extend experimental reach

Future … GRETINA

• GRETINA

• An array of highly segmented

Germanium Detectors

• Measure location and energy of

g-ray interactions

• Gamma-ray tracking

• 1p coverage

• Experiments in 2011

• Influence of weak binding

–Coupling to continuum, extended wavefunctions, …

• Transition rates can, in some circumstances, provide a way to isolate new effects of weak binding

• Extracted transition rates from 16C 20C (near dripline)

– Quantitative test of model(s) - require a consistent description from stable ”dripline” nuclei

• No evidence (here) for dramatic changes

– shell model appears to be able to track 2+ energies and B(E2)

– Mixed 2+ implies n-p coupling

Proton contributions important - measure proton spectroscopic factor: p1/2,3/2 (need to know this to understand (de)coupling)

Summary