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

Measurements of B(E2) transition rates in neutron rich carbon isotopes, 16 C- 20 C. Paul Fallon Lawrence Berkeley National Laboratory 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 EFES-NSCL Workshop on Perspectives on the modern shell model and related experimental topics. MSU Feb 4-6, 2010

Energy Levels in a Woods Saxon Potential In a well bound nucleus steady evolution of energy levels in a 1 body potential modified by 2-body NN interaction (s.t, Tensor) 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 states A.Bohr and B.R. Mottelson, Nuclear Structure, vol. 1

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 ( 14 C) N=16 dripline 22 C (cf 24 O) Occupation of n(s 1/2 ) (A 15) Weak binding ( 15,17,19 C) F.Rintaro. PhD Thesis (U.Tokyo 2002) Data from A. Ozawa, et al., NPA691, 599 (2001). Interaction cross sections for carbon isotopes. N > 8 g.s. large ns 1/2 component 2 + dominant neutron excitation B(E2) wavefunction; charge distribution; e n (eff) 8 neutrons

Disappearance of the N = 14 shell gap in the carbon isotopic chain M.Staniou et al., PHYSICAL REVIEW C 78, 034315 (2008) Oxygen Carbon Constant 2 + TBME V pn pp 1/2 - nd 5/2 attracts pp 1/2 - ns 1/2 repels

N=10: 2n valence nuclei 16 C and 18 O 16 C and 18 O 2 + state - dominant neutron excitation 18 O: B(E2) = 9.5(3) e 2 fm 4 = 3.2 W.u. 16 C: B(E2) = 4.15(73) e 2 fm 4 = 1.73 W.u. Core polarization ~ Z B(E2) 18 O *(6/8) 2 = 1.8 W.u 2 1 n ( 2 ds p ( p 2 ~ B(E2) 16 C

The 16 C B(E2) components p ( p 2 2 + B(E2) = 1/(2J i +1) * M n *e n + M p *e p 2 n ( ds 2 2 + B(E2) V int 0 + 15 C d 5/2 s 1/2 transition; derive e n ~ 0.4 (assume neutrons only) e n ~ 0.4 16 C B(E2;USD) ~ 3 e 2 fm 4 proton admixture B( E2) USD E2USD p 2 E2 p 4.15 e 2 fm 4 from 16 C 3 e 2 fm 4 from USD model 3.7 e 2 fm 4 from 14 C 2 2 ( 2 ( ds 0. p p 2 16 1 ; C 0.97n 24 94% 6% 2 Interaction matrix element V in β between proton holes and neutrons is ~ 1 MeV. Consistent with p -1 and (sd) 4 value in 19 F Arima and Hamamoto, Ann. Rev. Nucl. Sci. 21 (1971).. from M.Wiedeking et al., PRL 100, 152501 (2008)

Effective Charges B(E2) = 1/(2J i +1) * M n *e n + M p *e p 2 S. Fujii et al. Phys. Lett. B 650 (2007) 9 14 Effective charge a measure of coupling between valence particles and core (binding) Model-space dependent 16,18 C B(E2) strong dependence on e n (eff) neutron excitation 14 C expt 3.74(50) 14 C B(E2) weak dependence on e n (eff) proton excitation B(E2) constrains e(eff) n,p

Isospin Dependence of Effective Charges (Bohr Mottelson Vol 2) Sagawa et al PRC 70 (2004) 054316 E pol ~ Z/A e n Carbon Isotopes (A)

16 C: B(E2, 2 + 0 + ) 16 C Wiedeking et al 16 C Ong et al 16 C Imai et al

B(E2) [e 2 fm 4 ] Carbon Isotopes B(E2) Systematics B(E2) = 1/(2J i +1) * Mn*e n + Mp*e p 2 Shell Model H. Sagawa Ong Wiedeking Ong Elekes 12 C 14 C 16 C 18 C 20 C Lifetime measurement Inelastic scattering on C, Pb

Z. Elekes et al. PHYSICAL REVIEW C 79, 011302(R) (2009) B(E2) = 1/(2J i +1) * M n *e n + M p *e p 2 e n Carbon Isotopes (A)

A campaign of experiments (Feb 2009) to measure the lifetime of the 2 + state in 16,18,20 C 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

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

Carbon B(E2: 2 + 0 + ) Systematics (1) (2) C C C C C C a) b) c) (1) This work M.Petri (LBNL) (2) This Work P.Voss (MSU)

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

20 C Spectra: 22 O-2p 1620 kev

20 C 2 + State Mean Lifetime t = 10(3) ps (preliminary) B(E2) ~ 7.2 +3.1/-1.7 e 2 fm 4 30 degree detectors data 6ps 15ps 10ps 2 for 30 and 140 degree detectors 140 degree detectors Lifetime (ps)

Carbon B(E2: 2 + 0 + ) Systematics (1) x (2) x (3) x Shell Model: B.A.Brown WBP interaction A-dependent e(p,n) a) b) c) (1) This work M.Petri (LBNL) (2) This Work P.Voss (MSU) (3) This work M.Petri (LBNL)

Z. Elekes et al. PHYSICAL REVIEW C 79, 011302(R) (2009) B(E2) = 1/(2J i +1) * M n *e n + M p *e p 2 This work

Sagawa PRC 70, 054316 (2004) e(p) B(E2) = M p e p + M n e n 2 /(2J i +1) e(n) smooth dependence on A 20 C 18 C (expt) 20 C (LBL/MSU) 16 C (expt) 20 C expected 18 C 16 C 20 C (Elekes) 15 C (expt) p-sd shell model H.O wavefunctions WBP interaction (Alex Brown)

B(E2) [e 2 fm 4 ] Carbon Isotopes B(E2) Systematics F.Rintaro. PhD Thesis (U.Tokyo 2002) Proton ESPE (Z=6) Shell Model H. Sagawa 12 C 14 C 16 C 18 C 20 C proton neutron proton 2 + state component Reduced p 3/2 -p 1/2 gap

1-Proton Knockout Spectroscopic Factors A+1 N A C 2 1 n ( 2 ds p ( p 2 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 ( 16 C) ~ 0.2 ~5% proton occ. Calculated s (0 + /2 + Measured s (0 + /2 + 13% 21% 57% 10% 20% ( 18 C ) ~ 0.3 ~8% proton occ. ( 20 C ) ~ 0.5 ~23% proton occ. 20 C 2 + is a mixed state

Shell Model (A. Brown) M_p M_n 16C 1.54 9.22 18C 1.9 11.11 20C 3.33 11.65 20 C M_n remains high Neutron Contribution Oxygen Carbon 2 1 n ( 2 ds p ( p 2 Seniority Scheme B(E2, n) = [n (2j+1-n)/(2(2j-1)]* B(E2, n=2) Neutron shell closed at 14 C (N=8) and 22 C (N=16) 2j+1=8 (ns 1/2 +nd 5/2 ) 16 C M(E2, n=2) ~ 20 C M(E2, n=6) 22 C M(E2, n=8) ~ 0 (if N=16 closed) 0 (if N=16 broken)

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 Experiments with Fast beams - most neutron-rich RDDS (DSAM lineshape?) lifetimes good energy resolution efficiency GRETINA has efficiency and resolution to extend experimental reach

Summary 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 16 C 20 C (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: p 1/2,3/2 (need to know this to understand (de)coupling)