Stellar Electron-Capture Rates Accessed via the ( t , 3 He+ ) - - PowerPoint PPT Presentation

Shumpei Noji

(NSCL/MSU →) RCNP/Osaka

Stellar Electron-Capture Rates Accessed via the (t,3He+γ) Reactions

GRETINA at NSCL/MSU

βþ Gamow-Teller Transition Strengths from 46Ti and Stellar Electron-Capture Rates

• S. Noji,1,2,* R. G. T. Zegers,1,2,3 Sam M. Austin,1,2,3 T. Baugher,1,3 D. Bazin,1 B. A. Brown,1,3 C. M. Campbell,4
• A. L. Cole,5 H. J. Doster,1,3 A. Gade,1,3 C. J. Guess,6,7 S. Gupta,8 G. W. Hitt,9 C. Langer,1,2 S. Lipschutz,1,3 E. Lunderberg,1,3
• R. Meharchand,10 Z. Meisel,1,2,3 G. Perdikakis,11,1 J. Pereira,1 F. Recchia,1 H. Schatz,1,2,3 M. Scott,1,3 S. R. Stroberg,1,3
• C. Sullivan,1,2,3 L. Valdez,1 C. Walz,1 D. Weisshaar,1 S. J. Williams,1 and K. Wimmer11,1

1National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA 2Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, Michigan 48824, USA 3Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA 4Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 5Physics Department, Kalamazoo College, Kalamazoo, Michigan 49006, USA 6Department of Physics and Applied Physics, University of Massachusetts Lowell, Lowell, Massachusetts 01854, USA 7Department of Physics and Astronomy, Rowan University, Glassboro, New Jersey 08028, USA 8Indian Institute of Technology Ropar, Nangal Road, Rupnagar, Punjab 140001, India 9Department of Applied Mathematics and Sciences, Khalifa University of Science, Technology, and Research,

P.O. Box 127788 Abu Dhabi, UAE

10Neutron and Nuclear Science Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 11Department of Physics, Central Michigan University, Mt. Pleasant, Michigan 48859, USA

(Received 5 April 2014; published 25 June 2014) The Gamow-Teller strength in the βþ direction to 46Sc was extracted via the 46Tiðt; 3He þ γÞ reaction at 115 MeV=u. The γ-ray coincidences served to precisely measure the very weak Gamow-Teller transition to a final state at 991 keV. Although this transition is weak, it is crucial for accurately estimating electron- capture rates in astrophysical scenarios with relatively low stellar densities and temperatures, such as presupernova stellar evolution. Shell-model calculations with different effective interactions in the pf shell- model space do not reproduce the experimental Gamow-Teller strengths, which is likely due to sd-shell

• admixtures. Calculations in the quasiparticle random phase approximation that are often used in

astrophysical simulations also fail to reproduce the experimental Gamow-Teller strength distribution, leading to strongly overestimated electron-capture rates. Because reliable theoretical predictions of Gamow-Teller strengths are important for providing astrophysical electron-capture reaction rates for a broad set of nuclei in the lower pf shell, we conclude that further theoretical improvements are required to match astrophysical needs.

DOI: 10.1103/PhysRevLett.112.252501 PACS numbers: 23.40.-s, 25.55.Kr, 26.30.Jk, 27.40.+z

Introduction.—Electron-capture (EC) rates on nuclei are essential ingredients for the modeling of core-collapse and thermonuclear supernovæ (SNe) [1]. In addition, EC rates are important for the description of crustal heating [2] and cooling [3] processes in neutron stars. The estimation of EC rates requires detailed knowledge of Gamow-Teller (GT) transition strengths [BðGTÞ] in the βþ direction, associated with the transfer of spin (ΔS ¼ 1), isospin (ΔT ¼ 1), and no orbital angular momentum (ΔL ¼ 0). ECs on a large number of nuclei, primarily with 40 ≤ A ≤ 120, play a strengths for nuclei in the lower pf shell [with the neutron (N) and proton number (Z) just exceeding the magic number 20]. It is shown that leading configuration-interaction models in which the model space is truncated to excitations within the pf shell fail to reproduce the data. Calculations in the quasiparticle random phase approximation (QRPA), which are also frequently used for astrophysical purposes, fail to reproduce the data as well. GT strengths can be measured in β-decay experiments, but they only provide access to a limited Q-value window. PRL 112, 252501 (2014) P H Y S I C A L R E V I E W L E T T E R S

week ending 27 JUNE 2014

Contents

• 1. Stellar electron captures


& experimental approach

• 2. (t,3He+γ) experiments
• 3. Gamow-Teller strengths


& electron-capture rates

PHYSICAL REVIEW C 92, 024312 (2015)

Gamow-Teller transitions to 45Ca via the 45Sc(t,3He + γ ) reaction at 115 MeV/u and its application to stellar electron-capture rates

• S. Noji,1,2,* R. G. T. Zegers,1,2,3 Sam M. Austin,1,2 T. Baugher,1,3,† D. Bazin,1 B. A. Brown,1,2,3 C. M. Campbell,4
• A. L. Cole,2,5 H. J. Doster,1,3 A. Gade,1,3 C. J. Guess,6,‡ S. Gupta,7 G. W. Hitt,8 C. Langer,1,2,§ S. Lipschutz,1,2,3
• E. Lunderberg,1,3 R. Meharchand,9,∥ Z. Meisel,1,2,3 G. Perdikakis,1,2,10 J. Pereira,1,2 F. Recchia,1,¶ H. Schatz,1,2,3 M. Scott,1,3
• S. R. Stroberg,1,3,# C. Sullivan,1,2,3 L. Valdez,11 C. Walz,1,** D. Weisshaar,1 S. J. Williams,1 and K. Wimmer1,10,††

1National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA 2Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, Michigan 48824, USA 3Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA 4Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 5Physics Department, Kalamazoo College, Kalamazoo, Michigan 49006, USA 6Department of Physics and Applied Physics, University of Massachusetts Lowell, Lowell, Massachusetts 01854, USA 7Indian Institute of Technology Ropar, Nangal Road, Rupnagar, Punjab 140001, India 8Department of Applied Mathematics and Sciences, Khalifa University of Science, Technology, and Research,

P.O. Box 127788 Abu Dhabi, UAE

9Neutron and Nuclear Science Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 10Department of Physics, Central Michigan University, Mt. Pleasant, Michigan 48859, USA 11Orange High School, Orange, New Jersey 07050, USA

(Received 19 March 2015; published 17 August 2015)

SN, et al., PRL 112, 252501 (2014) SN, et al., PRC 92, 024312 (2015)

Electron Captures in Supernovæ

• Stellar electron captures (EC)
• Takes place in stellar interiors: high T
• Important process for supernovæ (SNe)
• Neutronizes stellar core, decreases electron abundance
• Reduces electron degeneracy pressure (which supports stars) → Leads to explosion

Stellar EC is a key to supernova evolution. cf.) Terrestrial electron capture bound (orbital) electrons

A ZX A Z−1Y

e−

νe

free electrons in hot plasma

Stellar Electron Captures

• Stellar electron captures (EC)
• Dominated by Gamow-Teller transitions
• ΔL = 0, ΔS = 1, ΔT = 1
• Capture of free electrons in hot plasma
• Can get excited to high Ex states incl. GTGR
• Electrons: Fermi-Dirac distribution
• Thermal ensemble of initial states
• ECs take place from excited states
• Many nuclei play an important role
• Majority are unstable nuclei

A ZX A Z−1Y

GTGR

Ex(AY)

10 5

Ee (MeV)

ρYe = 109 g/cm3

T = 10 × 109 K UF kBT

Impossible to measure even a sizable fraction of cases

• Accurate theory that constrains key model parameters
• Experimental information for most crucial cases (importantly contributing nuclei)


to guide and test development of theory

Sensitivity Study: Importance for SN Collapse

• Time evolution of the electron fraction in CCSNe center

arXiv:1508.07348v1, ApJ Chris Sullivan (NSCL) Evan O’Connor (NCSU) Remco G. T. Zegers (NSCL) Thomas Grubb (NSCL) Sam M. Austin (NSCL) Y

e

( s e c

• 1

) 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 10−9 10−8 10−7 10−6 10−5

−4

10 10−3 10−2 10−1 10 0 10 1

• 50-40 -30
• 20
• 10

total ~ l

• w

e r s d g s h e l l ~sd+pf shells ~s+p shells ~upper sdg + h shell

• 100

t - tb (msec) 5<A≤ 25 25<A≤ 65 65<A≤ 105 105<A≤ 145 145<A≤ 185 185<A≤ 225 Total Ye

Most important are n-rich pf & sdg-shell nuclei. Sensitivity of late SN evolution to electron-capture rates Identify most critical experiments
 to be performed in the future

1 2 5 10 20 50 1 5 2 10 50 20 100200 ˆ

σexp(t,3He) at 115A MeV

ˆ

σexp(3He,t) at 140A MeV

Fit to ˆ

σexp(3He,t) at 140A MeV

extrapolated A ˆ

σGT(A) (mb/sr)

Experimental Approach to Stellar Electron Captures

• β decays
• Strength B(GT) from life time
• Q-value restrictions
• Charge-exchange reactions
• Accessible to high Ex states
• Reliable B(GT) extraction from cross section


→ Proportionality


• T. N. Taddeucci et al., Nucl. Phys. A469 (1987) 125

• G. Perdikakis et al., Phys. Rev. C 83, 054614 (2011)

unit cross section: calibrated for (t,3He)

ˆ

σGT = 109/A0.65 σ∆L=0(0◦) ≈ ˆ σGTB(GT)

CE reactions on important pf-shell nuclei
 can be a powerful tool to study ECs

A ZX A Z−1Y

GTGR

β decay

Ex(AY)

A ZX A Z−1Y

GTGR

β decay

CE Ex(AY)

Charge-Exchange Reactions on pf-shell Nuclei

• B(GT) in pf-shell nuclei
• Studied with intermediate-energy CE reactions in β+ direction: (n,p), (d,2He), (t,3He)

A systematic study of EC rates: A. L. Cole et al., PRC 86, 015809 (2012) (p,n) inverse kinematics: M. Sasano et al., PRL 107, 202501 (2011), PRC 86, 034324 (2012)

• Shell models do generally well in predicting B(GT)


GXPF1 (M. Honma et al., EPJ A25, 499 (2005))
 KB3G

(A. Poves et al., NP A694, 157 (2001))


but significant deficiencies possible

• In light nuclei pf & sd mixing 


can affect low-lying states
 (not considered there)

20 20 28 28

60Ge 61Ge 62Ge 63Ge 64Ge 65Ge 66Ge 67Ge 68Ge 69Ge 60Ga 54Zn 55Cu 48Ni 50Co 46Fe 46Mn 44Cr 43V 42Ti 41Sc 40Ca 39K 40K 41K 42K 43K 44K 45K 46K 47K 48K 49K 50K 51K 52K 53K 54K 55K 56K 41Ca 42Ca 43Ca 44Ca 45Ca 46Ca 47Ca 48Ca 49Ca 50Ca 51Ca 52Ca 53Ca 54Ca 55Ca 56Ca 57Ca 42Sc 43Sc 44Sc 46Sc 47Sc 48Sc 49Sc 50Sc 51Sc 52Sc 53Sc 54Sc 55Sc 56Sc 57Sc 58Sc 43Ti 44Ti 45Ti 47Ti 48Ti 49Ti 50Ti 51Ti 52Ti 53Ti 54Ti 55Ti 56Ti 57Ti 58Ti 59Ti 44V 45V 46V 47V 48V 49V 50V 51V 52V 53V 54V 55V 56V 57V 58V 59V 60V 45Cr 46Cr 47Cr 48Cr 49Cr 50Cr 51Cr 52Cr 53Cr 54Cr 55Cr 56Cr 57Cr 58Cr 59Cr 60Cr 61Cr 48Mn 49Mn 50Mn 51Mn 52Mn 53Mn 54Mn 55Mn 56Mn 57Mn 58Mn 59Mn 60Mn 61Mn 62Mn 47Fe 48Fe 49Fe 50Fe 51Fe 52Fe 53Fe 54Fe 55Fe 56Fe 57Fe 58Fe 59Fe 60Fe 61Fe 62Fe 63Fe 51Co 52Co 53Co 54Co 55Co 56Co 57Co 58Co 59Co 60Co 61Co 62Co 63Co 64Co 49Ni 50Ni 51Ni 52Ni 53Ni 54Ni 55Ni 56Ni 57Ni 58Ni 59Ni 60Ni 61Ni 62Ni 63Ni 64Ni 65Ni 56Cu 57Cu 58Cu 59Cu 60Cu 61Cu 62Cu 63Cu 64Cu 65Cu 66Cu 55Zn 56Zn 57Zn 58Zn 59Zn 60Zn 61Zn 62Zn 63Zn 64Zn 65Zn 66Zn 67Zn 61Ga 62Ga 63Ga 64Ga 65Ga 66Ga 67Ga 68Ga

46Ti 45Sc

Charge-Exchange Reactions on pf-shell Nuclei

s1/2 s1/2 g9/2 protons neutrons [2] [8] [20] [28] [40] [50] d3/2 d5/2 p3/2 p1/2 p3/2 p1/2 f7/2 f5/2

46 22Ti

40Ca

→ 46

21Sc

• B(GT) in pf-shell nuclei
• Studied with intermediate-energy CE reactions in β+ direction: (n,p), (d,2He), (t,3He)

A systematic study of EC rates: A. L. Cole et al., PRC 86, 015809 (2012) (p,n) inverse kinematics: M. Sasano et al., PRL 107, 202501 (2011), PRC 86, 034324 (2012)

• Shell models do generally well in predicting B(GT)


GXPF1 (M. Honma et al., EPJ A25, 499 (2005))
 KB3G

(A. Poves et al., NP A694, 157 (2001))


but significant deficiencies possible

• In light nuclei pf & sd mixing 


can affect low-lying states
 (not considered there)

• This study
• Lightest pf nuclei 46Ti & 45Sc
• SM deficiency may be pronounced
• Specific interests:


pre-SN stars, neutron-star crustal heating

• B(GT+) in 46Sc & 45Ca


via the (t,3He) reaction

EC Rates: Importance of Detailed Low-lying Structure

• Electron-capture rates
• Phasespace
• Decreases as Ex becomes higher
• Increases as temp. & density become larger
• Contrib. from low-lying strength is important
• In particular at low temp. & density
• This study

0.0 1 2 3 4 5 6 7 8 9 10 0.2 0.4 0.6 0.8 1.0 Phasespace (normalized) Excitation energy (MeV)

ρYe = 1010 g/cm3

T = 10 × 109 K

(t,3He) “wide” Ex range (Ex ≤ 25 MeV) “high” resolution (a few 100 keV) γ rays more precise* Ex (≲ 10 keV) for low-lying states (≲ a few MeV)

λEC(T, ρ) = const.

• i,j

fij(T, ρ) Bij(GT) transition strength

* level structure may need to be known

Experiment

10 m National Superconducting Cyclotron Laboratory Michigan State University A1900 Fragment Separator S800 Spectrograph K500 K1200 production target 9Be 3525 mg/cm2 primary beam 16O 150 MeV/u, 150 pnA reaction target 46Ti, 45Sc 10 mg/cm2 secondary beam 3H 115 MeV/u, 5 Mpps, >99%

• 46Ti, 45Sc(t,3He+γ)46Sc at 115 MeV/u

Experiment

Cathode Readout Drift Chambers (CRDCs) plastic scintillator

3He

ejectile (ΔE, TOF) (x, y, a, b)

3H (triton)

beam

115 MeV/u ~5 Mcps, >99%

46Ti/45Sc

target

10 mg/cm2

• 46Ti, 45Sc(t,3He+γ)46Sc at 115 MeV/u
• S800 + GRETINA
• Forward kinematics
• 3H beam + stationary 46Ti/45Sc targets
• Missing mass method
• Ex in 46Sc & 45Ca 


→ d2σ/dθdEx (0 MeV ≤ Ex ≤ 25 MeV, 0° ≤ θcm ≤ 6°)

• Dispersion-matching beam transport


→ ΔE ~ 300 keV (FWHM) (w/o momentum measurement)

Excitation Energy Spectra

• Multipole Decomposition Analysis
• Experimental data points fitted


with sum of DWBA cross sections

• DWBA code FOLD/DWHI


for heavy-ion charge-exchange


[double-folding & microscopic form factor]

• Extract each ΔJπ component


(GT, dipole, quadrupole,...)


1 2 3 4 5 0.1 1 10 1 2 3 4 5 (deg)

cm

θ (mb/sr/MeV) E d Ω /d σ

2

d = 3.1 MeV

x

E = 10.0 MeV

x

E GT GT quadrupole quadrupole dipole dipole data best fit Example

σcalc(θcm, Ex) =

• ∆Jπ

a∆Jπσcalc

∆Jπ(θcm, Ex)

fit param.

Gamow-Teller component needs to be extracted

2.11◦ 3.80◦ 5.80◦

46Ti(t, 3He)46Sc

E = 115 MeV/u

θcm = 0.67◦

Data

∆L = 0 ∆L = 1 ∆L

5 10 15 d2σ/dΩdEx (mb/sr/MeV) Ex(46Sc) (MeV) 1 2 3 4 5 1 2 3 1 2 1 2

• Refs. T. N. Taddeucci et al., Nucl. Phys. A469 (1987) 125

• G. Perdikakis et al., Phys. Rev. C 83, 054614 (2011)

B(GT) Distribution

• B(GT) distribution from experiment
• GT Proportionality

ΔL=0 cross section from MD analysis Kinematical correction GT unit cross section 1 2 5 10 20 50 1 5 2 10 50 20 100200 1.0 0.5 0.0

• 10

10 20 30 40 50 Energy transfer ω (MeV) ˆ

σexp(t,3He) at 115A MeV

ˆ

σexp(3He,t) at 140A MeV

Fit to ˆ

σexp(3He,t) at 140A MeV

extrapolated Mass number A ˆ

σGT(A) (mb/sr)

2p1/2 2p−1

3/2

2p3/2 2p−1

3/2

1f5/2 1f −1

7/2

1f7/2 1f −1

7/2

F(q, ω)

B(GT) = σ∆L=0(q, ω) ˆ

σGT F(q, ω)

F(q, ω) = σ∆L=0(q, ω)

σ∆L=0(0, 0)

* Kinematical correction calculated by FOLD/DWHI

γ Rays for Detailed Information on Low-lying States

• Eγ (GRETINA) vs Ex (S800)
• Distinct Eγ = Ex line: no γ’s greater than Ex → Clean Ex selection possible
• Separation energies Sp & Sn: particle decay channels open
• γ decays from GT states (Ex gated Eγ spectrum)
• Lowest known 1+ state at 991 keV → decay with 547-keV γ ray


5 10 15 20 5 10 1 10 Eγ (MeV) Ex(46Sc) (MeV) Sp Sn Eγ = E

x

0.0 0.5 1.0 10 20 Counts/2 keV 216 147 227, 228 Sc)

46

(

x

E = 0.991 MeV

547 keV

Eγ (MeV) 0.0 444.137(13) 991.33(4) 227.767(9) 4+ 2+ 1+ GT 3+ 227 keV 216 keV

547 keV

46Sc

B(GT) = 0.009 ± 0.005 (exp.) ± 0.003 (tensor)

Comparison with Theory

• Shell model
• Full pf-shell model space


with quenched operator

• Interactions:
• GXPF1A

• M. Honma et al., PRC 65, 061301(R) (2002);


PRC 69, 034335 (2004); EPJ A25, 499 (2005)

• KB3G

• A. Poves, et al., NP A649, 157 (2001)
• FPD6

• W. A. Richter, et al., NP A523, 325 (1991)
• QRPA (P. Möller and J. Randrup, NP A514, 1, 1990)
• Frequently used


in astrophysical simulations

(στ+)eff = 0.744στ+

None of the calculations agree well with the data!

1 2 3 4 5 6 7 0.0 0.5 1.0 0.0 0.5 1.0 Exp dB(GT)/dE (MeV−1)

B(GT)

Ex(46Sc) (MeV)

46Ti → 46Sc

QRPA FPD6 KB3G GXPF1A

Comparison with Shell Model Calculations

• Intruder states


due to admixtures with states from sd shell
 play an important role in the lower pf shell

• Some low-lying levels
• Large B(E2) values for 42,44Ca

e.g.

15 18 Neutron number N Ca isotopes (Z = 20) Mass number A 20 22 24 26 28 38 40 42 44 46 48 10 5 B(E2↓) [W.u.] 42Ca 1837.3 0.0 0+ 0.0 0+ 889.286 2+ 2009.846 4+ 2611.0 0+ 2961.8 2+ 2+ 0+ 2+ 4+ 1524.70 2752.41 2424.17 46Ti

• At. Data Nucl. Data Tables 78, 1 (2001)
• Nucl. Data Sheet 92, 1 (2001)
• Nucl. Data Sheet 91, 1 (2000)

Results for 45Sc

• 45Sc(t,3He) at 115 MeV/u

d2σ/dΩdEx (mb sr−1MeV−1) 2.11◦ 3.80◦ 5.80◦ Data

∆L = 0 ∆L = 1

5 10 15 20 Ex(45Ca) (MeV) 1 2 3 4 5 1 2 3 1 2 1

∆L 2

E = 115 MeV/u

θcm = 0.67◦

45Sc(t, 3He)45Ca

Ex(45Ca) (MeV)

45Sc→ 45Ca

Exp QRPA FPD6 KB3G GXPF1A 5 10 dB(GT)/dE (MeV−1)

B(GT)

0.0 1.0 1.5 0.5 0.0 0.5 Sn Sp 1 10 Eγ =Ex Eγ (MeV) Ex(45Ca) (MeV) 5 10 15 20 5 10 174 7/2− 5/2− GT 174

45Ca

Counts/5 keV Eγ (MeV) Ca)

45

(

x

E = 0.174 MeV 174 0.1 0.2 0.3 0.4 0.5 1 2 3 4 5

EC rates & Comparison with Theory

• Electron-capture rate
• Conditions: Pre-SN evolution of massive stars = Lower pf-shell nuclei are important
• Electron density ρYe = 107 g/cm3; Temperature 2.5-4.5 GK
• Only transitions from the ground state are included to infer the rate
• Low-lying strengths dominate the total rate

λEC(T, ρ) = const.

• i,j

fij(T, ρ) Bij(GT) Remarks:

• Strength to the 991 keV state


dominates the total rate
 (except for the higher temps)

• SMs give lower rates


as strengths locate at higher Ex

• Among SMs, GXPF1A is closest,


but it is just coincidental
 given the overall poorer description

• QRPA overestimates the rate


due to larger low-lying strengths

• Similarly for the 45Sc case

phasespace transition strength

ρYe = 107 g/cm3

46Ti → 46Sc

Electron capture rate λEC (sec−1) Temperature (109 K) GXPF1A KB3G Exp FPD6 QRPA First 1+ state 2.5 3.0 3.5 4.0 4.5

• 11

10

• 10

10

• 9

10

• 8

10

• 7

10

• 6

10

EC rates & Comparison with Theory

• Electron-capture rate
• Conditions: Pre-SN evolution of massive stars = Lower pf-shell nuclei are important
• Electron density ρYe = 107 g/cm3; Temperature 2.5-4.5 GK
• Only transitions from the ground state are included to infer the rate
• Low-lying strengths dominate the total rate

λEC(T, ρ) = const.

• i,j

fij(T, ρ) Bij(GT) Remarks:

• Strength to the 991 keV state


dominates the total rate
 (except for the higher temps)

• SMs give lower rates


as strengths locate at higher Ex

• Among SMs, GXPF1A is closest,


but it is just coincidental
 given the overall poorer description

• QRPA overestimates the rate


due to larger low-lying strengths

• Similarly for the 45Sc case

phasespace transition strength

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10 Temperature (109 K) 2.5 3.0 3.5 4.0 4.5

ρYe = 107 g/cm3

45Sc →45Ca

Exp 174 keV KB3G GXPF1A FPD6 QRPA Electron capture rate λEC (sec−1)

Collaborators

GRETINA was funded by the US DOE - Office of Science. 
 Operation of the array at NSCL is supported by NSF under Cooperative Agreement PHY-1102511(NSCL)
 and DOE under grant DE-AC02-05CH11231(LBNL).

• S. Noji,1,2,* R. G. T. Zegers,1,2,3 Sam M. Austin,1,2 T. Baugher,1,3,† D. Bazin,1 B. A. Brown,1,2,3 C. M. Campbell,4
• A. L. Cole,2,5 H. J. Doster,1,3 A. Gade,1,3 C. J. Guess,6,‡ S. Gupta,7 G. W. Hitt,8 C. Langer,1,2,§ S. Lipschutz,1,2,3
• E. Lunderberg,1,3 R. Meharchand,9, Z. Meisel,1,2,3 G. Perdikakis,1,2,10 J. Pereira,1,2 F. Recchia,1,¶ H. Schatz,1,2,3 M. Scott,1,3
• S. R. Stroberg,1,3,# C. Sullivan,1,2,3 L. Valdez,11 C. Walz,1,** D. Weisshaar,1 S. J. Williams,1 and K. Wimmer1,10,††

1National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA 2Joint Institute for Nuclear Astrophysics, Michigan State University, East Lansing, Michigan 48824, USA 3Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA 4Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 5Physics Department, Kalamazoo College, Kalamazoo, Michigan 49006, USA 6Department of Physics and Applied Physics, University of Massachusetts Lowell, Lowell, Massachusetts 01854, USA 7Indian Institute of Technology Ropar, Nangal Road, Rupnagar, Punjab 140001, India 8Department of Applied Mathematics and Sciences, Khalifa University of Science, Technology, and Research,

P.O. Box 127788 Abu Dhabi, UAE

9Neutron and Nuclear Science Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 10Department of Physics, Central Michigan University, Mt. Pleasant, Michigan 48859, USA 11Orange High School, Orange, New Jersey 07050, USA *Present address: Research Center for Nuclear Physics, Osaka

University, Ibaraki, Osaka 567-0047, Japan.

†Present address: Department of Physics and Astronomy, Rutgers

University, Piscataway, New Jersey 08854, USA.

‡Present address: Department of Physics and Astronomy, Swarth-

more College, Swarthmore, PA 19081, USA.

§Present address: Goethe-Universit¨

at Frankfurt am Main, D-60438 Frankfurt am Main, Germany. Present address: Institute for Defense Analyses, Alexandria, VA 22311, USA.

¶Present address: Dipartimento di Fisica e Astronomia, Universit`

a degli Studi di Padova, I-35131 Padova, Italy.

#Present address: TRIUMF, Vancouver, British Columbia V6T 2A3,

Canada.

**Present address: Institut f¨

ur Kernphysik, Technische Universit¨ at Darmstadt, D-64289 Darmstadt, Germany.

††Present address: Department of Physics, University of Tokyo,

Bunkyo, Tokyo 113-0033, Japan.