Post on 14-Jan-2016
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The evaluation of a new method to extract spectroscopic factors using asymptotic normalization coefficients and the astrophysical 14C(n,γ)15C reaction
rate
Matthew McCleskey
Neutron capture on unstable nuclei• Neutron direct capture reaction cross sections on unstable nuclei are
needed for nuclear astrophysics (BBN, s- and r-processes), stockpile stewardship and for new reactor designs.
• Because no neutron target exists, and many of the nuclei of interest are short-lived indirect methods using inverse kinematics at laboratory energies need to be developed.
• Unlike proton direct capture, which is peripheral and where the cross section can be determined using the ANC, neutron capture is not as simple, may have a significant contribution from the interior – most n-capture is s-wave → Must use SF– some cases may be dominated by p-wave capture → Use ANC
New method
• Need peripheral reaction to determine ANC
• Need non-peripheral reaction to get SF
A new method to extract SFs has been proposed* that utilizes the ANC to fix experimentally the SPANC and thus determine the SF.
*AM Mukhamedzhanov and FM Nunes Phys Rev C 017602 (2005)
15C↔14C+n system is being used as a test case for this method. Will also use the ANC found to calculate the 14C(n,γ)15C reaction rate
New method
extnljnlj
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)( extnlj
nljDW T
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BjAxlsp
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CSF
The matrix element can be split into external and internal parts:
One can then define a function
the experimental counterpart of which is
Comparing these two functions experimentally fixes the SPANC therefore giving the correct SF:
13C(14C,15C)12C (peripheral- ANC)
Neutron transfer reaction with 12 MeV/nucleon 14C accelerated by the K500 cyclotron at TAMU Sept. 2007 and May 2009. Reaction products detected using the MDM spectrometer/Oxford detector.
15C→14C + n (peripheral- ANC) Breakup reaction measured at 60 MeV/u at GANIL and MSU C2 = 1.48 ± 0.18 fm-1 (Trache 2002), C2=1.64±.04 fm-1 (Summers 2008)
d(14C,p)15C (peripheral-ANC) (d,p) in inverse kinematics measured at 11.7 MeV/nucleon with TECSA
14C(d,p)15C (peripheral at low E- ANC, at higher E becomes non-peripheral-ANC and Spectroscopic factor)
Experiment performed at TAMU Feb. 2008 and Aug. 2010 with Ed=60MeV from K500, reaction products detected with MDM spectrometer/Oxford detector
Experimental Overview
13C(14C,15C)12C
MDM spectrometer
(D.M. Pringle et al. NIM A245 (1986) pg. 230-247)
Oxford detector
•ionization chamber filled with ~50 torr isobutane•anode plates to measure energy loss•plastic scintillator to measure residual energy•4 resistive wires (avalanche counters) to give position
Particle ID: 14C+13C
15C 14C48Ti/56Fe (imp.)27Al/28Si (imp.)16O (imp.)Elastic g.s.½+ 13C5/2+ / 3/2- 13C2+ 12C (imp.)
Reconstructed target angle
Foc
al p
lane
pos
itio
n∆E
Eres
Foc
al p
lane
pos
itio
n
Reconstructed target angle
½ + 15C (ground state)5/2+ 15C 0.74 MeV2+ 12C and 5/2+ 15C 5.17 MeV
Finding an OMP
V (MeV)
W (MeV)
rv (fm) rw (fm) av (fm) aw (fm) χ2 Jv (MeV fm3)
Rv (fm) Jw (MeV fm3)
Rw (fm)
WS1 77.1 13.32 0.987 1.209 0.703 0.723 3.09 225 4.480 68 5.206
WS2 118.7 14.15 0.927 1.191 0.690 0.739 3.4 292 4.275 69 5.182
WS3 162.4 15.03 0.891 1.169 0.674 0.767 3.59 357 4.132 71 5.169
WS4 203.1 16.04 0.894 1.133 0.627 0.825 3.6 438 4.038 71 5.183
WS5 248.8 16.66 0.885 1.115 0.606 0.848 3.65 516 3.965 72 5.180
• Grid search in V– Use OMP of WS form:
– Fit other 5 parameters for each V, pick several values of V for further fitting
OMP CU V iW V
• Double folding calculation–Semi-microscopic approach–Double folding calculation using JLM effective interaction–Only 2 parameters (normalizations) to fit
Finding an OMP
• Grid search in V– Use OMP of WS form:
– Fit other 5 parameters for each V, pick several values of V for further fitting
OMP CU V iW V
Transfer: 13C(14C,15C)12C
←using OMPs from grid search
←using OMP from double folding
DWBA calculations performed using PTOLEMY, using different potentials
ANC results from HI
SF2s1/2 1/2
22sC (fm-1) SF1d5/2
5/2
21dC x10-3 (fm-1)
WS1-WS1 1.22 2.30 1.13 4.45
WS2-WS2 1.16 2.18 1.02 4.03
WS3-WS3 1.04 1.95 1.13 4.46
WS4-WS4 0.98 1.83 1.20 4.74
WS5-WS5 1.14 2.14 1.25 4.94
DF 1.15 2.16 1.09 4.28
Average 1.12 2.09 1.14 4.48
Uncertainties: 4% target thickness, 3% normalization to the number of incident particles, 5% data extraction and disentanglement from the 1st excited state of 15C, 6% statistical uncertainty and 10%
systematic uncertainty in the calculations. This gives overall uncertainty of 14% for the ANC2
1st excited state had lower statistical uncertainty (~1%) giving an overall uncertainty for that ANC2 of 13%
BB aaBB
aaBB
aaBBlj jbxljAxl
DWjljla
jbxlB
jAxl bbCC
d
d22
22 )()(
d(14C,p)15C
TECSA(Texas A&M-Edinburgh-Catania Silicon Array)
TECSA : d(14C,p)15C
MARS
Radioactive beam from MARS
TECSA target TECSA silicon ring array
Distance to target determines angular range
For 14C beam, no primary (production) target in MARS is used.
TECSA target is CD2 ~250μg/cm2 thick
TECSA: d(14C,p)15C
ADWA calculation using FRESCO with CH89 nucleon potentials(Adiabatic Distorted Wave Approximation)
Results from d(14C,p)15C
22 1/2C =2.01 0.24s
2 31 5/2 (4.06 0.49) 10dC
ANC for ground state: fm-1
Uncertainties: 2% due to target thickness, 2% incident beam normalization, 4% for the analysis and < 2% for statistics. This combined with a 10% systematic uncertainty gives an overall error in C2 of 12%.
ANC for 1st excited state: fm-1
14C(d,p)15C
14C(d,p)15C
• 60 MeV deuteron beam impinges on thin, enriched 14C target
• Higher energy and light projectile means that this reaction is expected to be not peripheral, so we can extract the spectroscopic factor using the previously determined ANC
• Used MDM spectrometer and Oxford detector- Same setup as for HI, but with more gas pressure and a much thicker scintillator to stop protons
• Particle ID in scintillator:Protons
Deuterons
14C(d,p)15C
Position in focal plane (mm)
coun
ts
14C(d,p)15C
Angular distributions and ADWA calculations performed using FRESCO
Rexp vs RDW
Weak dependence indicates a peripheral reaction, so even at 60 MeV deuteron energy we can get the ANC… but no information about the SF
This figure shows an upper limit of r0 of ~1.15
fm, which corresponds to b2 = 4.01∙10-3 fm-1.
From the relation
one obtains a lower limit of SF=1.05
2
2
nljnlj
nlj
C
bSF
2
nt2
?i( )DW
nlj extnlj
expTR b
ddT R
b C
Recall:
1st exc. Rexp vs. RthGS Rexp vs. Rth
Summary of the ANC for 15C↔14C+n
22 1/2sC 2
1 5/2dCexperiment
HI transfer 2.09 ± 0.29 (4.48 ± 0.58)∙10-3
TECSA d(14C,p)15C
2.01 ± .24 (4.06±.49) ∙10-3
60 MeV (d,p) 1.76±0.29
Average 1.96±0.16 (4.23±0.38)∙10-3
Summary of the ANC for 15C↔14C+n
(fm-1) (fm-1)
Trache 2002 1.48±0.18
Timofeyuk 2006 1.89±0.11
Pang 2007 2.14
Summers 2008 1.64±0.03
Akram 2011 1.64±0.26 3.55±0.43
This work 1.96±0.16 4.23±0.38
5/2
21dC
1/2
22sC
Astrophysical 14C(n,γ)15C rate
• Important for:– Inhomogeneous BBN– Depletion of CNO isotopes in AGB stars– Effect on seed nuclei for r-process in core-collapse SN
• Dominated by p-wave capture → peripheral reaction, can use ANC• Calculate rate using the code RADCAP
– Include capture to GS and 1st exc state
Black squares are the direct measurement (Reifarth et al. PRC 77 015804 (2009)), blue is calculation using the ANC, red lines show uncertainty in the calculation due to the uncertainty in the ANC
AcknowledgementsCollaborators:
R. Tribble, L. Trache, A. Mukhamedzhanov, F. Carstoiu, A. Alharby, A. Banu, V. Goldberg, Y.-W. Lui, B. Roeder, E. Simmons, A. Spiridon
Special thanks:
N. Nguyen
Work funded by:
NNSA-SSAA, DOE