Transcript The ANC for 15C↔14C+n and the 14C(n,γ)15C astrophysical

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
A new method to extract SFs has been proposed* that utilizes the
ANC to fix experimentally the SPANC and thus determine the SF.
• Need peripheral reaction to determine ANC
• Need non-peripheral reaction to get SF
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
*AM Mukhamedzhanov and FM Nunes Phys Rev C 017602 (2005)
New method
The matrix element can be split into external and internal parts:
~ DWBA Cnlj ~
~
T

Tint [b]  Cnlj Text
bnlj
One can then define a function
~
T
~
R DW (bnlj )  int  Text
bnlj
2
the experimental counterpart of which is
d
 d 2
Clj
exp
R exp
Comparing these two functions experimentally fixes the SPANC therefore giving the
B
2
correct SF:
(
C
)
AxlB j B
SFl B( spjB) 
(bl B j B ) 2
Experimental Overview

13
C(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 nonperipheral-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
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
48Ti/56Fe
14C
Focal plane position
Eres
Focal plane position
(imp.)
½ + 15C
(ground state)
27Al/28Si
15
5/2+ C 0.74 MeV
(imp.)
2+ 12C16and
O (imp.)
5/2+ 15Elastic
C 5.17g.s.
MeV
∆E
15C
Reconstructed target angle
Reconstructed target angle
½+ 13C
5/2+ / 3/213C
2+ 12C (imp.)
Finding an OMP
• Grid search in V
– Use OMP of WS form:
UOMP  V  iW  VC
– Fit other 5 parameters for each V,
pick several values of V for
further fitting
WS1
WS2
WS3
WS4
WS5
V
(MeV)
W
(MeV)
rv (fm)
rw (fm)
av (fm)
aw (fm)
77.1
13.32
0.987
1.209
0.703
0.723
118.7
14.15
0.927
1.191
0.690
162.4
15.03
0.891
1.169
203.1
16.04
0.894
248.8
16.66
0.885
χ2
Jv
(MeV
fm3)
Rv (fm)
Jw
(MeV
fm3)
Rw (fm)
3.09
225
4.480
68
5.206
0.739
3.4
292
4.275
69
5.182
0.674
0.767
3.59
357
4.132
71
5.169
1.133
0.627
0.825
3.6
438
4.038
71
5.183
1.115
0.606
0.848
3.65
516
3.965
72
5.180
Finding an OMP
• Grid search in V
– Use OMP of WS form:
UOMP  V  iW  VC
– Fit other 5 parameters for each V,
pick several values of V for
further fitting
• Double folding calculation
–Semi-microscopic approach
–Double folding calculation using JLM
effective interaction
–Only 2 parameters (normalizations) to
fit
Transfer: 13C(14C,15C)12C
DWBA
calculations
performed using
PTOLEMY,
using different
potentials
←using OMPs from
grid search
←using OMP
from double
folding
ANC results from HI
 l B j B la ja
d
B
2
a
2
  (C AxlB jB ) (Cbxla ja ) 2
2
d jBlB
b AxlB jB bbxl
a ja
DW
SF2s1/2
C2s2 1/2 (fm-1)
SF1d5/2
C1d2 5/2 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 ANC 2
1st excited state had lower statistical uncertainty (~1%) giving an overall uncertainty for that ANC 2 of
13%
d(14C,p)15C
TECSA
(Texas A&M-Edinburgh-Catania Silicon Array)
TECSA target is CD2
~250μg/cm2 thick
TECSA target
TECSA : d(14C,p)15C
TECSA silicon ring array
MARS
Radioactive beam from MARS
Distance to target
determines angular range
For 14C beam, no primary
(production) target in MARS
is used.
TECSA: d(14C,p)15C
ADWA calculation using FRESCO with CH89 nucleon potentials
(Adiabatic Distorted Wave Approximation)
Results from d(14C,p)15C
ANC for ground state: C22s1/2 =2.01  0.24
fm-1
ANC for 1st excited state: C12d 5/2  (4.06  0.49) 103 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%.
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
Deuterons
• Particle ID in scintillator:
Protons
counts
14C(d,p)15C
Position in focal plane (mm)
14C(d,p)15C
Angular distributions and ADWA
calculations performed using FRESCO
Rexp vs RDW
2
Recall:
R
DW
?
Tint
(bnlj ) 
 Text  R exp
bnlj
GS Rexp vs. Rth
Weak dependence indicates a
peripheral reaction, so even at 60
MeV deuteron energy we can get
the ANC… but no information
about the SF
d
 d
C2
1st exc. Rexp vs. Rth
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 SFnlj 
2
Cnlj
2
bnlj
one obtains a lower limit of SF=1.05
Summary of the ANC for 15C↔14C+n
experiment
C22s1/2
C12d 5/2
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
C2s2 1/2
(fm-1)
C1d2 5/2
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
(fm-1)
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
Acknowledgements
Collaborators:
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