Estimation of neutron cross-sections for 16 O up to 5.2 MeV through R-matrix analysis S. Kunieda, K. Shibata, T. Fukahori T. Kawano, M. Paris, G. Hale
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Estimation of neutron cross-sections for 16O up to 5.2 MeV
through R-matrix analysis
S. Kunieda, K. Shibata, T. Fukahori
T. Kawano, M. Paris, G. Hale
Motivation -I
More than 30% of differences are seen between the measurements
Affect criticality benchmark calculations slightly
13C(α,n)16O
Alpha-particle Energy (MeV)
Bair & Haas + (73) Harissopulos+ (05)
Large difference in (n,α) or (α,n) cross sections
Neutron Energy (MeV)
16O(n,α)13C
Motivation -II Issue in lower energy region
- Ohkubo84, Johnson74 have plausible amount of hydrogen
Moxon74 Dilg71 Block75
Koester90
Ohkubo84
ENDF/B-VII.1 (our preliminary result is similar)
16O(n,total) Johnson74
- difference among the measurements (~3% or more )
Thanks : A. Plompen C. Lubitz
Purpose
Solve/reduce those issues -‐> R-‐matrix analysis to measurements
-‐ Experimental knowledge -‐ TheorePcal knowledge
σ (b
arn)
SensiPvity (barn/*)
Neutron Energy (MeV) Neutron Energy (MeV)
3/2- 3/2- 3/2+
Sensitivity of all the R-matrix parameter is always “zero” at peak positions due to the “unitarity limit” of S-matrix
16O(n,tot)
γdist. Rch.
Physical Constraint from R-matrix
CorrelaPon matrices
-‐ Traces of the unitary limit -‐ Certainly there are “correlaPons”
Physical Constraint from R-matrix -II
2 3 4 5345
-0.2
0
0.2
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
En (MeV), total En (MeV), alpha
Total cross-‐secPon Total v.s. (n,α)
R-matrix Analysis for 17O system
- Two partitions : (n+16Og.s.) and (α+13Cg.s.) - Neutron energy : En ≤ 5.2 MeV
- Levels in 17O : ENSDF + negative/distant levels
4.14 MeV 6.36 MeV
3.09
MeV
6.05
MeV
16O 13C 17O
n0 α0
1st
1st Code : AMUR
• Wigner-‐Eisenbuds’ formalism • Charged-‐parPcle reacPon • Generalized least-‐square method • KALMAN method
Reac1on Author Year Lab. Adopted range
O(n,total) Cierjacks+ 1968 KIT 0.5 MeV < En < 5.2 MeV
Schrack+ 1972 NBS 0.5 MeV < En < 5.2 MeV
Perey+ 1972 ORNL 0.5 MeV < En < 5.2 MeV
Johnson+ 1974 ORNL 50 keV < En < 5.2 MeV
Cierjacks+ 1980 KIT 3.1 MeV < En < 5.2 MeV 16O(n,total) Ohkubo 1984 JAEA 1 keV < En < 940 keV
13C(α,n)16O Harissopulos+ 2005 RUB Ethre < Eα < 3.5 MeV
16O(n,α)13C Giorginis+ 2007 IRMM 3.9 MeV < En < 5.2 MeV
Measurements Adopted
Cross-‐secPons only (preliminary)
Parameters to be fitted R-matrix parameters
Experimental parameters • Renormalization (EDA method, unitarity constraint)
• Channel radii (dependent on l and partition) • Reduced width amplitudes • Energy eigenvalues (level energies of 17O)
• Hydrogen content in Ohkubo84 and Johnson74 (the shape of σH is taken from ENDF/B-VII.1, G.Hale)
• Resolution (preliminary, to be shown later)
3 4 5
2
4
6
0 1 2 3 4 50
5
10
15
20
1 2 3 4 50
2
4
6
8
1 2 3 4 50
2
4
6
8
0 0.5 1
5
10
15
1 2 30
0.05
0.1
Cierjacks (1980) Johnson (1973)
Schrack (1972) Perey (1972)
Ohkubo (1984) Harissopulos (2005)
Incident Energy (MeV) Incident Energy (MeV)
Cross secPo
n (barn)
Results of R-matrix fit (examples)
13C(α,n)16O Harissopulos+ 9.24 1.521 ± 1.14% 16O(n,α)13C Giorginis+ -2.98
(limited points) 1.487 ± 1.31%
Reac1on Measurement χ2/N Renormaliza1on to
measurement O(n,total) Cierjacks68+ 2.48 0.967 ± 0.15%
Schrack+ 1.31 0.982 ± 0.09% Perey+ 1.75 0.996 ± 0.09% Johnson+ 1.54 1.018 ± 0.09% Cierjacks80+ 1.39 1.032 ± 0.35%
16O(n,total) Ohkubo 1.90 0.997 ± 0.02%
Renormalization
RenormalizaPon is large both for (α,n) and (n,α)
O(n,tot), Cierjacks1980 *1.03
13C(α,n), Harissopulos2005
Imposed χ2/N< 4.0 for Cierjacks1980 *1.03
reasonable soluPons are NOT found for 13C(α,n)16O
R-matrix parameters are “randomly” generated
O(n,tot), Cierjacks1980 *1.00
13C(α,n), Harissopulos2005
Imposed χ2/N< 5.0 for Cierjacks1980 *1.00
SituaPon is similar, but seems rather worse
R-matrix parameters are “randomly” generated
Reac1on Measurement L (m) Δt/L (ns/m) fixed
ΔL/L searched
O(n,total) Cierjacks (68) 57.5 0.063 0.00269 ± 3.2%
Schrack (72) 40.0 0.100 0.00489 ± 2.0%
Perey (72) 47.4 0.120 0.00423 ± 2.1%
Johnson (74) 198.3 - 0.00097 ± 3.9%
Cierjacks (80) 189.3 0.016 NA 16O(n,total) Ohkubo (84) 47.0 - NA
Experimental Resolution (preliminary)
Reac1on Measurement Const. FWHM (keV)
Searched Literature 13C(α,n)16O Harissopulos+ 34.6 ± 3.3% suggested 13 ~ 39 16O(n,α)13C Giorginis+ Fixed to literature value
Reasonable ??
Plausible Hydrogen Contents
Reac1on Exp. Ra1o to σH(E)
Effec1ve σH(Ethermal)
(n,total) Johnson+ 0.01665 (± 6.02%)
346 mb (± 21 mb)*
Ohkubo 0.00988 (± 8.38%)
205 mb (± 17 mb)*
* Uncertainty of hydrogen cross-‐secPon from ENDF/B-‐VII.1 is NOT considered
Plausible hydrogen (effective) cross-sections are obtained with uncertainty < 10%
Moxon74 Dilg71 Block75
Koester90
Ohkubo84
ENDF/B-VII.1
16O(n,total) Johnson74
Total Cross-section in Lower-energy
R-‐matrix cross-‐secPon is essenPally reduced, as present σthermal is 3.77 (barn) ± 0.35%
Present
Correlation Matrices
-‐ Traces of the unitary limit -‐ Long-‐ and medium-‐range correlaPons
Total (n,α)
Total Cross-sections with Uncertainty
0 1 2 3 4 5
(bar
n)m
0
5
10
15
20
Neutron Energy (MeV)0 1 2 3 4 5
Unc
erta
inty
(%)
-110
1
10
210
prior posterior
16O(n,total)
0.5% on average
(n,α) Cross-sections with Uncertainty
3 4 5
(bar
n)m
0
0.2
0.4
0.6
0.8
Neutron Energy (MeV)3 4 5
Unc
erta
inty
(%)
1
10
210
prior posterior
16O(n,α)13C
2.5% on average
Summary, Preliminary Conclusions
-‐ R-‐matrix analysis is carried out for 17O system (entrusted the physical constraint)
-‐ A large renormalizaPon is needed for 16O(n,a)13C and 13C(a,n)16O measurements -‐ Plausible hydrogen contents are obtained for total cross-‐secPons of Ohkubo84, Johnson74
-‐ Neutron cross-‐secPons are preliminary esPmated up to 5.2 MeV with covariance/uncertainty
Tasks Ahead
-‐ Inclusion of experimental angular-‐distribuPon in R-‐matrix analysis -‐ Inclusion of gamma-‐ray channel in AMUR
-‐ EvaluaPon for fast energy region (OpPcal model + Hauser-‐Feshbach ?)
-‐ Inclusion of another experimental parameter in R-‐matrix analysis if needed
-‐ Extend upper energy limit
Thank you for alenPon
Motivation
“Low-fidelity data” are given in the evaluated files
ENDF/B-VII.1 JENDL-4.0
16O(n,total)
Uncertainty/Covariance issues
Neutron Energy (MeV) Neutron Energy (MeV)
σ (b
arn)
σ (b
arn) U
ncertainty (%)
Uncertainty (%
)
Heil et al., PRC78 025803 (2008) 13C(α,n)16O, S-factor from measurements
Similar difference is seen between and FIG. 5
2 3 4 5345
-0.2
0
0.2
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Correlation Matrices Total v.s. (n,α)
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