Neutron cross sections for carbon and oxygen from new R-matrix analyses of the 13,14C and 17O systems

We report the latest results from R -matrix analyses of reactions in the 13,14 C and 17 O systems that are of interest in reactor applications and nuclear astrophysics. These were done in order to provide separate cross sections for the stable isotopes (12,13 C) of natural carbon, and to contribute improved cross sections for 16 O to the CIELO project. Although particular attention was paid to the data in the standards region ( +16 O, the analyses extend to several MeV neutron energy for all the systems. The fits to the data included are generally quite good, in keeping with the unitary constraints of R -matrix theory. The cross sections for 12,13 C give results for natural carbon that are close to the previous evaluation by Fu et al. at energies below 1 MeV. Above that energy, the deviations become larger, especially near the narrow resonances. The thermal cross section for 16 O is at the upper end of the range of recommended values, in excellent agreement with a high-precision measurement by Schneider. At higher energies, the 17 O analysis follows in great detail high-resolution measurements of the total cross section, and agrees quite well with the 13 C(α,n)16 O cross section measurement of Bair and Haas at roughly their original normalization scale. We will discuss the implications of these new evaluations for critical benchmarks and astrophysical applications.


Introduction
Reactions in the 13,14 C and 17 O systems are of much interest in reactor applications and nuclear astrophysics. Since there are many oxides and carbides (as well as graphite) in reactor materials, the neutron cross sections for oxygen and carbon are of great importance. In astrophysics, the 13 C(α, n) 16 O reaction is thought to be a source of neutrons in slow-neutron (s-process) capture. The neutron capture cross sections for 12,13 C and 16 O are themselves not very well known at energies above thermal.
We have performed R-matrix analyses of data for these light systems in order to provide separate neutron cross sections for the stable isotopes ( 12,13 C) of natural carbon, and to contribute improved cross sections for n+ 16 O to the CIELO project. This was done using the versatile Los Alamos R-matrix code EDA [1], which implements standard R-matrix theory [2] without any approximations. In addition, it uses the Wolfenstein density matrix formalism [3] to calculate the results of any possible measurement for two-body reactions, and relativistic kinematics throughout. The result is a description of the experimental data in terms of the usual R-matrix parameters (reduced-width amplitudes and eigen-energies) that ensures three basic properties of hadronic scattering theory: unitarity of the S-matrix, reciprocity (time-reversal invariance), and causality. These properties (especially unitarity) impose powerful constraints on the fits to the experimental data. In the following sections, we will give summaries of the data included and show the quality of the fits obtained for each of the analyses, starting a e-mail: ghale@lanl.gov with 17 O. Then we will conclude with a discussion of the implications of the new cross sections for various applications.

17 O system analysis
The 17 O system analysis included all possible reactions between the channels n+ 16 O and α+ 13 C. This is summarized in Table 1. Particular attention was paid to the data in the low-energy region for n+ 16 O, shown in Fig. 1. The thermal cross section is lower than before, but still at the upper end of the range of recommended values, in excellent agreement with a high-precision measurement by Schneider [4]. At higher energies, as shown in Fig. 2, the 17 O analysis follows in great detail the total cross section measurements of Ohkubo [5], Johnson [6], Fowler [7], and Cierjacks [8] with reasonable re-normalizations (−2% to +4%). It also agrees quite well with the 13 C(α,n) 16 O cross section measurement of Bair and Haas [9] at roughly their original normalization scale (0.94), a consequence of the unitarity imposed by an R-matrix description. The resulting 16 O(n, α) 13 C cross sections are shown in Fig. 3. They agree with the measurements and evaluation done at IRMM by Giorginis [10], which are 30 -40% higher than the ENDF/B VII.1 cross sections.

13,14 C system analyses
The 13 C system analysis included reactions among the channels n+ 12 C, n+ 12 C*, and γ + 13 C. A summary of the channel configuration and data for the reactions included is given in Table 2. Although particular attention was paid to the data in the standards region (E n < 2 MeV) for the    Figure 2. n+ 16 O total cross section compared to experimental data [5][6][7][8]. The insert shows the fit to the 13 C(α, n) measurement of Bair and Haas [9], renormalized by 0.94. carbon isotopes, the analyses extend to several MeV for both the 13,14 C systems. The types of data used are mostly differential and integrated (total) cross sections, but some analyzing-power measurements are also included. The fits to the data are generally quite good, as can be seen in Figs. 4 and 5. Some changes were also made in the n+ 12 C   channel a c (fm) l max n+ 12 C(0 + ) 4.6 4 n+ 12 C*(2 + ) 5.0 1 γ + 13 C 50. 1 reaction energy range # data observables (MeV) points 12 C(n, n) 12 C E n = 0−6.45 6940 σ T , σ (θ), A n (θ ) 12 C(n, n ) 12 C* E n = 5.3−6.45 443 σ int , σ (θ ) 12 C(n, γ ) 13 C E n = 0−0.2 7 σ int total: 7390 5 capture cross section, as can be seen in Fig. 6. The flat region between 0.2 and 7 MeV in ENDF/B VII.1 has been replaced with a more physically reasonable behavior when joined to the higher-energy data above 10 MeV.
The n+ 13 C ( 14 C system) analysis has been done in two versions. The first was a single-channel analysis that went only up to 5 MeV. That analysis included total cross section data and differential cross sections for elastic scattering. A preliminary ENDF/B evaluation for 13 C based on this analysis, which also included the capture cross section, was submitted in August of 2015. The second analysis was completed recently for inclusion in ENDF/B VIII.0. It is a six-channel analysis that goes up to 20 MeV, but includes experimental data only for the total cross section. The results from that analysis are shown in Fig. 7. The total cross section from that analysis is similar to the one obtained earlier at energies below 5 MeV.

Natural carbon
These cross sections for n+ 12,13 C combine to give results for natural carbon that are very close to the previous evaluation (ENDF/B VII.1) by Fu et al. at energies below 1 MeV. Between 1 and 2 MeV, the deviations become larger, approaching 2% just below the first resonance, and are even larger at higher energies, especially near the narrow resonances. Earlier this year, Andrej Trkov (IAEA) merged the 2015 ENDF/B file for 13 C with the TENDL file at energies above 5 MeV to produce an evaluation that extends to 150 MeV. Using those cross sections with the new ones for 12 C, he made a plot of the n+ nat C elastic scattering cross section that is shown in Fig. 8. The error bars on the measured data are large, but they tend to support the trend of the new 12 C cross section to higher values in the region below 2 MeV. On the other hand, a recent measurement of the total cross section by Danon (RPI) that was not included in the 13 C analysis appears to support the lower cross sections in this energy region.

Summary and conclusions
The EDA analyses of reactions in the 13,14 C and 17 O systems described here give very good fits to all the data included, with values of chi-square per degree of freedom in the range 1.5-1.7. The neutron cross sections from these analyses are highly constrained by the unitarity property mentioned earlier. For the 17 O system, the lowenergy n+ 16 O scattering cross sections are now in better agreement with high-precision measurements, and the (n, α 0 ) cross section agrees with the data of Bair and Haas [9] and Giorginis [10]. A post-analysis check showed good agreement also with σ T measurements done at RPI by Danon. The evaluated 16 O file CIELO 3/16 = ENDF/B VIII.0-β2 extends to 150 MeV, and is the same as ENDF/B VII.1 above 9 MeV (except for capture). The changes in the cross sections from ENDF/B VII.1 appear not to have made much difference in the benchmarks that have been tested so far. Changes in k eff of −50 to −100 pcm have been reported, which is rather surprising, considering the ≈ 40% changes in the reaction cross section. For further discussion of the implications of this new evaluation for the CIELO project, please see the paper of Chadwick, et al. [11] in the proceedings of this conference. The scale of the 13 C(α, n) 16 O cross section at low energies has been fixed by the 17 O analysis, which should lead to a better determination of this important s-process source reaction in astrophysics. We plan further improvements on the astro-physically important 16 O(n, γ ) reaction, by putting in the resonant structure of the capture cross section above the first resonance.
The EDA analysis of the 13 C system gave quite reasonable results for the n+ 12 C cross sections at energies up to about 6.5 MeV, and resolved the large discrepancy between the experimental scales of two recent measurements of the inelastic cross section to the first level (see Fig. 5). The analysis also clarified the level structure of the 13 C system in the region around E x = 10.9 MeV.
In recent work on the 14 C system, more channels were added to the existing single-channel analysis in extending it to higher energies (20 MeV). Above that energy, we plan to merge with the existing evaluation in the TENDL file. The 12,13 C(n, γ ) cross sections have been improved, and give better agreement with the MACS in the KADoNIS data base (J.-C. Sublet). However, there are questions from recent benchmarking work on graphite about the value of the thermal cross section for n+ 13 C capture. The elastic scattering cross section for natural carbon becomes ≈ 2% larger than ENDF/B VII.1 around 2 MeV. That difference exceeds the maximum estimated uncertainty (0.6%) of the standard cross section at the upper end of its energy range (1.8 MeV), but may be in better agreement with the measurements. These changes in the cross sections for natural carbon produce about a 70 pcm reduction (the right direction) in the reactivity of the HMI006 benchmark set, according to calculations done by Andrej Trkov at the IAEA.