Nuclear Science and Engineering Research

4-1 Pursuit of Accurate Nuclear-Reaction Cross-Sections in the Resonant Region
ᴪ Synergy between Nuclear-Data Measurement and Theory ᴪ

0.3

Cross-section (b)13Bair & Haas (1973)
Harissopulos+ (2005)
Present analysis

16C(α, n) O

α+13C

17O

n+16O

Internal
wave function

External
wave function

0.2

External
wave function
0.1“Cross-sections”
0〜∫ ￨Amplitude￨ d䃈2(䃈: solid angle)
123

4Alpha-particle Energy (MeV)

Fig.4-3 The systematic difference between themeasurements together with the estimated values fromthe present analysis
We found that the systematic discrepancy among different
experimental data could be resolved by a synergetic
comparison between measurements and theory. In thisexample, an approximately 30% difference was observed
between the old and recent measurements. Through shapeanalysis of the experimental data using R-matrix theory(which satisfies the quantum-mechanical conservation law),
we obtained a result that supports the old measurement inthis case.

Fig.4-4 Concept of the resonant nuclear-reaction theory(R-matrix)
In the resonant nuclear-reaction theory adopted in this study,
the matching condition of the internal and external wave
functions is the parameter required for the calculation ofthe cross-sections. Note that the calculated cross-sections
always satisfy the quantum-mechanical conservation law. In
this study, we developed a computer code to obtain a valueof the parameter from the shape of the experimental data.

Reactions occur in the nucleus with probabilities that
depend on the energies of incident particles such as neutrons,protons, and alpha particles. Such probabilities, which arecalled nuclear-reaction cross-sections (or nuclear data), arefundamental values for nuclear engineering. With the recent
progress of nuclear technology, cross-section data require
ever-higher accuracy. Furthermore, the uncertainty values ofthese data must be fully accountable. To meet these demands,
we are performing studies to enhance the general-purpose
Japanese Evaluated Nuclear Data Library (JENDL; latest
version is JENDL-4.0).
The cross-section shows resonant peaks in the lowenergy particle reactions, reflecting the internal structure of
the nucleus. Since those peaks are very difficult to predict
only using nuclear theories, the most useful approach for
determining the values is to conduct nuclear-data experiments
at accelerator facilities with a combination of detectors. Here,let us indicate that we always see differences among measured
data to a lesser or greater extent. An example is illustrated
in Fig.4-3, in which an old measurement of the 13C(α, n)16O
reaction from 1970s and a recent one are systematicallydifferent by ~30%. Such a typical systematic difference isusually ascribable to uncertainty in the sample density.
In this study, we applied the R-matrix theory to the analysisof those experimental data (Fig.4-4). We adopted this theory
essentially because it is strictly based on the quantum
mechanics; hence, the theoretical calculation always obeys
the quantum-mechanical conservation law (i.e., unitarity ofthe scattering matrix). The parameters in this theory are thosefor the matching condition of the internal and the external
wave functions. We estimated those values from the shapeof experimental data, assuming their absolute values to beunknown. The solid curve in Fig.4-3 shows the results of thepresent analysis, where the estimated values are consistent
with the old experimental data. Moreover, the uncertainty ofthe present values is ~2.5% on average, which is signiﬁcantly
smaller than the difference in the measured data.
Uncertainty is always included in any measurement toa lesser or greater degree. However, we have presented
a possibility for reducing the problem using a synergetic
comparison between the measured nuclear data and the theory.

Reference
Kunieda, S. et al., Covariance of Neutron Cross Sections for 16O through R-Matrix Analysis, Nuclear Data Sheets, vol.123, 2015, p.159-164.

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JAEA R&D Review 2016-17