Design study of benchmark experiment for large-angle scattering cross section for non-solid target with 14 MeV neutron

. Accuracy of large-angle scattering cross section in nuclear data has a large contribution on precision of neutron transport calculation in fusion reactor design. In the previous research, benchmark experiments for a solid target were carried out, however, non-solid targets, which are enclosed in a container, could not be dealt with. This is because we were not able to remove the effect due to existence of the container in the previous method. In this study, we performed design study of advanced benchmark experiment for large-angle scattering cross section especially for a non-solid target in a container. In addition, we also carried out benchmark experiments for silicon, which is important for the fusion reactor, however, is one of the elements that are difficult to obtain a solid target. In conclusion, we successfully developed an advanced benchmark experimental method for non-solid targets and verified it numerically by Monte Carlo calculation. In addition, we also found experimentally that large-angle scattering cross section of silicon is underestimated in JENDL-4, ENDF-B/VIII and JEFF-3.3.


Introduction
Nuclear data are used in neutron transport calculations in the design of nuclear fusion reactor and quality of nuclear data have large influence on the accuracy of the calculations. One of the challenging issues is the calculations in the blanket structure. There are many gaps in complicated blanket structure of ITER, though the neutron flux intensity is very high. Therefore, a large amount of neutron leaking through the blanket is anticipated and would bring about material damages. In the previous study, low accuracy of neutron transport calculation in the blanket structure was pointed out in the benchmark experiments carried out by Konno in JAEA [1]. Also, Ohnishi's experiment in OKTAVIAN facility, Osaka University showed that uncertainty of large-angle scattering cross section in nuclear data would be a contributory factor of the low accuracy [2]. Figure 1 shows neutron elastic scattering cross section of silicon from 9 MeV to 15 MeV, which is an important element for fusion reactor. As seen in the figure, large-angle scattering cross section of silicon in JENDL-4 [3] significantly differs from JEFF-3.3 [4] and ENDF/B-VIII [5]. Elastic scattering cross sections in ENDF-VIII and JEFF-3.3 are completely the same because both of them are originated from the same nuclear data library; ENDF-VI.
Silicon is difficult to obtain a solid sample. Moreover, large-angle scattering cross section is generally smaller than forward scattering cross section by two or three orders of magnitude. Therefore, it is difficult to carry out benchmark experiments for large-angle scattering cross section of silicon, and there are a few benchmark experimental studies carried out so far. For these reasons, we performed benchmark experiments for large-angle scattering cross section of silicon in the present study.   The system consists of a DT neutron source, niobium foil, iron shadow bar, flaky silicon sample, stainless container, aluminium lid of the container and concrete wall of about 1 m thickness. The shadow bar is an iron trapezoidal conical bar and set up to shield direct incident neutrons to the niobium activation detector. The silicon sample is flaky and filled in a stainless container of 1 mm thickness. The container is a cylinder with a thickness of 22.8 cm, which is twice the mean free path of silicon for 14 MeV neutron, covered with an aluminium lid. Using a two mean free path sample, we can reduce contribution of forward scattering neutrons.

Experimental method
In this method, we performed four experiments. We used two shadow bars shown in Fig. 2, thin and thick ones, and carried out experiments with and without the silicon sample in each shadow bar system. Figure 3 shows these four experimental systems. These four systems are named as follows: S1TC and S1C are systems using a thin shadow bar with and without sample, respectively. S2TC and S2C are systems using a thick shadow bar with and without sample, respectively.
In addition to the neutron source and activation foil, the systems have five components which neutron can pass through: the shadow bar, silicon flaky sample, aluminium lid, stainless container, and concrete wall.
Therefore, there are 31 combinations of components that are assigned as paths, which an incident neutron passes through before entering the activation foil. In these paths, 12 paths are physically unrealizable, for example, a path that neutron enters the silicon sample without passing through the lid or container is unrealizable. As the result, there are 19 physically realizing paths in the systems. Table 1 shows these paths.
In path 6, neutrons pass through the lid and sample and then enter the foil. This is the large-angle scattering neutron. This pathway only exists in the S1TC system. This is because the sample does not exist in the S1C system and neutron cannot enter the sample without passing through the shadow bar in thick shadow bar systems, S2TC and S2C. In the previous study, our group showed that we can estimate the reaction rate by large-angle scattering neutrons by Eq.(1) [6].
where is reaction rate of activation of niobium foil in each system, is incident neutron flux to the foil in each system. Na is the number of niobium atoms in activation foil, σ is activation cross section of niobium foil, and are reaction rate and flux of large-angle scattering neutrons, respectively.
In Eq.(1), we assume a relation expressed in Eq.(2). This is because we found from physical consideration that contributions of neutrons passing through other paths are cancelled out with each other or very small to be ignored. Therefore, we can regard the residual contribution as the estimation error of the present benchmark method. Fig. 3 Outline of four benchmark experimental systems. S1TC S1C S2TC S2C Table 1 Combinations of components in each path.

Simulations
To verify availability of Eq.(1), we calculated the reaction rates of all the paths in the four experimental systems, and the reaction rate of neutrons passing through path 6 in the S1TC system using Monte Carlo code, MCNP5 [7]. Table 2 shows the result. In Table 2, hyphen means the path which does not exist.
As you can see in Table 2, RS1TC,path6 and (RS1TC -RS1C) -(RS2TC -RS2C) are the same, showing that the contributions of neutrons which pass through paths other than path 6, and RS1TC,path6 can correctly be expressed by Eq.(1).

Results
We performed benchmark experiments for silicon by using flaky sample and measured reaction rates in the four systems described in chapter 2. In addition we also calculated the reaction rates of niobium foil using silicon elastic scattering cross sections in JENDL-4.0, ENDF/B-VIII, JEFF-3.3 by MCNP5. We compared the experimental results with calculated values. Table 3 shows the results. In the table, calculated reaction rates in the systems are largely different from their experimental result. The C/E values of (RS1TC -RS1C) -(RS2TC -RS2C) are smaller than unity in every nuclear data library we used in this study. The results show the flux intensity of silicon large-angle scattering neutrons is 30--50 % smaller than the experimentally obtained values. Therefore, we have concluded that large-angle scattering cross sections of silicon are underestimated in all the nuclear data libraries, JENDL-4, JEFF-3.3 and ENDF/B-VIII.
Although elastic scattering cross section is completely same in JEFF-3.3 and ENDF-VIII, the C/E results differ between these two libraries. Neutron reaction such as inelastic scattering cross section in JEFF-3.3 was newly estimated using GLUCS evaluation. We think this is the reason of the difference.

Conclusion and Future work
In this study, we established an advanced large-angle scattering cross section benchmark experimental system for a non-solid sample with two shadow bar technique. In the method, we divided the neutron path in the experimental system into 19 pathways, and we successfully removed contributions of neutrons other than large-angle scattering neutron. We verified this method numerically by using MCNP5 and showed that we can extract contribution of large-angle scattering neutron by the present method. We then performed benchmark experiments for silicon to extract large-angle scattering neutrons using a flaky sample. As the result, calculation values using JENDL-4 and JEFF-3.3 were about 50% smaller than the experimental values and that of ENDF/B-VIII was about 40% smaller than the experimental value. We concluded that large-angle scattering cross sections of silicon are underestimated in JENDL-4, JEFF-3.3 and ENDF/B-VIII.
In the future, we will carry out benchmark studies for large-angle scattering cross sections using non-solid targets of light elements like oxygen, nitrogen, boron and so on.