# A Study of Stray Neutron Field Measurements for the Neutron Scattering Instruments at CSNS
## 3 Experiments and Discussion
### Results and Discussion  
The counting rates of the ERBSS were used to calculate the neutron spectra by employing the SAND-II iterative method [18]. The standard deviation limit, \(Q^{k}\), between the calculated and measured counting rates of the ERBSS can be expressed as follows:  
\[Q^{k}=\left\{\frac{1}{N-1}\sum_{i=1}^{N}\left[(A_{i}-A_{i}{}^{[K]})/A_{i} \right]^{2}\right\}^{1/2} \tag{1}\]  
where the \(N\) is the total number of the ERBSS, \(A_{i}\) is the measured counting rate for a specific BSS, and \(A_{i}{}^{[K]}\) is the calculated counting rate by the \(K\)-th iteration spectrum. In this study, the standard deviation limit, \(Q^{k}\), was assumed as 0.05. For the number of the sphere less than the energy bins in the neutron spectra, a prior spectrum was required. Because of the unsatisfactory validation statistics for location B, the prior spectrum simulated by MCNPX  
Figure 3: Counting rates of ERBSS at two measurement locations. ERBSS sphere type indicated above bars. at location A was used as the initial spectrum to start the unfolding procedure for all of the cases. To obtain good validation statistics, the secondary source-term technique was employed in the simulations. A surface source with a cross-sectional area of 10 cm \(\times\) 10 cm located 100 cm away from the moderator was used. The F5 card was adopted to simulate the neutron spectrum in a vacuum sphere with a diameter of 20 cm. Comparisons between the calculated stray neutron spectra and those measured by the ERBSS at the two locations are shown in Figure 4. At location A, it can be seen that the portion of the thermal neutron was very high and the measured thermal neutron spectra agree well with the simulations. These low-energy stray neutrons may have a great impact on the neutron scattering instrument, since the neutron detectors installed inside the scattering room are highly sensitive to them. It can be also observed in Figure 4a that there are deviations in the epithermal regions with the energy between 1 eV and tens of keV. The main reason is considered to be the deviations between the simulations and the measurements; for instance, the supporting structures for the BSS made of thin stainless steel were not included in the simulation model. At location B, as shown in Figure 4b, the measured spectra agreed well with the calculations, which demonstrated the validity of the measurements and data processing. Figure 4c,d show that the PE plates had a negligible effect on the neutron spectra in shape. To quantify the difference between the measured and calculated neutron spectra, Table 1 lists the integral neutron fluence rate in different energy regions, including the thermal neutrons (below 1 eV), epithermal neutrons (1 eV-1 keV), intermediate energy neutrons (1 keV-1 MeV), and fast neutrons (>1 MeV). Because there was no shielding material between location A and the neutron beam aperture, the total neutron fluence rates of the stray neutrons at location A in each energy range were much higher than those at location B. Although the spectra differed, the portion of fast neutrons at location A was only 2.4%. The total integral flux at location A was about 38% lower than the simulated value, while all the measurements were around 10% higher for location B.  
Figure 4: Comparisons between measured and simulated neutron spectra, (**a**) location A without PE plate; (**b**) location B without PE plate; (**c**) location B with a 1 cm PE plate; (**d**) location B with a 2 cm PE plate. Table 2 presents the H*(10) values for the neutrons with different energies, which were derived from the neutron spectra shown in Figure 4 and the ICRP recommended conversion coefficients [15]. The results demonstrate that the discrepancies in the dose rates, contributed by epithermal and fast neutron at location A, were clearly due to the differences in the neutron fluences. On the other hand, at location B, the total neutron dose rates were dominated by the thermal neutrons because of their relatively strong intensity.