3.1 Experimental arrangement

The arrangement for the total cross-section experiment should exhibit "good geometry", including the target, collimators, sample changer, and neutron detector, as shown in Fig. 2. Two experimental stations, i.e., Endstation#1 and #2 are constructed in the neutron beam line [10]. A sample changer that can hold several samples is located at Endstation#1. The neutron detector is at Endstation#2, which is a distance of approximately 76 m from the spallation target. The distance between the sample and the detector is approximately 20 meters. The scattered neutrons can be reduced for this distance and good collimation between the sample and the detector.

Fig. 2.Full-screen View

Geometry for the present experiment [10].

There are two collimators in the neutron beam line and their diameters can be selected. The diameter of the detector is 50 mm, and the diameter of collimator2 is set to be 30 mm, whereas the diameter of collimator 1 is 60 mm.

3.2 Detection system

A multi-layer fast ionization chamber is located in the neutron beam line at Endstation#2, as shown in Fig. 3 [16]. Three ²³⁵U and three ²³⁸U cells are located in the detector. By counting and analyzing the fission events of ²³⁵U (n, f) and ²³⁸U (n, f) reactions, the neutron counts can be determined.

Fig. 3.Full-screen View

A photo of the FIC (a) and the schematic view (b), figure (b) from Ref. [16]. In (b), from left to right, the cells are Fe, U238-1, U235-1, U235-2, U238-2, U, U235-3, U238-3, respectively.

The fission signal was collected by the MSI-8 preamplification and the Back-n public DAQ system that was developed by the University of Science and Technology of China. The DAQ system mainly includes an SCM module (Signal conditioning module), an FDM module (Field Digitizing module), a TCM module (Trigger & Clock module) and a data center for storing waveform data [17]. The start signal of the FDM module is provided by the TCM, and the trigger signal of the TCM is provided by the external T0 signal. This signal originates from the accelerator proton target signal

The block diagram of the entire detection system is shown in Fig. 4. The proton monitor at the CSNS is used to measure the proton count, which is then used to normalize the neutron count. The acquired neutron signals are then saved in the DAQ data center for offline processing after the experiment is completed. The UTC of each proton pulse corresponds to that of every event number in the DAQ data center.

Fig. 4.Full-screen View

Block diagram of the detection system

3.3 Sample

To increase the accuracy of the measurements, the number of scattered neutrons must be minimized. The main contribution of the scattered neutrons depends on the size of the sample and its position in the NTOX. Considering the scattering process, the sample should be smaller and thinner. A thick sample should be selected if the statistics of the neutron counts are emphasized. Taking both factors into consideration, a T of 0.5 to 0.7 is preferred in the actual measurement [18].

A simulation based on the Monte Carlo N-Particle (MCNP) code was performed to determine the thickness of the sample. The sample used in this work was a cylindrical natural graphite. The results indicate that the neutron energy range corresponding to a transmission of 0.5 to 0.7 is 2 MeV to 20 MeV when the graphite sample is 40 mm thick and the total cross-section of the resonance region in carbon is more desirable. The physical parameters of the sample used in the experiment are given in Table 1. The calculated density of the sample was 1.86 g/cm³, which is lower than the normal graphite density (2.25 g/cm³). Preliminary judgment is that this 17% difference is caused by the production process. Therefore, the atomic density (0.3741 atoms/barn) should be an apparent value.

A sample changing system was used to change the sample’s position in a few seconds, as shown in Fig. 5. The sample holders can mount several samples and they are positioned at the top of the sample changer. In addition, they can be driven horizontally and vertically. By centering a sample before measurements are performed and recording the data at the center of a neutron beam, samples could be moved to the expected positions using a motor controlled by a computer in the control room. The positioning accuracy is 0.001 mm.

Fig. 5.Full-screen View

Sample changer

4.1 Amplitude spectra

The amplitude distributions of the ²³⁵U and ²³⁸U fission cells in addition to the measured backing and alpha signals are shown in Fig. 6. The signal amplitude is mainly due to α-particle decay and electronic noise, and it must be subtracted from the neutron spectrum. The threshold could be determined by analyzing the amplitude spectrum. It is the center of the amplitude spectrum valley.

Fig. 6.Full-screen View

Amplitude distributions of ²³⁵U (a) and ²³⁸U (b) cells under open-beam.

4.2 Energy calibration

The neutron energy $E_{\text{n}}$ is given as follows:

where $m_n$ is the mass of a neutron and c is the speed of light, ${\beta }_n=\frac{{\upsilon }_n}{c}=\frac{L}{cTof}$ where ${\upsilon }_n$ is the neutron speed, L is the length of the flight path and Tof is the neutron time of flight, which is given as follows:

where $T_{ff}$ is the start time of the fission signal recorded via the DAQ system, $T_{gamma}$ is the start time of the gamma flash recorded by this system. It is obtained by measuring gamma-flash at the 90 mm neutron beam window at 2 atm. The details of the measurement method will be presented in another report. $To{f}_{gamma}$ is the gamma-ray time of flight for the flight path, $To{f}_{gamma}=L/c$. By substituting for $Tof$ and solving for $T_{ff}-T_{gamma}$, we have:

Using a known approximate flight path of 76 m to obtain a neutron time of flight spectrum and then comparing to the one calculated using ENDF/B-VIII.0. [12], the 8.77 eV resonance is determined. By performing a Gaussian fit of the 8.77 eV resonance of ²³⁵U in this work, $T_{ff}-T_{gamma}$ is determined to be $1853660\pm 20$ ns. Substituting into Eq. (5), a neutron flight path of 75.939 m of the first ²³⁵U fission cell can be obtained.

Using the signal for the first ²³⁵U fission cell for sample-in based on the same method, a flight path of 75.938 m is obtained. This value has a difference of 0.013‰ compared to 75.939 m. Similarly, the neutron flight path of the other two ²³⁵U fission cells can be obtained. By using the ²³⁵U and ²³⁸U fission cell geometric distance, the neutron flight path of the three ²³⁸U fission cells can also be obtained, as shown in Table 2.

The uncertainty of the flight path is less than 0.04‰. The difference between the distance between the two fission cells obtained by calculation and the actual geometric distance of the two fission cells is within the uncertainty of the flight path.

If the time of flight is known based on Eq. (4) and the flight path, the neutron energy spectrum can be obtained. Figure 7 shows the amplitude-energy two-dimensional distribution of the first ²³⁵U cell when open beam(a) and sample-in (b). When the neutron energy is below 300 keV, there is an amplitude boundary of approximately 250 ch between the fission and α-particle signal in the distribution. When neutron energy is in the range of 300 keV-10 MeV, the boundary is relatively blurred. This is because of the large number of fission events and high energy α-particle events generated by (n, α) reaction.

Fig. 7.Full-screen View

Amplitude-energy 2D distribution map of the first ²³⁵U cell for open beam(a) and sample-in (b).

The neutron energy spectra for which the neutron count is normalized by the proton count can be obtained using Eq. (3), as shown in Fig. 8. To increase the statistical count of the low-energy region, the bin is larger than that the case when the flight distance (1000 ns / bin) is determined and is divided by log (eV) with 100 bins for each order.

Fig. 8.Full-screen View

The normalized neutron energy spectrum with the first ²³⁵U fission cell (a) and the first ²³⁸U fission cell (b).

4.3 Total cross-section

Using Eq. (2), the transmission with the first ²³⁵U and ²³⁸U fission cell can be obtained based on the normalized energy spectrum, as shown in Fig. 9.

Fig. 9.Full-screen View

Measured transmission of carbon with the first ²³⁵U fission cell (a) and the first ²³⁸U fission cell (b).

The neutron total cross-sections with three ²³⁵U and three ²³⁸U fission cells can be obtained using Eq. (1), as shown in Fig. 10. The large statistical fluctuation within the energy range of 3–30 eV in Fig. 10 (a) is derived from insufficient neutron counts (~20 counts/bin) with one fission cell.

Fig. 10.Full-screen View

The neutron total cross-section with ²³⁵U (a) and ²³⁸U (b) fission cells.

To increase the statistical count, the count with three identical fission cells can be added. The transmission with ²³⁵U and ²³⁸U fission cells can be calculated after the neutron count is added as follows:

where $I_I{(E_i)}_{51}$, $I_I{(E_i)}_{52}$ and $I_I{(E_i)}_{53}$ are the neutron counts for the sample-in, $I_O{(E_i)}_{51}$, $I_O{(E_i)}_{52}$ and $I_O{(E_i)}_{53}$ are the neutron counts for the open beam with U235-1, U235-2, U235-3, respectively, ${\eta }_{51}$, ${\eta }_{52}$ and ${\eta }_{53}$ are the fission count efficiency, and $m_{51}$, $m_{52}$ and $m_{53}$ are the effective mass for detecting neutrons of ²³⁵U. $T{(E_i)}_8$ is the transmission with ²³⁸U fission cells after superimposing the neutron count.

The neutron count ratio with all the fission cells and the uranium mass ratio for every fission cell are shown in Table 3. The uncertainty of the uranium mass is approximately 1%. The difference between the neutron count ratio with a fission cell and the mass ratio of Uranium is less than 3%. Therefore, the nonuniformity of the uranium distributed on the backing is negligible and the uranium mass can be used in Eq. 6 and Eq. 7 instead of the effective mass. The fission count efficiency and the uranium mass should be only considered when neutron counts are added.

The fission count efficiency of fission cells can be seen in Table 4. The details of the fission count efficiency calculations will be presented in a separate report.

After the addition, the neutron total cross-section with ²³⁵U and ²³⁸U fission cells are as shown in Fig. 11. The statistical uncertainty is less than that with one cell.

Fig. 11.Full-screen View

The neutron total cross-section with ²³⁵U and ²³⁸U fission cells after adding the neutron counts.

As shown in Table 5, the neutron statistical uncertainty for each bin with ²³⁵U fission cells is different in different energy regions. Compared to one cell of the ²³⁵U fission cells, the neutron statistical uncertainty is reduced by approximately 45% with three superimposed ²³⁵U fission cells.

The neutron statistical uncertainty for each bin with ²³⁸U fission cells is shown in Table 6. Compared to one piece of ²³⁸U fission cell, the neutron statistical uncertainty is reduced by approximately 42% with three superimposed ²³⁸U fission cells.

5.1 ²³⁵U (n, f) resonance peak

The fission count-neutron energy spectrum is compared with the fission cross-section from ENDF/B-VIII.0 in Fig. 11. There is a good agreement for all the fission resonances in the energy range of 5 eV to 20 eV, and only a few differences in some detail structures are observed. In addition to the 8.77 eV resonance peak, there is a good agreement for many resonance peaks, such as 12.4 eV and 19.3 eV in Fig. 12. The results indicate that the detection system is reliable.

Fig. 12.Full-screen View

The neutron energy spectrum measured with the first ²³⁵U cell (open beam) compared to the evaluated data.

5.2 Total cross-sections of carbon

Given that the width of the proton beam pulse is 50 ns and the beam is in the double mode, it will cause superposition and broadening in the energy region above keV. The effect of the neutron energy spectrum measurement in double mode is approximately 1.8%–8.8% in the energy range of 1 MeV to 20 MeV. Therefore, the evaluated data cannot be directly compared to the experimental results. The carbon data evaluated in ENDF/B-Ⅷ.0 was broadened using the Gaussian function as shown in Fig. 13. To achieve broadening, the energy-total cross-sections from ENDF/B-Ⅷ.0 were initially converted into TOF-total cross-section with a flight path of ~76 m and an energy range of 1–20 MeV. Each energy point was then broadened using a standard normal distribution function with an FWHM of 52 ns, a pulse width of 50 ns. The resolution of the detector was 5.7 ns. The broadened data of the single bunch and the double bunch with an interval of 410 ns was then obtained. Finally, the broadened TOF-total cross-sections were converted into energy-total cross-section. From Fig. 13, a smaller cross-section of resonance peaks can be seen in the broadened data, and it is caused by the FWHM of 50.3 ns, which is set in the calculation.

Fig. 13.Full-screen View

Gaussian broadening for single mode (red line) and double mode (blue line) neutron beams on the cross-section of the evaluated data.

The presented results are compared with the broadened data in Fig. 14. In the energy range of 1–20 MeV, the measured neutron total cross-sections with ²³⁵U fission cells are in good agreement with that the ²³⁸U fission cells and the deviation is from 0.5% to 4.4%; it is generally less than 3%. The measured results with ²³⁵U and ²³⁸U cells are preliminary compared to the broadened data and the deviations are 0.5%–9% and 0.4%–9%, respectively. The experimental result is in good agreement with the evaluated data in ENDF/B-Ⅷ.0 for the 2.077 MeV resonance peak.

Fig. 14.Full-screen View

The measured neutron total cross-sections of natural carbon compared with the broadened data.

5.3 Study on the separation of the measured spectra

Based on the unfolding procedure developed by the project team members, the separated neutron spectra were obtained. The unfolding procedure was developed based on the Bayesian principle. More detailed information on the procedure will be provided in an upcoming report that will be published by the project team members. Using the unfolding procedure, the neutron total cross-section of the single bunch can be obtained, as shown in Fig. 15.

Fig. 15.Full-screen View

The measured neutron total cross-section (after unfolding) of natural carbon compared with the broadened data.

The neutron total cross-section after unfolding is generally consistent with the broadened single mode data. The results for the ²³⁸U fission cells fluctuate greatly in the range of 1 MeV to 1.5 MeV due to the insufficient fission count. In the energy region from 1 MeV to 1.5 MeV, the count of a bin is from 39 counts to 987 counts and the average count is 255 counts/bin. Insufficient fission counts lead to a large error during unfolding. Given the time resolution of the fission chamber and the 50 ns proton bunch width, the 5 MeV and 5.37 MeV peaks are superimposed. Therefore, they are not easily identified in Fig. 15. There will be a dedicated short-bunch operation mode with a bunch length of 1.5 ns or 3.3 ns in rms in the future. This mode can be further developed to the single-bunch operation mode. For 1.5 ns, this corresponds to 0.1%–0.6% in rms time resolution for the neutron energy from 10 keV to 100 MeV [10].