Experimental Evaluation of Energy Resolutions for Pulsed Neutron Beam in the KURNS-LINAC

. In this study, experimental evaluations for the energy resolution of pulsed neutron flux in the neutron path were carried out. The capture gamma-rays from a Ta-181 sample were measured by BGO detectors with a TOF method, and the TOF spectra for well-known resonances were obtained. The energy resolution was evaluated by comparing a full width at half maximum of the Ta-181 resonances in the JENDL-4.0. In order to obtain relationships between the energy resolution and the pulsed neutron beam width, the measurements were carried out with the pulsed neutron beam width of 4 μ sec, 1 μ sec and 0.1 μ sec, respectively. As the experimental results, the energy resolution of neutron energy range from 4 eV to 125 eV corresponding to each pulse width were evaluated. For example, the energy resolution at 4.28 eV (Ta-181 first resonance peak) was about 0.5 % for a pulse width of 4 μ sec.


Introduction
The electron linear accelerator at the Institute for Integrated Radiation and Nuclear Science, Kyoto University (KURNS-LINAC) was established in 1965. The KURNS-LINAC can be used as various radiation sources such as electron, photon, and neutron, depending on the research purpose. The KURNS-LINAC has a feature that pulse width of the electron beam can be easily changed, and the facility has two operational modes depending on the beam pulse width. One is a long pulse mode with the pulse width of 0.1-4.0 μsec, repetition rate of 1-120 Hz, and a peak current of about 0.5 A. Another is a short pulse mode with the pulse width of 2-100 nsec, a repetition rate of 1-300 Hz, and peak current of about 5 mA. Time Of Fight (TOF) measurement for nuclear data are performed using pulsed neutron source at the KURNS-LINAC. In the measurement, resonance peaks are broadened by time resolution. The time resolution consists of two main components in the KURNS-LINAC. One is a pulse width of the electron beam. The pulse width contributes to uncertainty for neutron generation times. The other is moderation of neutrons. The neutrons are generated in a tantalum target through the (γ,n) reaction caused by the bremsstrahlung X ray. The generated neutrons are moderated in a light water moderator. In this moderation process, the TOF uncertainty is caused by the neutron moderation time. Time resolution contributes to energy resolution. It is necessary for accurate resonance analysis to evaluate the energy resolution. In the KURNS-LINAC, the numerical analysis of energy resolution has been performed [1]; * Corresponding author: yasu.0621.0922@gmail.com however, an experimental evaluation of energy resolution has never been performed. In this study, experimental evaluations of energy resolution with several pulsed neutron beam width in the KURNS-LINAC were carried out.

Experiment
The experimental system is shown in Fig.1. Figure 2 shows a pulsed neutron source with a moderator at the KURNS-LINAC. The pulsed electron beam accelerated to 30 MeV was injected into the tantalum target, and bremsstrahlung X ray was generated. High energy neutrons were emitted isotopically by (γ,n) reaction from the tantalum target. The moderator was light water. The geometry of moderator was cylindrical with a height of 30 cm and a diameter of 20 cm. A sample was located at 135° to the electron beam, and 12.65 m away from the tantalum target. The neutron beam was narrowed to 1.5 cm by lead and boron collimators located upstream from the sample. The sample was a square foil of tantalum-181(17 mm×17 mm×0.03 mm t ), which has well-known resonance parameters and has natural abundance of about 100 %. Prompt capture gamma rays from the sample were detected by twelve BGO detectors located around the sample. Figure 3 shows a block diagram of the measurement circuit. The measurement signals from each detector were summed by a Dual Sum & Inverter. The data acquisition system used the WE7562 as a Multi Channel Analyzer (MCA). The MCA registered pulse arriving time and pulse height signal by time stamp format. The TOF was obtained from the difference between the pulse arriving time from BGO and the reference time signal from the LINAC Injector. Thus, signals from the BGO detectors were acquired as two-dimensional data on TOF and pulse height. We carried out the experiments with different pulse widths (4, 1, 0.1 μsec). The LINAC operational conditions for each measurement are shown in Table 1. Runs 1 and 2 were operated by the long pulse mode, and Run3 by the short pulse mode. The repetition rate was set to 50 Hz in the long operational mode and 200 Hz in the short operational mode. In the measurement of short pulse mode, a cadmium filter was set on the neutron flight path in order to prevent overlap of neutrons produced in the previous pulse. The measured two-dimensional data with TOF and pulse height data of Run3 are shown in Fig.4. The resonance captures were clearly obtained. In the figure, the horizontal axis is the TOF spectrum, and the vertical axis is the pulse height spectrum.

Evaluation of FWHM
Full width at half maximum (FWHMexp) at each resonance absorption were obtained from the measured TOF data. In Fig.4, a peak of the pulse height is observed in the area marked in red line. This peak is prompt gamma rays from hydrogen nuclides in the moderator. The pulse height data higher than this region were used in the FWHMexp analysis. The FWHMexp was obtained from a fitting curve with a Gaussian function to the net counts at each resonance capture reaction as following.
Here, t is TOF spectrum, is variance, a is normalization factor, b is median and c is background. FWHMexp contains the broadening of the resonance by the self shielding and Doppler effect. In order to evaluate the broadening by the self shielding and Doppler effect, we performed calculation by Monte Carlo code PHITS 3.23 [2] with JENDL-4.0 [3]. The calculational geometry is shown in Fig.5. In the calculation, neutrons were injected into a Ta-181 sample with the same geometry as the experiment; a spectrum of the capture reaction rate was obtained. Here, resonance broadening by neutron moderation in the moderator and the neutron pulse width were not considered. To allow for negligible statistical error, the number of generated neutrons in those calculations was set to 1×10 8 particles. Resonance width (FWHMcal) was obtained by Gauss fitting for each resonance same as the experiment.   The calculational FWHM decreased with increasing the neutron energy. The FWHMcal is narrower than all FWHMexp, the differences are exactly the time resolution. The difference is larger on the high energy side.

Evaluation of energy resolution
The time resolution was obtained by comparing FWHMexp and FWHMcal. The time resolution was obtained from Eq.3.

Energy resolution (
) is related to the time resolution ( ) by Eq.4.
Here, is time resolution by accelerator and detector ( sec), L is neutron flight path (m), is constant value (72.3 eV 1/2 sec/m), is energy resolution of moderator. The equation (4) shows that the first term in the right-hand side depends on the neutron energy, and the second term is constant. The evaluation of the energy resolution is shown in Fig.8. The energy resolutions at each pulse width depend on the neutron energy. Those results are consistent with the first term on the right-hand side of equation (4). In Run 1, the energy resolution is about 3.8 % at energy of 60 eV. The energy resolutions in Runs 2 and 3 are 2.2 % -2.7 % at 125 eV. At the energy of 4 eV, the energy resolutions with all pulse width are about 0.5 %. Thus, the energy resolution of moderator ( ) is less than 0.5 %. On the other hand, although the pulse width of Run 2 (pulse width: 1 sec) is 10 times longer than Run 3 (pulse width: 0.1 sec), the differences of the energy resolutions between Run 2 and Run 3 are not much. An investigation of the difference between the results of Run 2 and Run 3 is a future topic.

Conclusion
In this study, the evaluations of energy resolutions for pulsed neutron beam in the KURNS-LINAC were carried out. The experimental conditions were that a cylindrical light water moderator with a diameter of 20 cm was used, and the neutron flight path was 12.65 m. The energy resolutions were obtained by the difference between the experimental and the calculational FWHM in resonance capture of Ta-181. In addition, the experiments were carried out with different pulse widths (4, 1, 0.1 μsec). The energy resolutions were evaluated an on energy range of 4 eV to 60 eV with the pulse width of 4 sec, and on an energy range of 4 eV to 125 eV with the pulse width of 1 and 0.1 sec. As a result, the energy resolution of the 20 cm diameter light water moderator in KURNS-LINAC was less than 0.5% and was not dependent on the pulse width.