Study on Moderation Properties of Cold Mesitylene using KUANS

Neutron moderation properties from the cold mesitylene moderator have been studied. Kyoto University Accelerator driven Neutron Source has been used for these experiments. The container of the mesitylene moderator is situated in front of the polyethylene moderator and the change of the time of flight spectrum has been recorded as a function of the temperature of the mesitylene moderator. By fitting the Maxwell distribution to the obtained TOF spectra, the neutron temperature corresponding to the mesitylene temperature is estimated.


Introduction
In recent years, compact neuron sources have been developed. In spite of their low neutron flux, they may be useful by specific scientific domains. For study of nanoscale structure in materials using small angle scattering, or reflectometry, cold neutrons are commonly used because the separation between the incident and the diffracted neutron beams are roughly proportional to the wavelength and larger and easier to measure with cold neutrons.
For producing such long-wavelength neutrons, cold neutron sources (CNS) are employed. For most of such CNS, liquid hydrogen or solid CH4 are used as cold moderator. For compact sources, however, such materials are not suitable because a) they are gas in room temperature and the volume change is quite large when they become liquid or solid, and b) they are explosive in the gas state. Mesitylene having three metyl's around the benzene ring and staying liquid over a large range of temperatures has been suggested as a good moderator for small neutron sources [1].
In the present study, we measured the wavelength distribution from the cooled mesitylene moderator in order to clarify the moderation properties for neutrons of cold mesitylene using Kyoto University Acceleratordriven Neutron Source (KUANS).
In KUANS neutrons are produced by 9 Be(p, n) 9 B reaction using pulsed 3.5MeV-proton beam. The neutrons are moderated by the polyethylene and the moderated neutrons are emitted to the direction perpendicular to the proton beam [1]. The mesitylene moderator is situated in front of the polyethylene moderator having the size of 120x120x85 mm 3 in room temperature. The mesitylene container with 25(t)x96(w)x100(h) mm 3 is held in a vacuum container with the size of 43(t)x123(w)x155(h) mm 3 . The moderators are surrounded by the graphite reflector. . The neutrons emitted from the moderator surface go through the 20 (h)x5 (w) mm 2 -slit situated at 1710 mm from the moderator surface and are detected with 3He 1dimensional position sensitive detector (PSD) at 1546 mm from the slit. With the PSD, it is possible to measure 1dimensional `pin hole image' over the moderator as well as the time of flight (TOF) spectrum. The TOF spectra presented in this report are taken from the mesitylene area of the PSD data. Total flight length is 3256mm and T0 (time between the system trigger and emission of thermal neutron from the moderator) is 70 s for KUANS. The repetition rate and pulse width of the proton pulse are 100Hz and 60s, respectively. Average proton current was about 60 A. Since the time bin for TOF measurements is 10 s, 6 successive channels of TOF data are arithmetically averaged. Mesitylene moderator was cooled with cryostat from room temperature to 28K. During cooling process (about 10hr), the accelerator was operated, and the neutron spectra were measured. The TOF data are summed up for  Fig. 2. Change of the spectrum is small for over 200K which is close to the melting point of mesitylene. As the TM decreased, the peak intensity is lowered and shifted to the longer wavelength side. The relative neutron intensity versus wavelength for TM= 204, 141, 84, 28K comparing to that for 251K is shown in Fig. 3.   Fig. 3. Relative neutron intensity for some temperature comparing to that for 251K.

Measurements
For wavelength longer than 0.25nm, the ratio is larger than unity and increases as the wavelength becomes longer and as TM lowers. At the lowest temperature of 28K and at wavelength of 0.4nm, neutron intensity is six times higher compard to that at 251K.

Discussion
In order to obtain the neutron temperature, we fit a Maxwell distribution to the neutron wavelength distribution shown in Fig.2. The aim of the fit is to obtain the temperature of the neutrons Tn in the cold mesitylene moderator. Hence the fitting is carried out for neutrons with wavelength longer than 0.2nm. Examples of the fit results are shown in Fig.4. The fit function is the neutron flux and has the following form for neutron wavelength of : (1) where 0=0.178nm, and T0=300K are the wavelength and corresponding temperature for 25meV-neutron. The fit parameters are A and Tn, the latter of which represents the moderated neutron temperature. Fig.2 in the 251K (red) and 28K (blue) case.

Fig. 4. Examples of Maxwellian fit to neutron TOF data shown in
The red and blue line in Fig.4 represent the spectrum for TM=251K and 28K, respectively. For the former case Tn=239K, and for the latter Tn=61.9K, respectively. There may be two reasons why Tn is higher than TM : (1) Because the number of excitation levels around several meV range in mesitylene is not enough, some neutrons are emitted before being fully moderated. (2) Thickness 25mm of the mesitylene moderator container is not enough for full moderation of neutron. Hence the discrepancy between the fit function and TOF spectrum in the short wavelength range is due to the under-moderation of the neutrons.
Repeating the same procedure for other temperature of mesitylene, the relation between TM and Tn has been obtained. The result is shown in Fig.6.   Fig. 6. The relation between TM and Tn.
In the figure, the solid line stands for the relation TM = Tn. When TM>100K, Tn changes along TM, which means that the neutron temperature follows the mesitylene temperature.
On the other hand, when TM<100K there appears discrepancy between TM and Tn, which means that at low mesitylene temperature neutrons are under-moderated; their temperature stays above the mesitylene temperature. In spite that, cooled mesitylene enables us to obtain an increase of flux of long wavelength neutrons with the factor 10 at 0.5nm compared to ambient temperature.
The slowing down distance for mesitylene is estimated to be about 6cm, since that for H2O is about 5cm and is reverse proportional to the hydrogen density (6.7x10 22 , 5.19x10 22 for H2O and mesitylene, respectively) [3]. The size of the mesitylene container is 25x96x100 mm 3 in the present experiments, and the `thickness' 25mm is too short for fully moderation. The neutron flux may be improved if the neutron is emitted the `side' of the container.

Conclusions
Neutron TOF spectra from the mesitylene moderator cooled from the room temperature to 28K were measured. Measured spectra have changed corresponding to the mesitylene temperature. As the mesitylene temperature decreases, the peak of the spectrum shifts to longer wavelength side, and the neutron counts in the wavelength range longer than 0.2nm increases. At 0.4nm, the ratio of the neutron counts from the cooled mesitylene against uncooled mesitylene becomes about 6. The neutron counts with the wavelength over 0.2nm, is well reproduced by the Maxwellian distribution. From the fit, neutron temperature is obtained and is almost the same in the temperature range above 100K, and the difference appears under 100K. The neutron flux may be improved by the optimization of the arrangement of the moderator system.