1 Introduction

The Am-Be and ²⁵²Cf neutron sources are widely used in neutron dosimetry laboratories. The important features of Am-Be source is its long half-life and emission of fast neutrons with rather wide energy spectra, while ²⁵²Cf yields a highly concentrated and reliable neutron spectrum from a small assembly. The last feature of both sources is helpful in covering the energy domain of interest for many applications in ambient and personal dosimetry. Nevertheless, the neutron energy spectrum depends on materials and dimension of the capsule and on amount and physio–chemical properties of active material, thus affecting relevant quantities such as spectrum-averaged fluence-to-dose equivalent conversion coefficient ^[1-6]. It is important to be know the neutron flux accurately so as to measure different quantities related to a neutron source ^[7].

Neutron detection has a key role in development of nuclear technology and its applications ^[8,9]. High sensitive neutron detectors are required. However, most of the neutron detectors are also sensitive to gamma rays. Therefore, an effective technique is required to eliminate the gamma background for accurate neutron measurements. Generally, methods used to recognize neutron interactions within a detector rely on second-order effects. Two neutron interactions used for a variety of thermal neutron detectors are the ¹⁰B(n,α)⁷Li ^{[9, 10]} and ⁶Li(n,α)³H reactions ^{[11, 12]}. The α particles can be easily detected.

Low atomic number materials, such as high-density polyethylene (HDPE), which has a high concentration of hydrogen, tend to have relatively high elastic scattering cross sections for fast neutrons, and often (n,p) reactions from fast neutrons interacting in hydrogen-filled materials are manipulated for fast neutron detection. For detection of thermal or low energy neutrons, polymers-based SSNTDs, i.e. Solid State Nuclear Track Detectors (such as CR-39), can be used only in combination with a neutron reactive film which converts neutrons into other detectable radiations, recoil nuclei ^{[13, 14]}. Use of a BF₃ or ³He neutron detector, one can measure the optimum thickness of the moderator accurately, which is essential to avoid excessive thermal neutron absorption in the moderator. The neutron activation analysis can determine accurately the major and trace elements in different samples ^{[10–12, 15]}. In practice, aromatic hydrocarbons are considered as the most radiation-resistant hydrogenous substances and have properties to moderate slow neutrons more effectively ^[16].

A paraffin wax moderator assembly has been developed to find out optimum thickness of paraffin wax. It can be utilized for fast neutrons from various neutron-producing reactions on an accelerator or for measurement of neutron yield from a Mather type plasma focus device ^[17–20]. The assembly has been utilized to find out neutron flux of a neutron probe which contains Am-Be as a neutron source ^[21]. Neutron flux comparison and neutron activation are used to the measure neutron flux ^[24]. A 50 mCi Am-Be neutron probe is used as a neutron source for the measurement of moisture in soils ^[21].

The moderating materials should be of large scattering cross-section, small absorption cross-section and large energy loss per collision ^[23], and paraffin wax is just a desired moderator. Its optimum thickness was calculated for 3 MeV neutrons ^[24], and was experimentally determined at 7 cm and 2.5–4.5 cm for Am-Be and ²⁵²Cf neutron sources, respectively ^{[25, 26]}. The results were based on the maximum gamma ray yield due to neutron activation. The optimum thickness of HDPE moderator was measured at 4–6 cm for 2.8 MeV neutrons. For theoretical calculations, different codes such as MNCP, MNCPX, SRIM etc. are used ^{[27, 28]}. The present paper is designed to determine the optimum moderator thickness that is required to be wrapped around a BF₃ detector used in monitoring fissile material. The experimental results are compared with MC simulations for Am-Be neutron source using MCNP5 code version 1.40 ^[29].

2 Material and Methods

2.2. Experimental Approach

The paraffin wax moderator assembly consists of two parts as shown in Fig.1. The first part consists of a removable paraffin wax discs, neutron detector and a neutron source (i.e. Am-Be/ ²⁵²Cf neutron sources). The second part is a mounting frame with two parallel spring-loaded Φ12 mm steel rods, each fixed at one end with the frame. The other two ends are fixed to a movable plastic ring around a 1.4 cm thick paraffin wax disc. The purpose of the plastic ring is to give strength to the paraffin wax discs. A number of paraffin wax discs are used. Sized at Φ27 cm × 0.6–1.4 cm, each disk is mounted in a 6 mm thick plastic ring. The paraffin wax discs can be assembled easily on the mounting frame, between two semi cylindrical fixed pipes with the assembly at the same axes, one for the neutron detector and the other for the neutron source. The two parallel rods act as a guide for the paraffin wax discs, and keep the discs in close contact with each other. The Φ27 cm discs keep the axis same with respect to the axes of the neutron detector and the neutron source. Paraffin wax discs can be added or removed for measurement of optimum thickness of paraffin wax, where the neutron detector counts is the maximum. Two BF₃ (Φ1″and 2″) and one ³He (Φ0.5″) neutron detectors are used for measuring the optimum thickness with Am-Be or ²⁵²Cf neutron sources. The associated electronics with detector assembly consisted of pre-amplifier, amplifier, single channel analyzer and counter/timer manufactured by the ORTEC.

Fig. 1Full-screen View

Sketch of the paraffin wax moderator assembly.

The background counts per second were measured without the neutron sources, and they were subtracted from the actual neutron count rates emitted from neutron sources. For different paraffin wax thicknesses, counts emitted from either Am-Be or ²⁵²Cf neutron sources, were taken for 100 seconds by using the BF₃ and one ³He neutron detectors. For both the Am-Be and ²⁵²Cf neutron sources, the paraffin wax thicknesses were increased to find the maximum counts, and on further increase in thickness, the counts started decreasing. Here, the maximum counts represent optimum paraffin wax thickness that is required to thermalize fast neutron (of course, the process is the tradeoff between absorption and moderation). To minimize scattering from the walls, the heavy shielding was placed about 4 m away from the source. The scattering contribution at the detector position was checked with and without the shielding, with the source at its position. The difference was negligible and hence an evidence of no scattering contribution from shielding walls was seen. Furthermore, BF₃ or ³He detectors can detect only slow or thermal neutrons and the gases have very low interaction cross-section for fast or scattering neutrons.

The moderator assembly (Fig. 1) was also used for the measurement of neutron flux emitted from the Am-Be and ²⁵²Cf neutron sources to check the validity of the optimum thickness of the paraffin wax moderator, using the neutron flux comparison method and the neutron activation analysis method ^[22].

2.2.1. Neutron flux comparison method

The comparison of counting rates was carried out, between the standard Am-Be neutron source of known flux (F₁) and that from the neutron probe of unknown flux (F₂) under conditions insensitive to the energy of neutrons. Let C₁ be the average counts per sec for F₁ recorded by a BF₃ (Φ1″) neutron detector in contact with the 6 cm thick paraffin wax moderator and C₂ be the average neutron counts per sec, with their background subtracted, from the neutron probe under the same condition. The neutron flux F₂ from the neutron probe is given by F₂ = F₁ C₂/ C₁.

2.2.2. Neutron activation analysis method

The paraffin wax moderator assembly was used to measure the neutron flux of the neutron probe through activation analysis technique by using silver foil, and the 6 cm optimum thickness of the paraffin wax moderator was validated.

Thermal neutron activation analysis is the absolute method to determine the neutron flux of a neutron probe. The silver isotopes of ¹⁰⁸Ag (T_1/2 =0.39 min) and ¹¹⁰Ag (T_1/2 = 24.6 sec) are produced through nuclear reactions of ¹⁰⁷Ag(n, γ)¹⁰⁸Ag and ¹⁰⁹Ag(n, γ)¹¹⁰Ag with thermal neutron. After a few half-lives of ¹¹⁰Ag most of the radioactivity in silver foil is due to ¹⁰⁸Ag ^[30]. A G.M counter with Mylar end-window is used for the neutron activation analysis. The silver foil is placed at the Mylar window. Both the neutron probe and the end-window of G.M detector are placed at the same axis in opposite and in contact with the paraffin wax moderator (Fig.2).

Fig. 2Full-screen View

The G.M detector with the end Mylar window, Ag foil, the paraffin wax moderator and the neutron probe.

The optimum paraffin wax thickness of 6 cm was used in the moderator assembly. At the termination of activation, the flux φ of the neutron probe (in n/cm²/sec) is given by φ =[A₀w(1−e^−λt)/(σA_avαm)]ε(4π/Ω) ^[24], where A₀ is the activity of ¹⁰⁸Ag at t =0, w is the atomic weight of silver, λ is the decay constant, t is the irradiation time, σ = 37.6 barns (taken from the ENDF library ^[31]) is the thermal neutron capture cross section of ¹⁰⁷Ag, A_av is the Avogadro’s number, α is the natural isotopic abundance of ¹⁰⁷Ag, m is the mass in grams of ¹⁰⁷Ag, ε is the intrinsic efficiency of the detector, and Ω is the solid angle subtended by the G.M detector at the neutron source (Am-Be) of the probe.

The intrinsic efficiency of the G.M detector was determined from a ¹³⁷Cs γ-ray source of known activity. The silver foil was activated for 5 min. Although both ¹⁰⁸Ag and ¹¹⁰Ag are produced, most of the activity is due to ¹⁰⁸Ag at the time of counting. The neutron probe was taken far away from the moderator assembly as quickly as possible, so the G.M detector background count was made almost negligible at the time of counting. The activated silver foil was counted immediately, and was repeated several times for better results. The background of the G.M detector was measured in advance.

3 Results and Discussion

The measured counts per 100 seconds for different wax thicknesses by using the three neutron detectors for the Am-Be and ²⁵²Cf neutron sources plotted against wax thickness are shown in Fig.3. The maximum counts for each neutron detector and source represent the optimum paraffin wax thickness that is required to thermalize fast neutrons. From Fig.3, the optimum paraffin wax thicknesses were 6 cm and 5.5 cm for Am-Be and ²⁵²Cf neutron sources, respectively. The yield of thermal neutrons increases with the thickness of paraffin wax from 1.6 to 6 cm, due to fact that the fast neutrons lose their energy through elastic collision with hydrogen atoms of paraffin wax. The yield of thermal neutrons at these thicknesses is found to be maximum, as a large number of fast neutrons lose their maximum energy through elastic collisions. However, on further increase in thickness of the paraffin wax from 6.5 cm to 12 cm, the yields of thermal neutron decreases due to elastic and inelastic scattering reactions. The neutrons lose their energy through the interactions until they are captured by paraffin wax (shielding material) ^[23]. Normally, the neutron capture cross section is larger only for thermal neutron energies, that is why the neutrons slowing down by scattering are important before capture ^[23].

Fig. 3Full-screen View

The paraffin wax thickness versus neutron counts, with different neutron detectors for Am-Be (a) and (b) ²⁵²Cf neutron probes.

To validate the optimum thickness of paraffin wax, the neutron flux was calculated. By the neutron flux comparison method, the average neutron counts per second, C₁, were 141.3 ± 0.66 with the known neutron flux of F₁ = (8.3±0.66)×10⁴ n/s. With C₂ =199.1 ± 0.79 of the neutron probe, the F₂ was (1.17 ± 0.09)×10⁵ n/s. On the other hand, the neutron flux deduced by the activation method was (1.19 ± 0.1)×10⁵ n/sec. The two results are virtually the same, considering the measurement errors. The neutrons emerging out of paraffin wax are of both thermal and epithermal in energy. The fluence of epithermal neutrons was estimated from Ref. [30]. The ratio of epithermal to the total neutrons at a distance of 18.9 cm in air from the neutron source is 5.56% where the total fluence is maximum as calculated from Ref. [33]. Therefore, this ratio is the same for the paraffin moderator at 6 cm in thickness.

By using MCNP5, the energy spectra of Am-Be neutron source at 3, 5, and 8 MeV were produced with the relative probabilities of 1.000, 0.986 and 0.551, respectively. The simulation results for the Am-Be source are shown in Fig.4, and the counts are maximized at 6 cm thickness of the paraffin wax moderator, agreeing well with the experimental results.

Fig. 4Full-screen View

The Monte Carlo simulation for the Am-Be neutron probe versus the paraffin wax moderator thickness.

4 Conclusion

The paraffin wax moderator assembly can be used easily to thermalize fast neutrons of various energies produced from neutron-producing reactions on an accelerator. Neutron flux comparison and neutron activation techniques are used for accurate determination of neutron flux of the neutron probe to validate the optimum thickness of the paraffin wax moderator in the assembly. The neutron flux of (1.17 ± 0.09) ×10⁵ n/s by the neutron flux comparison method agree well with the flux of (1.19 ± 0.1) ×10⁵ n/s by neutron activation analysis method. The techniques can be utilized for the measurement of neutron yield from Mather type plasma focus device. The optimum thickness of the paraffin wax moderator is 6 cm for Am-Be and 5.5 cm for ²⁵²Cf neutron sources.