SHIELDING BEHAVIOUR OF MULTILAYER SHIELDS CONTAINING PE AND BX

M. A. Quasema, Md. Sazzad Hossainb, S. M. A. Islama and M. A. Zamana 

a) Physics Department, Jahangirnagar University, Savar, Dhaka, Bangladesh, b) Physics Department, National University, Gazipur, Bangladesh

ABSTRACT
Neutron shielding properties of Polyethylene (PE), and Borax mixed Ilmenite-Magnetite concrete (BX) and the multilayers PE+BX and their reversed combinations have been investigated using a 252Cf point source whose emission characteristics are similar to that of inside a reactor core. For the detection of neutron a BF3 long counter detector have been used. The shielding characteristics such as transmission factors, removal cross sections, and flux spectra have been measured. MCNP code has been adopted for the calculation. The multilayered shields are found to show better performance than the single layered ones. The observation supports applicability of the shields quite well for practical application purpose. 

1.  Introduction
In any nuclear establishment shielding of neutrons and gamma rays is an important aspect. Fast neutrons are very effectively slowed down by collision with hydrogen atoms, and are converted to thermal neutrons which may subsequently be eliminated by materials, such as lithium, boron, or cadmium having high thermal neutron absorption cross section.  It is well known that neutrons lose their energy by elastic scattering with hydrogenous materials. Hence for designing shielding for fast neutrons, one attempts for maximizing the hydrogen content in the shielding materials by using hydrogenous materials [1]. In neutron shielding problem one has to deal with fast neutrons that are emitted from a nucleus. They are to be moderated first in the biological shield using heavy element by inelastic scattering. Then hydrogen is used to slow down the fast and the intermediate energy neutrons by elastic scattering [2]. Karni and Greenspan [3] suggested that neutron shielding ability of polyethylene can be improved by adding a good shielding material such as boron. 

The scattering cross-section of hydrogen is inversely proportional to neutron energy. Hence for effective slowing down of very high energy neutrons, hydrogenous materials are mixed with moderate and / or high mass number elements such as lead (Pb). It reduces the energies of fast   neutrons through inelastic collisions. Lead is toxic, and its use has now become restricted. Concrete, on the other hand, is a mixed material susceptible to tailoring by adding / changing the ingredients and matrix of composition. A wide variety of concrete compositions are accessible and hence concretes have now become more popular. A number of heavy concretes (HC) had been tested and found to serve the purpose better [4]. Efforts are continued to improve the system. Attenuation of fast neutron beam through graphite, paraffin, poly-ethylene-boron-lead, poly-ethylene-lithium and steel was studied by Gujrathi and D’Auria [5] and that through multilayer shields composed of steel, polyethylene and borated materials by Maruyama and Bouts [6]. This idea is also supported by other works [7-9]. The present work is an effort for investigating the performance of some multilayered shields containing a light one (PE) suitable for neutron shielding purpose and a heavy ones, e.g., BX that can shield gamma effectively.

2. Empirical Formulae for Removal Cross-section Values
An effort has been made in the present work to investigate the thickness dependence of removal cross sections. This aspect has come to a focus through a few works already done. Against the present concept of thickness independence of removal cross section a number of authors [10-12] claim strongly of its thickness dependence. In the present work such a feature could be observed as shown in Figs. 1-2. Removal cross section values are found to vary significantly within the shield thickness 5 cm to 40 cm.

Both the experimental data and the calculations show the same trend of variation. Extracted removal cross section values both from experiment and calculation have been fitted to an equation given by

r  = A0+A1t+A2t2+A3t3+A4t4+A5t5+A6t6 +A7t7

The values of the constants  A1, A2, A3 ………. etc. have been determined and are shown in Table 1.

The difference in shield thicknesses is due to difference up to which the data are available. Fitting was done for each of them within such limits; and the parameters are expected to reproduce removal cross-section at any thickness up to this.

The quality of fitting can be observed from the chi-square values and the correlation coefficients of the Table 1. Throughout the study the quality of fitting is found to be very good.

3. The Common Features of Neutron transmission
A few clear and common features that could be identified from the study of transmission factors for the given shields are mentioned below:
a.	Multilayer transmission curves lie in between the component shields, being closer to that of the hydrogenous material e.g., PE.
b.	Multilayers are more effective at larger thickness of the shields.
c.	Multilayers formed by placing PE first are found to attenuate neutrons more effectively than the reverse setups.
d.	PB has greater effectiveness on its multilayers than those of PE [13].
e.	The predictions of MCNP regarding transmission factors of the single as well as multilayers are found to agree well with experimental data.

4. The Experimental Arrangement
The experiment was done at the Institute of Nuclear Science and Technology (INST), Atomic Energy Research Establishment (AERE), Savar, Dhaka. The experimental arrangement consisting of a radiation source 252Cf (point source of strength 3.7  104 Bq), the shielding arrangement and the detector is shown in Fig. 3. The source was chosen as its neutron and gamma ray spectra are similar to that of 235U used in a nuclear reactor. The source was placed at a distance of 110 cm away from the detector. 

These materials in the shape of slabs of lateral dimensions 20 cm x 10 cm or 26.5 cm x 13 cm were placed between the source and the detector (Fig.3). First, a single slab was placed very close to the source and subsequently one by one, more and more slabs were added taking care that the gap between successive slabs remains as minimum as possible. A broad beam geometry was adopted in the experiment. In the case of multi-layer shield, slabs of different components were alternately placed. 

For each setting neutron flux was measured initially for 200 s without placing any shielding slab between the source and the detector. Then the first slab closest to the source was placed and the flux was measured. The subsequent measurements were made for increased thickness of the shield by increasing the number of slabs by one at a time. The maximum shielding thickness studied was 100 cm.

A Hanson-Mckibben type long counter [14] was used for neutron detection. It was constructed incorporating the modification suggested by other workers [15]. The counter was found to be almost independent of energy over a long range of energy that made it most suitable for monitoring neutrons.

5. The MCNP Code
The MCNP code was developed on the basis of Monte Carlo method of neutron transport and it does not solve an explicit equation, but rather obtains answers by simulating individual particle and recording some aspects (tallies) of their average behavior. The experimental results were compared with the predictions of the general purpose MCNP code MCNP4A.  

To generate a continuous probability density function for the point isotropic 252Cf fission source a built- in analytic function of MCNP4A was utilized. Point detectors with the axial symmetry were considered to calculate the highest flux at the point of interest. An arbitrary three-dimensional configuration of materials in geometric cells bounded by first- and -second-degree surfaces and fourth-degree elliptical core is used by the code. 

Enough particles were considered to keep the relative error below 0.04. It may be mentioned here that this number actually depends on the thickness of the shield. The detector was considered to lie just outside the maximum shielding surface which is, in the present case, about 100 cm away from the source position

Nuclear data tables exists for different types of neutron interactions from which appropriate ones may be selected through unique identifiers for each table, called  ZAIDs. The code uses [16] continuous-energy, nuclear and atomic data libraries, the primary sources of which are the Evaluated Nuclear Data File (ENDF) [17] system, the Evaluated Nuclear Data Library (ENDL) [18], the Activation Library (ACTL) [19] compilations from Livermore, and evaluations from the Applied Nuclear Science group  (ANS Group) [20-22] at Los Alamos. The evaluated data are processed into a format appropriate for MCNP with the help of codes such as NJOY [23, 24].

6.  Results and Discussions
6.1 Transmission Factors of Fission Neutrons
6.1.1 Single Layer Shields
Of the two single layers PE proves to be better for shielding fission neutrons. This is also supported by the MCNP calculation [25]. In case of transmission factors of PE, at low shielding thicknesses its curve falls at a quicker rate compared to BX. Consequently it almost merges with that of BX respectively at around 60 cm and 70 cm of thicknesses. These observations are simultaneously been supported by experiment and the MCNP calculations (Figs. 4-5).

6.1.2 HVLs and TVLs
The results of the discussion made previously about the attenuating performances are shown in Table 2 which gives a comparison between the different shielding arrangements. Thicknesses corresponding to the transmission of 25% and 5% radiation have been shown in the table in addition to the HVLs and TVLs of the shields. The transmission factors calculated by MCNP are found to be in good agreement with the experimental values. The difference between them is about 6-10% in the shields thickness range of 5 cm to 50 cm.

6.2 Removal Cross Section of Fission Neutrons
6.2.1 PE Shield
The experimental values of fission neutron removal cross section r for PE at 5 cm is 0.059 cm-1 from where it rises steadily up to 0.146 cm-1 at 25 cm for fission neutrons. After 25 cm thickness (Figs. 1-2) the removal cross section values increase at a slow rate. Throughout the whole range of thickness there is an excellent agreement between theory and experiment. The thickness dependence is again a smooth function. 

Among the single layer shields PE and BX investigated, PE shows some similarity in their removal cross section values. Between the thicknesses 5 cm and 25 cm of the shields PE show a sharp variation of removal cross section values. The curves then become approximately straight having positive gradient which remains so up to a thickness of 85 cm. The sharp rise between 5 cm to 25 cm thickness is due to high content of hydrogen and carbon elements in PE. These elements play a vital role in slowing down neutrons by elastic collision. Within a short thickness in the shields the neutrons are slowed down and removed; the process being prominent within the thickness of 25 cm. Beyond this thickness the slow neutrons only remain and their removal cross sections do not vary much.
6.2.2. BX Shield 
Removal cross section for BX at 5 cm is found 0.056 cm-1 which rises up to 0.078 cm-1 for fission neutrons, the maximum variation being 0.003 cm-1. The agreement between calculated and experimental results are good which can be observed from the maximum variation 4%. It is found that the removal cross section values are very high for PE at all the penetration distances compared to BX. This is expected and can be explained in terms of the hydrogen content of the shielding materials. 

6.2.3 PE, BX, PE+BX and BX+PE
It can be observed from Fig. 2 that the multilayer PE+BX shield behaves more alike the PE shield throughout the whole range of its thickness. The HVLs obtained by experiment of the shields PE, BX, PE+BX and BX+PE are respectively 8.25 cm , 11.4 cm, 8.35 cm and 10.35 cm. Corresponding TVLs are 18.0 cm, 34.5 cm, 19.5 cm and 21.6 cm respectively. For neutron shielding the PE +BX is found to be more effective than the BX+PE multilayer setup (Fig. 2), and thus the attenuation curve of PE +BX is depressed more. All the above mentioned points made from experimental observations are well supported by the MCNP calculations. 

6.2.4  PE+BX and BX+PE Shields
Removal cross section values for different shield thicknesses for the fission neutrons and multilayers PE+BX are displayed in Fig. 2. The curve shows a sharp rising trend up to 30 cm thickness then it becomes more or less flat showing that there is no considerable variation of removal cross section with the increase of shield thicknesses. Both the experiment and the MCNP results support these observations. The MCNP results give larger values than that of experiment ; the difference being 2.47% (PE+BX), 2.43% (BX+PE) at thicknesses of 100 cm and 95 cm respectively.

The curves for the reversed combinations e.g., BX+PE (Fig. 2) also show zigzag pattern for which average value of the removal cross section now remains almost same for thicknesses 35 cm to 10 cm of measurements carried out in the present work. As of the multilayers containing PE the removal cross sections of the multilayers PE+BX and also of their reversed arrangements BX+PE are also higher (Figs. 1-2) than those of the heavier components; but is less than PE in every case. The explanation for this observation also follows the previous case.

Both types of removal cross-section values increase with shield thickness up to a distance of 25 cm and then it declines to show any specific variation pattern (MCNP calculations) where it decreases continuously from a maximum value at 5 cm thickness.

Fig. 2 shows that the removal cross section for the multilayer PE+BX falls in between those of its composites PE+BX up to a thickness of 25 cm; where as, it is more than its composites at higher thicknesses (less than 25 cm).

6.2.5 Common Features
In general removal cross-section values are found to increase from 5 cm shield thickness to 20-25 cm for the experimental cases; and then show a decreasing trend with thickness. Rising of removal cross-section values after some shield thickness can be explained on the basis of decrease of neutron energy due to collision. A neutron starts with the highest possible energy that it can possess. It then travels and loses its energy due to collision with the atoms of the shielding materials. After the decrease of neutron energy through this process, the capture probability (through (n,) process) increases; with which the removal cross-section values also increase.

Removal cross sections obtained using MCNP code although increases with thickness initially like the experimental case, but do not fall subsequently with increase in thickness. The MCNP code calculates considering ideal case for which a shielding material possesses uniform distribution of molecules. Experimentally this is very difficult to attain. Again the proportion of components may differ between theory and experiment. All such discrepancies may finally contribute for such sort of a mismatch. Of course for the common material, e.g., PE this discrepancy between theory and experiment is not much.

6.3 Neutron flux Spectra for the single Layer Shields
6.3.1 Neutron Flux Spectra for PE
As in the case of PB single layer shield neutrons appear as two different lots of energy 0 to 2.3 MeV and 2.3 to 8.5 MeV (Fig. 6). For all the thicknesses these two divisions could be observed. In the 25 cm thickness the first type of neutrons are less in number compared to that of the second energy range ones. This is expected, since at such small thickness neutron energy loss was not prominent. Again a long tail appear in this case also. The peak to peak ratio of the neutron flux values with respect to 5 cm shield thickness flux are 1.0, 0.39 and 0.024 for the first type and 1.0, 0.48 and 0.045 for the second type respectively. The neutron flux values at each energy decrease with the increase in shield thickness appreciably. 

6.3.2 Neutron Flux Spectra for BX
Fig. 7 shows the flux spectra for fission neutrons for various shield thicknesses and gives the calculated spectra at various thicknesses of the shield BX. The peak to peak ratio for both the shields are same. Maximum number of neutrons possess energy 1.3 MeV at shield thickness 5 cm, and 10 cm. The maximum number of neutrons corresponds to 4.5 MeV, again are available at both the thicknesses. Before 50 cm almost all the neutrons are absorbed by the shield. 

The number of neutrons found for the different shield thicknesses are found to decrease with thickness. The small proportion of the neutrons that could be observed at 50 cm thicknesses possesses energy in between 1 MeV and 2 MeV for both the shields PE and BX. Again both the shields possess two minor groups each on the lower energy side of the first group – the feature being prominent in thicknesses 5 cm, 10 cm and 25 cm.

6.3.3 Neutron Flux Spectra for PE+BX and BX+PE
The fission neutron spectra for the PE+BX multilayer shield are similar to that of the PB+BX multilayer shield. Fig. 8 shows the neutron spectra for the PE+BX shield. The figure shows how quickly the features disappear with the increase of shield thickness. The curve for PE+BX and BX+PE (Fig. 9) are similar to a large extend to PB+BX and BX+PB respectively. 

7. Conclusions 
Single layer shields PE and BX and their combination have been studied.  Removal cross sections, flux spectra and transmission factors for fission neutrons and 14 MeV neutrons shielding have been investigated. MCNP calculations have been done to compare its prediction with the experimental measurements.

The present study reveals that for fission neutron shielding, two single layers studied show a clear pattern of their comparative behavior of shielding ability up to around 100 cm shield thickness. PE has more fission neutron shielding ability than BX for 14 MeV neutrons.

Among the two single layer shields PE for 14 MeV energy neutrons show maximum variation in the transmission factors and removal cross section in the range of 5 cm to about 40 cm of shield thickness (Figs. 1, 2 and 4); removal cross section show a tendency to rise within these limits. However, for the shield BX removal cross sections show a tendency to decrease up to around 10 cm and thereafter it shows a tendency to rise.

It appears from our study that neutrons having energy around 2.34 MeV are rarely transmitted through the shields studied. These neutrons, to a large extent, are removed in the shielding process. On the other hand, two distinct major groups of neutrons e.g., 0.82 to 2.3 MeV are found inadequate numbers in the single layer shields studied (Figs. 6-7). In addition to these two major groups, two other minor groups between 0 to 0.36 MeV and 0.36 to 0.82 MeV energy were observed in the shields. Maximum number of neutrons detected are found to have energies around 1.5 and 5 MeV.

From the flux (Figs. 8-9) spectra investigations of 14 MeV neutron, peaks are found at 4.966, 7.408 and 12.214 MeV and the absorption troughs are found at 0.821, 2.365, 6.065 and 8.607 MeV in the shields. It is also observed that the behavior of the transmitted neutron flux through the PE-multilayers do not change appreciably on reversing the components of the multilayer arrangements.

On the basis of the above discussions it may be concluded that multilayer shields can be made by adding two single layers alternately- one of which may be a light / hydrogenous one suitable for shielding neutrons effectively. Multilayers formed by placing a hydrogenous material (PE) first are found to attenuate neutrons more effectively than the reverse setups.

Characteristics of PE- multilayers for fission neutrons are found to be dependent on their uncommon component shields. On reversing the components the shielding characteristics change, but the relative characteristics of the uncommon components do not. 

Fig.  1   A block diagram of the experimental set-up

Fig.  2   Variation of fission neutron removal cross section (Expt. and MCNP) with thicknesses of the shields PE,  BX as compared to PE + BX 

Fig.  3   Variation of fission neutron removal cross section (Expt. and MCNP) with thicknesses of the shields PE + BX as compared to BX + PE  

Fig.  4   Variation of fission neutron transmission factors (Expt. and MCNP) with thicknesses of the shields PE, BX and PE +BX

Fig.  5   Variation of fission neutron transmission factors (Expt. and MCNP) with thicknesses of the shields PE + BX as compared to BX +PE

Fig.  6   Flux spectra for fission neutrons at 5, 10, 25 and 50 cm thicknesses for the shield PE

Fig.  7   Flux spectra for fission neutrons at 5, 10, 25 and 50 cm thicknesses for the shield BX

Fig.  8   Flux spectra for fission neutrons at 5, 10, 25 and 50 cm thicknesses for the shield  PE  + BX

Fig.  9   Flux spectra for fission neutrons at 5, 10, 25 and 50 cm thicknesses for the shield BX + PE

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