Studies on thermal neutron perturbation factor needed for bulk sample activation analysis

doi:10.1016/S0168-9002(02)00568-5

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment

Volume 488, Issue 3, 11 August 2002, Pages 634-641

https://doi.org/10.1016/S0168-9002(02)00568-5 Get rights and content

Abstract

The spatial distribution of thermal neutrons produced by an Am–Be source in a graphite pile was measured via the activation foil method. The results obtained agree well with calculated data using the MCNP-4B code. A previous method used for the determination of the average neutron flux within thin absorbing samples has been improved and extended for a graphite moderator. A procedure developed for the determination of the flux perturbation factor renders the thermal neutron activation analysis of bulky samples of unknown composition possible both in hydrogenous and graphite moderators.

Introduction

Among the instrumental analytical methods the thermal neutron activation analysis (TNAA) has kept its leading position in solving special problems [1]. More than 70 natural elements include nuclides which possess activities in the 1 s and 100 d interval induced by the (n,γ) reaction. The main advantages of the TNAA as compared to fast neutron activation [2] are related to the high-activation cross-sections and to the fact that no interfering reactions exist. A serious limitation of the TNAA is the perturbation of thermal neutron flux by highly absorbing and extended samples. The flux perturbation factor F is defined by the following relation: F=〈φ〉/〈φ₀〉 where 〈φ〉 and 〈φ₀〉 denote the average thermal neutron fluxes in the sample and in the same volume of a moderator, respectively. Factor F can be given as a product of the self-shielding coefficient G of the sample for thermal neutrons and the flux depression H in the medium surrounding the sample, i.e. F=GH=(〈φ〉/φ_s)(φ_s/〈φ₀〉) where φ_s is the flux at the surface of the sample. For the calculations of the coefficients G and H the theoretical formulae [3], [4] require knowledge of the composition of the samples. In practice, the exact composition of the sample to be analyzed is unknown, therefore, the flux perturbation factor F cannot be calculated. For the determination of factor F for a thin absorbing sample a simple experimental method based on the activation of Dy and Au foil stacks of various thicknesses was developed [5]. The distribution of the thermal neutron flux in the foil stacks placed in a H₂O moderator could be described by the following expression: $φ(x)=(ax^{2} +bx+c)^{−1}$ where x is the distance from the surface of a given foil stack while a, b and c are fitting parameters.

The irradiation arrangement used in our experiments is shown in Fig. 1. The average neutron flux in a disk-shaped sample of thickness d is given by $〈φ〉=(1/d) ∫ 0 d φ(x) d x$ from which it follows that the flux should be measured in principle only in three points, e.g. at the two edges and the center of the sample for determining 〈φ〉. The unperturbed flux density 〈φ₀〉 must be measured in these positions, too, by the same detector replacing the sample with the moderator material. The thermal neutron flux density is isotropic in a moderator, therefore, Eq. (2) is valid for any orientations of a thin (∼1–2 mm) sample placed at the same distance from a point source.

In addition to the dimension of the sample the value of the flux perturbation factor F depends strongly on the moderator medium, therefore, it seemed to be worthwhile to check the validity of Eq. (1) for graphite which has very different neutron diffusion properties as compared to light water and other hydrogenous media. The spatial distribution of the thermal neutron flux around a point source changes significantly in the H₂O moderator [6], which makes the use of the TNAA for bulky samples difficult. A comparison of the advantages and limitations of hydrogenous and graphite irradiation facilities used for elemental analysis of bulk samples was the main purpose of this work.

Section snippets

Experimental procedure

Thermal neutrons were produced by an Am–Be source of 2.26×10⁶ n/s intensity placed in the center of the graphite pile at the High-Energy Accelerator Research Organization (KEK), Tsukuba, Japan. The dimensions of the graphite pile are 250(L)×190(W)×190(H) cm³ with a gross density of 1.75 g/cm³. The thermal neutron flux distribution was measured by the foil activation method between 10 and 80 cm from the source in 10 cm steps along the central line. The activity of the Au foils of 2×2 cm² and 0.05 mm

Results and conclusions

The flux distribution of thermal neutrons measured in a graphite pile around an Am–Be source, shown in Fig. 2, agrees well with the MCNP-4B calculations within experimental errors from 10 to 80 cm distances from the source. The 1.34×10⁻³ n/cm²s Y flux density normalized to the source yield, Y, at 10 cm from the source is less by about a factor of 2 as compared to the value of 2.83×10⁻³ n/cm²s Y obtained by a ²⁵²Cf source in a water moderator (Table 1) [6]. The thermal neutron distribution for

Acknowledgements

One of the authors (J.Cs.) is indebted to the Japan Society for the Promotion of Science for the invitation. This work was supported in part by the International Atomic Energy Agency, Vienna (Contract No. 10886/R0) and the Hungarian Research Fund (OTKA Contract No. T037190).

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