In nuclear emergencies, it is necessary to estimate the activity of radioactive rapidly and efficiently. This paper proposes an activity estimation method of linear gamma-ray source based on the single Compton scattering of gamma-ray. The paper establishes a physics model of radiation detection, and deduces the relation of the full-energy peak count and the single Compton scattering count. Based on the physics model and the relation of the full-energy peak and single Compton scattering count, the activity estimation method of linear gamma-ray source is built, which can be applied to different shield and the radioactivity of the linear gamma-ray source can be estimated rapidly and efficiently.
Currently, radioactive sources are widely used in various fields, such as medical, industrial, agricultural, health, scientific research (F. Abdollah Mianji, 2007) [
When disposing the disused and lost radioactive sources, we need to make a preliminary estimation of the radioactivity of the source, firstly. But it is a difficult work, when the source is under shield which thickness usually is unknown. Ajith Gunatilaka et al. (2010) [
Activity estimation method of linear gamma-ray source is proposed in this paper, which estimates the activity of the source and the thickness of the shield by deducing the relation of the full-energy peak count and the single Compton scattering count, and it can be applied to estimate the activity of linear gamma-ray source under different structures and material shield, efficiently and reliably.
In general, to be sure radiation safety, the linear gamma-ray source is under shield, and the common structure of shield is box, cylinder and sphere. In nuclear emergencies, the thickness of the shield and the activity and the length of the linear gamma-ray source are all unknown, so the gamma-ray spectrometry is the most effective means to quickly estimate the thickness of the shield and activity of gamma-ray. The physics model of the activity estimation method is established, as shown in
As
If the linear gamma-ray source is not under shield, the intensity ϕ 0 of gamma-ray into detector is given as follows,
ϕ 0 = ∫ L Ω 4 ⋅ π ⋅ L ⋅ A ⋅ η ⋅ λ ⋅ d L (1)
where, Ω is the solid angle of the detector to the dL, A is the radioactivity of the source, η is the emission ratio of the gamma-ray, λ is linear density of the source, L is the length of the source.
As shown in
ϕ = 2 ⋅ ∫ β ϕ 0 L ⋅ e − μ 1 ⋅ d cos β ⋅ d ⋅ sec 2 β ⋅ d β (2)
where, μ 1 is the linear attenuation coefficient of the shielding material, d is the thickness of the shield, β is the angle of entering detector.
Similarly, if the gamma-ray source is under the shield, when the gamma-ray goes through the shield and the Compton Scatter occurs, as shown in
ϕ s = 1 π ⋅ ϕ ⋅ Σ ( θ ) ⋅ ∫ β ∬ Ω e − μ 1 ⋅ d ⋅ ( cos α − sin α tan θ ) cos β ⋅ e − μ 2 ⋅ d ⋅ sin α cos β ⋅ sin θ ⋅ d ⋅ sec 2 β ⋅ sin α ⋅ d α ⋅ d φ ⋅ d β
ϕ s = 2 ⋅ ϕ ⋅ Σ ( θ ) ⋅ ∫ β ∫ 0 θ e − μ 1 ⋅ d ⋅ ( c o s α − sin α tan θ ) cos β ⋅ e − μ 2 ⋅ d ⋅ sin α cos β ⋅ sin θ ⋅ d ⋅ sec 2 β ⋅ sin α ⋅ d α ⋅ d β (3)
where, Σ ( θ ) is the probability that gamma-ray is scattered in shield material through unit length with the θ scattering angle, μ 2 is the linear attenuation coefficient of the shielding material when the gamma-ray is scattered with the θ scattering angle, α is the angle of incidence.
The full-energy peak count of characteristic gamma-ray in the spectrum can be represented as follows,
I = 2 ⋅ ∫ β ϕ 0 L ⋅ e − μ 1 ⋅ d cos β ⋅ d ⋅ sec 2 β ⋅ d β ⋅ ε 1 ⋅ t (4)
where, I is the full-energy peak net count, ε 1 is the intrinsic full-energy peak detection efficiency of the detector, t is the measurement time.
Similarly, the count of single scattering ray with a scattering angle θ in the spectrum can be represented as follows,
I s = 2 ⋅ ϕ ⋅ Σ ( θ ) ⋅ ∫ β ∫ 0 θ e − μ 1 ⋅ d ⋅ ( c o s α − sin α tan θ ) cos β ⋅ e − μ 2 ⋅ d ⋅ sin α cos β ⋅ sin θ ⋅ d ⋅ sec 2 β ⋅ sin α ⋅ d α ⋅ d β ⋅ ε 2 ⋅ t (5)
where, I s is the net scattered count, ε 2 is the intrinsic detection efficiency of scattered ray, t is the measurement time.
When the gamma spectrum is recorded by the detector, the thickness of the shield can be represented as follows,
I I s = ∫ β 1 L ⋅ e − μ 1 ⋅ d cos β ⋅ d ⋅ sec 2 β ⋅ d β ⋅ ε 1 Σ ( θ ) ⋅ ∫ β ∫ 0 θ e − μ 1 ⋅ d ⋅ ( c o s α − sin α tan θ ) cos β ⋅ e − μ 2 ⋅ d ⋅ sin α cos β ⋅ sin θ ⋅ d ⋅ sec 2 β ⋅ sin α ⋅ d α ⋅ d β ⋅ ε 2 (6)
As shown in
Based on the model assumptions and associated equations, a radioactivity estimation method can be developed as follows:
(1) Use the WinXCOM code (Gerward et al., 2004) [
(2) Determine the scattering angle θ ,
(3) Calculate Σ ( θ ) as below,
Σ ( θ ) = d σ d Ω ⋅ n ⋅ Z
where, d σ d Ω is the differential cross-section, n is the nucleon density, Z is the
atomic number of shielding material,
(4) Use the Monte Carlo code MCNP5 to calculate ε 1 and ε 2 , respectively,
(5) Calculate the thickness d of the shield by Equation (6),
(6) Calculate the radioactivity A of the source by Equations (4) and (1).
In this article, we propose a radioactivity estimation method of the disused and lost linear radioactive source, this method congregates the advantages of the numerical calculation and Monte Carlo simulation. The numerical calculation shows that the method can be used in nuclear emergencies, and help us reduce the risk factor and workload in disposing the disused and lost radioactive source. However, it still needs further discussion for practical applications due to the influence of detector type, the type of radioactive source, etc.
I would like to give my sincere gratitude to my supervisor Mr. Zhang, who gave me great help during the whole process of my thesis writing. Thanks to his patience, kindness, encouragement and good advice, I can successfully finish my paper.
The authors declare no conflicts of interest regarding the publication of this paper.
Xiong, M.L., Yang, J. and Guan, X. (2020) Activity Estimation Method of Linear Gamma-Ray Source under Shield Based on Single Compton Scattering. Open Access Library Journal, 7: e6557. https://doi.org/10.4236/oalib.1106557