Sourceless efficiency calibration method for γ spectrum based on numerical analysis

Fig. 10. Detection efficiency comparison of numerical calculated $ε_{c}$ and MC simulated $ε_{s}$ of point source at different source-detector distances (a) NaI(Tl), (b) LaBr₃(Ce)

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Fig. 11. Detection efficiency comparison of $ε_{c}$ and $ε_{s}$ of surface sources of different radii at different source-detector distances(a) LaBr₃(Ce) r=1.5 cm, (b) NaI(Tl) r=1.5 cm, (c) LaBr₃(Ce) r=3 cm, (d) NaI(Tl) r=3 cm

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Fig. 12. Detection efficiency comparison of $ε_{c}$ and $ε_{s}$ of volume sources of different radii at different source-detector distances(a) LaBr₃(Ce) r=1.5 cm, (b) NaI(Tl) r=1.5 cm, (c) LaBr₃(Ce) r=2 cm, (d) NaI(Tl) r=2 cm

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Table 1. Parameter expressions

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Table 1. Parameter expressions

位置 Position

ρ

φ_{0}

t_{i}

θ_{i}

正上方

Directly above

d c o s φ + p

t_{1} = \frac{h}{c o s θ}

t_{2} = \frac{ρ}{s i n θ} - \frac{s}{c o s θ}

θ_{1} = a t a n (\frac{ρ}{h + s})

θ_{2} = a t a n (\frac{ρ}{s})

侧上方

Diagonally above

d c o s φ - p

a s i n (\frac{R}{d})

$t_{1} = \frac{s + h}{c o s θ} - \frac{ρ}{s i n θ}$ , $t_{2} = \frac{h}{c o s θ}$

$t_{3} = \frac{ρ + 2 p}{s i n θ} - \frac{s}{c o s θ}$

$θ_{1} = a t a n (\frac{ρ}{h + s})$ , $θ_{2} = a t a n (\frac{ρ + 2 p}{h + s})$

$θ_{3} = a t a n (\frac{ρ}{s})$ , $θ_{4} = a t a n (\frac{ρ + 2 p}{s})$

侧面

Lateral side

d c o s φ - p

a s i n (\frac{R}{d})

$t_{1} = \frac{h - s}{c o s θ} - \frac{ρ}{s i n θ}$ , $t_{2} = \frac{2 p}{s i n θ}$

$t_{3} = \frac{s}{c o s (π - θ)} - \frac{ρ}{s i n (π - θ)}$

$θ_{1} = a t a n (\frac{ρ}{h - s})$ , $θ_{2} = a t a n (\frac{ρ + 2 p}{h - s})$

$θ_{3} = π - a t a n (\frac{ρ + 2 p}{s})$ , $θ_{4} = a t a n (\frac{ρ}{s})$

Table 2. Comparison of $ε_{c}$ and $ε_{s}$ of ¹³⁷Cs detection efficiencies

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Table 2. Comparison of $ε_{c}$ and $ε_{s}$ of ¹³⁷Cs detection efficiencies

源状态 Source state	位置 Position	溴化镧 LaBr₃（Ce）			碘化钠NaI(Tl)
源状态 Source state	位置 Position	$ε_{c}$	$ε_{s}$	Δ / %	$ε_{c}$	$ε_{s}$	Δ / %
点源 Point source	1#	2.30×10^-3	2.26×10^-3	1.77	1.82×10^-3	1.77×10^-3	2.82
	2#	1.15×10^-3	1.13×10^-3	1.77	9.11×10^-4	8.81×10^-4	3.41
	3#	2.37×10^-3	2.32×10^-3	2.16	1.85×10^-3	1.80×10^-3	2.78
面源 Surface source	4#	2.27×10^-3	2.23×10^-3	1.79	1.80×10^-3	1.75×10^-3	2.86
面源 Surface source	5#	2.21×10^-3	2.17×10^-3	1.84	1.76×10^-3	1.71×10^-3	2.92
体源 Volume source	6#	1.93×10^-3	1.91×10^-3	1.05	1.53×10^-3	1.49×10^-3	2.68
体源 Volume source	7#	1.89×10^-3	1.86×10^-3	1.61	1.50×10^-3	1.46×10^-3	2.74

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Erlei YE, Chunxia SHEN, Hongjie NAN, Yongfang LAI. Sourceless efficiency calibration method for γ spectrum based on numerical analysis[J]. NUCLEAR TECHNIQUES, 2024, 47(9): 090204

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