Radiation protection calculations for an Am-Be neutron source

Abstract

When calculating dose rates around an Am–Be source, one typically focuses on the neutron emission. In high activity Am–Be sources, there is a need to consider two additional contributors to the dose: low-energy photon emission from the ²⁴¹Am decay (59.5 keV and an additional 4.4-MeV photon from the de-excitation of ¹²C* (created by the nuclear reaction of the alpha captured by ⁹Be). Usually, the dose rate constants (gamma factors) found in the literature provide a good estimation for the dose rates around a point source. For ²⁴¹Am however, the gamma-ray dose constant varies significantly (up to 50%) among different publications and is not reproducible by different methods. In order to overcome this challenge, we performed dose calculations using FLUKA – a multipurpose Monte Carlo code for the transport and interaction of elementary particles and heavy ions. This work shows the calculated dose rates around a 1.85-GBq Am–Be source and compared to analytical calculations and results from radiation measurements. It was discovered that the contribution of the photons to the dose rates is in the same order of magnitude as the dose rates from the neutrons.

1. INTRODUCTION

One of the most common neutron sources in use is the Am–Be source. Their availability, small size, the long half-life of ²⁴¹Am, and the wide energy range of neutrons it produces make it fit for many applications, such as dosimetry, research, and instrument calibration (Hoedlmoser et al., 2012; Bedogni et al., 2014).

While the Am–Be source is mainly known for its neutron emissions, the source has two additional photon emissions:

59.5 keV from the ²⁴¹Am decay.

4.4 MeV from the de-excitation of ¹²C*, created by the nuclear reaction of the alpha captured by ⁹Be. This reaction produces 0.6 photons per neutron emission (Croft, 1989; Knoll, 2000).

When one calculates dose rates around an Am–Be source, it is important to take those two additional sets of photon emissions into account. Furthermore, in some cases the main contributor to the dose can be the 4.4-MeV photon emission, as most shielding designs will consider primarily the neutron radiation and can neglect the energetic photon. Therefore, calculating the dose rates from all the different contributors to the dose rate is of high importance.

2. METHODS

During our work, we used three different methods in order to evaluate the dose rates from an Am–Be source: analytical calculations, Monte Carlo simulations using the FLUKA Monte Carlo code, and experimental measurements. Radiation dose rates were calculated for neutrons, photons, and high-energy photons (4.4 MeV) separately.

All calculations, simulations, and measurements were performed for an Am–Be source capsulated in a stainless steel cylinder with an activity of 1.85 GBq and with the yields of 8.1·10⁴ (n·s⁻¹). This Am–Be source is used for detector calibration and experiments at the Soreq Applied Research Accelerator Facility (SARAF), located at the Soreq Nuclear Research Center. According to Israeli regulations, any operation with an Am–Be source above 10 kBq requires a regulatory licence. Dose rate assessments were conducted as part of the licensing procedure.

2.1. Analytical calculations

The radiation dose rates were calculated separately for neutrons, low-energy photons (59 keV), and high-energy photons (4.4 MeV).

2.1.1. Neutrons

In order to estimate the dose rates, we used the neutron fluence and the effective dose per fluence factor from ICRP Publication 116 (ICRP, 2010). The neutron fluence is given by Eq. (1):

$$\varphi ={\displaystyle \frac{s}{4\pi R^2}}$$

(1)

where $\varphi$ is the neutron fluence (#·s⁻¹·cm⁻²), s is the neutron emission rate (#·s⁻¹), and R is the distance from the source (cm). The effective dose per fluence E1 for 5-MeV neutrons, in an AP exposure geometry from ICRP Publication 116 (ICRP, 2010), is given by Eq. (2):

$$\mathrm{E}1=494\cdot {10}^{-12}[\mathrm{Sv}\cdot {\mathrm{cm}}^2]$$

(2)

It is important to note that the effective dose per fluence factors are given for monoenergetic neutrons, while the Am–Be source has a wide range of energies. We used the factor for the closest energy to 4.2 MeV – the average Am–Be energy (ISO, 2021). The dose equivalent rate D1 at a distance of 100 cm is given by Eq. (3):

$$\mathrm{D}1=\varphi \cdot \mathrm{E}1={\displaystyle \frac{s}{4\pi R^2}\cdot E1=1.1[\mu \mathrm{Sv}\cdot {\mathrm{h}}^{-1}]}$$

(3)

2.1.2. Photons: Am decay

The dose rate as a result of the ²⁴¹Am decay was calculated according to the dose rate constant, $\mathrm{\Gamma }$ (mSv·m²·MBq⁻¹·h⁻¹), as shown in Eq. (4):

$$\mathrm{D}2={\displaystyle \frac{\mathrm{\Gamma }\cdot A}{d^2}}$$

(4)

where A is the source activity (MBq) and d is the distance from the source (m). The dose rate constant for ²⁴¹Am (Peplow, 2020) is given by Eq. (5):

$$\mathrm{\Gamma }=5.413\cdot {10}^{-6}[\mathrm{mSv}\cdot {\mathrm{m}}^2\cdot {\mathrm{MBq}}^{-1}\cdot {\mathrm{h}}^{-1}]$$

(5)

The dose rate D2 at a distance of 100 cm is given by Eq. (6):

$$\mathrm{D}2=10.0[\mu \mathrm{Sv}\cdot {\mathrm{h}}^{-1}]$$

(6)

As the energy of these photons is quite low (just below 60 keV), we have to take into account the attenuation of the stainless steel capsule which contains the source. The thickness of the capsule is 2.4 mm, which is one TVL for ²⁴¹Am (CNSC, 2023). The attenuated dose rate at a distance of 100 cm, considering one TVL is given by Eq. (7):

$$\mathrm{D}3=1.0[\mu \mathrm{Sv}\cdot {\mathrm{h}}^{-1}]$$

(7)

2.1.3. Photons: 4.4 MeV

The resulting dose assessment from 4.4-MeV photons was evaluated similarly to the neutrons, by using the photon fluence and the dose per fluence factor. The 4.4-MeV photon fluence is 0.6 times the neutron fluence, as 0.6 photons are produced for each neutron emission (Croft, 1989; Knoll, 2000). Therefore, the dose per fluence factor E2 for 5-MeV photons, according to the AP exposure geometry from ICRP Publication 116 (ICRP, 2010), is given by Eq. (8):

$$\mathrm{E}2=13.4\cdot {10}^{-12}[\mathrm{Sv}\cdot {\mathrm{cm}}^2]$$

(8)

The dose rate D4 at a distance of 100 cm is given by Eq. (9):

$$\mathrm{D}4=0.02[\mu \mathrm{Sv}\cdot {\mathrm{h}}^{-1}]$$

(9)

2.2. Monte Carlo simulations

For our calculations, we used the FLUKA Monte Carlo code – a multipurpose Monte Carlo code for the transport and interaction of elementary particles and heavy ions (Battistoni et al., 2015; Ahdida et al., 2022) and the Flair graphic user interface (Vlachoudis, 2009). In FLUKA we defined the photon and neutron source separately, using a special source routine with the Am–Be expected spectrum (ISO, 2021). The code then calculates the fluence in each point and converts it to dose using the ICRP Publication 116 (ICRP, 2010) conversion coefficients.

2.3. Measurements

To measure the neutron and photon dose rates, we used an Atomtex detector, models AT1117M PU2 and model AT1123, respectively.

The uncertainty can reach up to 60%. The uncertainty is the result of multiple factors: the accuracy of the detectors and their calibration, the detector's location inside the device, the geometry of the source, and its position during the measurements.

The uncertainty in the results comes mainly from the accuracy of the detectors (±50%). On top of that, the detectors were calibrated for certain ranges (5 µSv·h⁻¹–5 mSv·h⁻¹ for neutrons and 3 µSv·h⁻¹–2 Sv·h⁻¹ for photons) which adds to the uncertainty when one measures dose rates outside those ranges. In addition, as the detector is placed in the centre of a 30-cm cone, the distances reported between the detector and the source have up to ±3% accuracy (the closer the source to the detector, the higher the uncertainty is for the measured distance).

The fact that the source is encapsulated inside a stainless steel cone should also be taken into account. Since the container's thickness is asymmetrical, the position of the capsule during the measurement will influence the radiation rates in different directions. As the stainless steel cone is wrapped in a plastic casing and surrounded by an opaque sponge, the position of the capsule during the measurement is unknown.

3. RESULTS

Table 1 summarises the values of the dose rates as measured by the Atomtex neutron and photon detectors, simulated by FLUKA, and calculated analytically in Eqs. 3, 7, and 9. For the analytical calculations at 30-cm distance, we used the inverse square law.

Table 1.

Neutrons and photon dose rates at a distance of 30 cm and 100 cm from the 1.85-GBq Am–Be source.

Distance (cm)	Neutron dose rates (µSv·h−1)			Photon dose rates (µSv·h−1)
	Measurements	Calculations	FLUKA	Measurements	Calculations	FLUKA
30	12.9 (55%)	12.2	10.16 (1%)	10.5 (55%)*	10.0 (10%)	10.1 (1%)
100	1.3 (60%)	1.1	1.0 (1.5%)	1.0 (55%)*	1.0 (10%)	1.1 (3%)

*After the subtraction of the background radiation of 95 nSv·h⁻¹.

The results from the measurements, analytical calculations, and Monte Carlo simulations are in good agreement – the relative difference between the measurements and the two other methods is below 23% for the neutron dose calculations and below 10% for the photon dose calculations. All the computational and analytical calculations are within the range of the measurement uncertainty. As was detailed in the measurements section, the differences between the measurements and the calculated dose rates are as a result of uncertainty in the detectors, the detectors’ calibration ranges, the measurement geometry – the location of the detector's active volume inside the device, and the position of the asymmetrical capsule of the source.

The minor differences between the analytical calculations and the FLUKA dose rate derive from the use of average neutron energy for the analytical calculations vs the use of a detailed neutron spectrum in FLUKA. As for the photons, the use of the dose rate constant for sources with low-energy photon emission can lead to inaccuracy. Choosing a different dose rate constant for the calculation, for example, 6.029·10⁻⁶ (mSv·m²·MBq⁻¹·h⁻¹) from Peplow (2020), can increase the photon dose rate results by 10%.

It should be noted that the contribution of the photons to the dose rates is in the same order of magnitude as the dose rates from the neutrons. This is caused mostly (around 98%) by the low-energy photons emitted from the ²⁴¹Am decay.

4. DISCUSSION AND CONCLUSIONS

An Am–Be source is a common neutron source used in many applications and research. As such, when using this source, one is aware of the dangers posed by the source's neutron radiation and the corresponding necessity for safety precautions. The photon dose rate is sometimes neglected or ignored, especially the 4.4-MeV photons. These photon emissions with the 59.5-keV photons should be taken into account when considering safety procedures.

In this work, we used three different methods – analytical calculation, MC simulation, and measurements – in order to evaluate the dose rates produced by a 1.85-GBq Am–Be source. The results from all three methods were in good agreement: the relative difference between the measurements and the two other methods is below 23% for the neutron dose and below 10% for the photon dose.

Surprisingly, it was discovered that the contribution of the photons to the dose rates is in the same order of magnitude as the dose rates from the neutrons. Meaning it is necessary to consider the photon dose rates when calculating the dose from an Am–Be source. Since low-energy photons (∼60 KeV) contribute the majority of the photon dose rates (98%), this can be solved easily with a relatively thin coating of stainless steel that will block the photons without affecting the neutron emission.

It is important to note that although the dose rates from the monoenergetic 4.4-MeV emission are negligible in our case, for a high activity source, it can be a significant contributor to the dose rate. Shielding design for an Am–Be source should take into account the need to attenuate all three kinds of radiation – neutrons, low-energy photons, and 4.4-MeV photons.