© N.T. Le, Published by EDP Sciences 2025

1 Introduction

There are various types of neutron measuring devices (referred to neutron meters) to be used for measuring neutron physical quantity (i.e., integrated neutron fluence rate, ϕ) and/or neutron operational dosimetric quantities (i.e., ambient dose equivalent rate, $\dot{H}*(10)$; personal dose equivalent rate, ${\dot{H}}_p(10)$) for the purposes of radiation protection and safety assessment. For different purposes of measurements, neutron meters are maybe in active (Fuji Electric; Model 12-4-Ludlum; VF Nuclear) and/or in passive (The Thermo Fisher Scientific) types.

For ensuring the proper operations of neutron meters, calibrations must be done prior to, and periodically after their first use (IAEA, 2000). In a calibration certificate, in term of physical quantity (i.e., ϕ) and/or operational dosimetric quantities (i.e., $\dot{H}*(10)$; ${\dot{H}}_p(10)$), radiation quantities (i.e., neutron fluence-spectrum-averaged energies,$\overline{E}$ and/or fluence-to-ambient dose equivalent conversion coefficient, h*) must be mentioned since indicators of neutron meters are dependent on those quantities. Recent years, neutron reference fields have been established for calibrations of neutron meters, in world-wide (Mazrou et al., 2008; Guzman-Garcia et al., 2015; Vykydal et al., 2015; Vega-Carrillo and Martinez-Ovalle, 2016) as well as in Viet Nam (Le et al., 2016, 2017, 2018, 2019, 2024 ; Nguyen et al., 2024).

In this work, technical parameters (including physical, operational dosimetric, and radiation quantities) were presented at different distances from the sources’ centers. The technical parameters were respectively presented in manners of theoretical calculations (i.e., for the ISO-8529 neutron reference field of a bare ²⁴¹Am-Be source) and of experimental data using the Bonner sphere spectrometer (BSS) system (i.e., for the ISO-12789 simulated workplace neutron reference fields of the ²⁴¹Am-Be source moderated by different polyethylene spheres and for the ISO-12789 simulated workplace neutron reference field of the ²³⁹Pu-Be source). The combined standard uncertainties of technical parameters of neutron reference fields were also investigated.

2 Material and method

2.1 Neutron reference field in Viet Nam

The neutron room at the Institute for Nuclear Science and Technology (INST) has inner dimensions of 700 cm × 700 cm × 700 cm, satisfied the ISO-8529 recommendation (ISO 8529-2, 2000). The layout of the neutron calibration room can be found in Figure 1. In recent years, a X14-type ²⁴¹Am-Be neutron source has been installed at the room’s center for calibration purposes. The neutron emission rate of the X14-type ²⁴¹Am-Be source (supplied by Hopewell Designs, Inc., USA) was 1.299 × 10⁷ s⁻¹ on 23 January 2015 with the expanded uncertainty of 2.9% (k = 2, shown in a certificate), it is traceable to the USA National Institute of Standards and Technology. The source anisotropy correction factor at the angle of 90 degrees (perpendicular to the cylindrical neutron source’s central axis at the source center), F₁(90) was investigated as 1.030 using the MCNP5 Monte Carlo simulation code, with the standard uncertainty of 0.1% (k = 1). The half-life of ²⁴¹Am-Be source is 432 yr, considered as an economy advantage point for routine calibrations. More detailed information about the source can be found in Ref. (Le et al., 2018).

Based on this neutron source, several neutron reference fields were established at the INST (Hanoi, Viet Nam), following the international criteria: i.e., ISO-8529 series (Le et al., 2018) and ISO-12789 series (Le et al., 2019). These neutron reference fields are routinely used for calibrations of neutron meters at the INST (Le et al., 2019; Nguyen et al., 2020) as well as for delivering standard neutron dose equivalents (Nguyen et al., 2024).

The neutron room at the Military Institute for Chemical and Environmental Engineering (MICEE, Hanoi, Viet Nam) is a cubic one with inner dimensions of 700 cm × 700 cm × 700 cm. The room was constructed at an unoccupied area and at basement floor. The values of $\dot{H}*(10)$ outside the room were measured before putting the room into operation and yearly investigated to ensure the safety working conditions for radiation workers and public, complied with Vietnamese legal requirements. The MICEE neutron source of ²³⁹Pu-Be was granted by Russia some decades ago. It had been stored as a disused source till being used for establishing the neutron reference field at MICEE by 2020. The neutron source strength of the ²³⁹Pu-Be source was 4.6 × 10⁶ s⁻¹ in 1981 with the standard uncertainty re-assessed within 5.0% (k = 1). This neutron emission rate is considered as constant during usage process since the source’s half-life is as long as 2.41 × 10⁴ yr. The cylindrical shape of the ²³⁹Pu-Be source has a height of 3.3 cm and a diameter of 2.9 cm, which was installed at the floor’s center and pumped to the height of 150 cm for irradiation. The source anisotropy correction factor, F₁(90) was investigated as 1.029 using the MCNP6 Monte Carlo simulation code, with the standard uncertainty of 0.3% (k = 1) (Nguyen et al., 2024). The layout of the neutron calibration room can be found in Figure 2.

This neutron reference field was established and being used for calibration purposes at the MICEE.

Fig. 1 Top view and side view of neutron calibration room at the Institute for Nuclear Science and Technology.

Fig. 2 Top view of neutron calibration room at the Military Institute for Chemical and Environmental Engineering.

2.2 Bonner sphere spectrometer system

In this work, the Bonner sphere spectrometer (BSS) system was used with different spherical moderators to measure the count rate, M_i (unit in count per second, cps; and “i” stands for the BSS sphere diameter in inches) caused by neutrons from the moderated ²⁴¹Am-Be, and ²³⁹Pu-Be sources. The BSS system has a ⁶LiI(Eu)  thermal neutron sensitive detector and 6 different high density (ρ = 0.95 g.cm⁻³) polyethylene Bonner spheres with respective different diameters of 2, 3, 5, 8, 10, and 12 inches (i.e., i = 0, without a moderator; 2; 3; 5; 8; 10; and 12). The cylindrical thermal neutron detector of the ⁶LiI(Eu) scintillation crystal has 96% purity of ⁶Li with a height of 0.4 cm and a diameter of 0.4 cm. The BSS system was used to detect neutrons from thermal energy up to 20 MeV.

The different diameters of the BSS system have different neutron fluence-response functions, R_ib(E_b). A neutron fluence-response function of a BSS is considered as the distribution of the BSS count rate, R_ib(E_b) in the energy bin E_b, as a function of neutron fluence in that energy bin). The values of R_ib(E_b) of different Bonner spheres were investigated using both of MCNP5 and MCNP6 Monte Carlo simulation codes. More detailed information about the values of R_ib(E_b) can be found in previous works (Nguyen et al., 2024; Le, 2020).

2.3 Neutron spectrum unfolding

In order to find a neutron fluence spectrum (understood as the distribution of spectral neutron fluence rate, ϕ_b(E_b) as a function of neutron bin energies, E_b), a neutron spectrum unfolding code is needed to solve a series of equation (1). $$\begin{array}{c}\hfill M_i={\displaystyle \sum _{b=1}^n}{M}_{ib}(E_b)\hfill \\ \hfill ={\displaystyle \sum _{b=1}^n}{R}_{ib}(E_b){\varphi }_b(E_b)\hfill \end{array},$$(1)

where, the values of M_i and R_ib(E_b) are the input data for the unfolding code. More information about the unfolding codes can be found in Refs. (Le et al., 2018, 2019; Nguyen et al., 2024).

In this work, the FRUIT unfolding code (Bedogni et al., 2007) was used to unfold neutron fluence spectra. As results, neutron fluence spectra at the points of interest were derived (i.e., the values of ϕ_b(E_b) are available with the unit can be converted to cm⁻².s⁻¹).

2.4 Calculation of neutron reference field parameter

For the direct component of neutrons from the ²⁴¹Am-Be source following the ISO-8529 criteria, it was confirmed in previous work (Le et al., 2018) that: there was good consistence (within 3.0%) in the physical quantity (i.e., ϕ) and operational dosimetric quantity (i.e., $\dot{H}*(10)$) between Monte Carlo simulation, theoretical calculation, and BSS experimental data. Therefore, in this work, the conventional true values of ϕ and $\dot{H}*(10)$ for the direct component of neutrons from the ²⁴¹Am-Be source (following the ISO-8529 criteria) were calculated using equations (2) and (3). Where, B_b(E_b) is neutron source strength in the individual E_b energy bin (unit in s⁻¹) at the time of calculation; F_A(l) is the air attenuation correction factor (calculated based on guidance from Ref. (ISO 8529-2, 2000); F₁(90) is the anisotropy correction factor of the source; l is the distance (unit in cm) from the source’s center to the detector’s center; h^*(E_b) can be taken from international published data, i.e., ICRU-57 (ICRU, 1998). $$\begin{array}{c}\hfill \varphi ={\displaystyle \sum _{b=1}^n}{\varphi }_b(E_b)\hfill \\ \hfill =\frac{{\sum }_{b=1}^n{B}_b(E_b)\times F_A(l)\times F_1(90)}{4\pi l^2}\hfill \end{array},$$(2) $$\dot{H}*(10)={\displaystyle \sum _{b=1}^n}{\varphi }_b(E_b)\bullet h*(E_b),$$(3)

In the other hand, for the total component of neutrons from reference fields of the moderated ²⁴¹Am-Be source and of ²³⁹Pu-Be source, the field characterization process (following the ISO-12789 criteria) was performed in such sequent steps: (i) the BSS count rates (M_i) were measured for all BSS sphere at the point of interest during a suitable period so that the statistical uncertainty of M_i less than 1.0%; (ii) the values of M_i and R_ib(E_b) were prepared as input data for the FRUIT unfolding code; (iii) neutron fluence spectrum was unfolded using the FRUIT code with some constrain conditions (i.e., the standard deviation between unfolded and input BSS count rates must be less than 3.0%; calibration factor of BSS as 1.0). As results, the unfolded spectral neutron fluence rates, ϕ_b(E_b), were achieved, the conventional true values of $\varphi ,\dot{H}*(10)$, as well as the radiation quantities (i.e., $\overline{E}$ and h*) were then respectively calculated using equations (4)–(7). $$\varphi ={\displaystyle \sum _{b=1}^n}{\varphi }_b(E_b),$$(4) $$\dot{H}*(10)={\displaystyle \sum _{b=1}^n}{\varphi }_b(E_b)\times h*(E_b),$$(5) $$\overline{E}=\frac{{\sum }_{b=1}^n{E}_b\times {\varphi }_b(E_b)}{\varphi },$$(6) $$h*=\frac{\dot{H}*(10)}{\varphi }.$$(7)

2.5 Assessment of combined standard uncertainty of technical parameter

Based on the uncertainty propagation principle, one can figure out that the combined standard uncertainties of all quantities (i.e., physical, operational dosimetric, and radiation quantitites − calculation models in equations (2)–(7)) have the same uncertainty propagation rule. In other words, the combined standard uncertainty of an individual quantity (u_Q) is equal to square root of summed squares of its all uncertainty budgets (u_b). In general, the value of u_Q can be calculated using equation (8). $$u_Q=\sqrt{{\displaystyle {\displaystyle \sum }_{b=1}^{all}}{u}_b^2}$$(8)

3 Result

3.1 Technical parameter of neutron calibration field

Table 1 shows the technical parameters (including of physical − ϕ, operational dosimetric − $\dot{H}*(10)$, and radiation − $\overline{E}$, h*, quantities) at different distances from the sources’ centers for different neutron reference fields.

3.2 Combined standard uncertainty of technical parameter

Table 2 shows the combined standard uncertainties of conventional true values of technical parameters of different neutron reference fields in conjunction with the uncertainty budgets.

4 Discussion

4.1 Feasible range for calibration

From Table 1, ones can figure out that the feasible range of $\dot{H}*(10)$, for calibrations of neutron meters, is from 10 to 150 μSv/h (for the calibration distance from 100 to 250 cm). This range is limited for calibrations of neutron meters at higher measuring range of $\dot{H}*(10)$. However, it is acceptable for calibrations of neutron meters with preferred measuring range at radiation protection level.

In the investigated distances, the feasible delivery range of ϕ is from 15 to 105 cm⁻².s⁻¹ while the fluence-spectrum-averaged energies ($\overline{E}$) of the neutron fields vary from 0.83 to 4.16 MeV (corresponding to the values of h* from 134 to 391 pSv.cm²).

For calibration of neutron meters following the ISO-8529 criteria, the contribution of scattered neutrons to the reading of meter to be calibrated must be less than 40% that of the direct component. It was found that it corresponds to the distance less than 250 cm from the source’s center.

For calibration of neutron meters following the ISO-12789 criteria, the total component of neutrons can be used. Therefore, the calibrations can be done since the statistical uncertainty of neutron meters whose readings have a statistical uncertainty less than 10%. It was found that the distance from the source’s center less than 250 cm is acceptable.

4.2 Accuracy in neutron field parameter

From Table 2, ones can see that the combined standard uncertainties of technical parameters of the neutron reference fields are acceptable in conjunction with those stated in international publications, i.e., acceptable standard uncertainties in determination of ϕ as 5.0-10%; in determination of h* as 15% (ISO 12789-2, 2008). That means the acceptable combined standard uncertainty (k = 1) in determination of $\dot{H}*(10)$ can be even higher than 15% (based on uncertainty propagation principle of equation (7)). Even, the acceptable standard uncertainty in determination of$\overline{E}$ is not yet mentioned in Ref. (ISO 12789-2, 2008) but it could be understood that the uncertainty of $\overline{E}$ can be acceptable if it does not cause the change in $\dot{H}*(10)$ over 15%.

5 Conclusions

Various neutron reference fields were established in Viet Nam for calibrations of neutron meters. The technical parameters of neutron reference fields were characterized and presented in this work, such as: physical quantity (integrated neutron fluence rate, ϕ), operational dosimetric quantity (neutron ambient dose equivalent rate, $\dot{H}*(10)$) as well as radiation quantities (neutron fluence-spectrum-averaged energy, $\overline{E}$; fluence-to-ambient dose equivalent conversion coefficient, h*). The combined standard uncertainties of technical parameters were also investigated and presented in this work. The conventional true values of technical parameters of the neutron fields indicate that the determination of those conventional true values are reliable with the acceptable combined standard uncertainties. That means the neutron fields can be feasibly used in calibrations of neutron meters in Viet Nam following the ISO-8529 (direct component of neutrons) and the ISO-12789 (total component of neutrons) criteria.

Acknowledgments

Ph.D student Ngoc-Quynh Nguyen (INST) and M.Sc. Minh-Cong Nguyen (MICEE) are highly appreciated for their assistance.

Funding

This research was partly funded by Viet Nam National Foundation for Science and Technology Development (NAFOSTED) under grant 103.04-2021.140.

Conflicts of interest

There is no competing interests regarding the publication of this paper.

Data availability statement

Data will be available upon request.

References

All Tables

All Figures

	Fig. 1 Top view and side view of neutron calibration room at the Institute for Nuclear Science and Technology.
In the text

	Fig. 2 Top view of neutron calibration room at the Military Institute for Chemical and Environmental Engineering.
In the text