Radioprotection No. 60-1 | Page 92

86 N. T. Le: Radioprotection 2025, 60( 1), 84 – 90 previous work( Le et al., 2018) that: there was good consistence( within 3.0 %) in the physical quantity( i. e., f) and operational dosimetric quantity( i. e., H_ ð10Þ) between Monte Carlo simulation, theoretical calculation, and BSS experimental data. Therefore, in this work, the conventional true values of f and H_ ð10Þ for the direct component of neutrons from the 241 Am-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); F 1( 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).

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

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, f b( E b) asa function of neutron bin energies, E b), a neutron spectrum unfolding code is needed to solve a series of equation( 1).

M i ¼ Xn

¼ Xn b¼1 b¼1

M ib ðE b Þ

R ib ðE b Þf b ðE b Þ; ð1Þ

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 f b( E b) are available with the unit can be converted to cm �2. s �1).

2.4 Calculation of neutron reference field parameter f ¼ Xn

¼

Pb¼1 n f b ðE b Þ

b¼1 B bðE b ÞF A ðlÞ F 1 ð90Þ 4pl 2;

_ H ð10Þ ¼ Xn b¼1 f b ðE b Þ∙h ðE b Þ;

In the other hand, for the total component of neutrons from reference fields of the moderated 241 Am-Be source and of 239 Pu-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, f b( E b), were achieved, the conventional true values of f; H_ ð10Þ, as well as the radiation quantities( i. e., E and h *) were then respectively calculated using equations( 4)–( 7). f ¼ Xn

_ H ð10Þ ¼ Xn b¼1

b¼1 f b ðE b Þ;

f b ðE b Þh ðE b Þ; ð2Þ

E ¼

P n ð3Þ

ð4Þ

ð5Þ b¼1 E b f b ðE b Þ; ð6Þ f