Epithermal neutron activation dosimetry–(n, γ) reactions under boron-based filters

Abstract

Neutron activation dosimetry is the primary method for the determination of the neutron flux or fluence, and in general, it is sensitive to the thermal and resonance energy ranges (radiative capture reactions–$(n,\gamma )$ reactions) and the fast energy range (threshold reactions). However, there are very few nuclear reactions which are sensitive specifically to neutrons in the intermediate–epithermal–energy region. This energy region, along with the fast energy range, will become particularly important in the development and deployment of new reactor technologies (Generation IV reactors and Small Modular Reactors–SMRs), which are currently being championed as technologies enabling a meaningful contribution to decarbonization and the fight against climate change, as well as nuclear fusion. The epithermal neutron energy range is also of particular importance for Boron Neutron Capture Therapy (BNCT), a neutron-based cancer therapy, particularly effective for the treatment of head and neck cancer, malignant meningioma, melanoma and hepatocellular carcinoma. This work investigates and demonstrates the applicability of a particular set of $(n,\gamma )$ reactions in conjunction with boron-based neutron filters to achieve sensitivity in the epithermal energy region, and discusses avenues for future research in this context.

Introduction

Most advanced reactor concepts currently being developed in the framework of the Generation-IV forum¹ as well as Small Modular Reactors (SMRs) are designed to operate with neutrons in the fast and intermediate–epithermal–energy range, due to important advantages, in particular increased efficiency of the use of uranium resources and the possibility of transmuting long-lived actinides, which are the most problematic in nuclear waste management. In nuclear fusion reactors, e.g. tokamaks, neutrons originating from fusion reactions are also in the fast energy range; the neutron spectrum in the immediate vicinity of the reactor is characterized by a fast component and an epithermal component, which is due to neutrons slowing down by interactions with the surrounding materials. The ability to accurately measure neutrons in the fast and epithermal range is therefore of significant importance in future advanced fission and fusion reactors, in particular to monitor the reactor power level, achieved by on-line nuclear instrumentation, and to assess neutron fluence levels in critical reactor components, giving rise to radiation induced effects in materials and systems. Figure 1 displays neutron spectra in different nuclear environments obtained by Monte Carlo simulations: the XAMR® molten salt fast neutron microreactor designed to utilize spent nuclear fuel, as a representative of fast fission systems (courtesy of the NAAREA SAS company), the ITER tokamak² as a representative of fusion reactors, the Krško Nuclear Power Plant (NPP)³ and the Jožef Stefan Institute (JSI) TRIGA research reactor⁴ as representatives of thermal fission systems. The thermal, epithermal and fast energy ranges are highlighted.

Fig. 1

Calculated neutron spectra in different nuclear environments: NAAREA XAMR® molten salt fast fission microreactor, ITER fusion reactor, Krško NPP and JSI TRIGA thermal fission reactors. The thermal, epithermal and fast neutron energy ranges are highlighted.

Boron Neutron Capture Therapy (BNCT) is a tumor-selective particle radiotherapy, relying on preferential boron accumulation in tumorous tissue and neutron irradiation. Epithermal incident neutron beams are used for irradiation, on account of neutron thermalization in tissue prior to capture in $^{10}$B, giving rise to therapeutic energetic charged particles ($\alpha$ particles and $^7$Li recoil nuclei). Epithermal neutron beams are achieved at nuclear reactors or accelerator facilities equipped with neutron producing targets, through specifically designed configurations including neutron moderating and absorbing materials as well as photon shielding components. Source neutrons are typically slowed down from the fast energy range to the thermal and epithermal energy ranges by a moderator (e.g. pure polyethylene), after which the thermal component in the neutron spectrum is absorbed by a thermal neutron filter (e.g. cadmium or borated polyethylene). Prompt and delayed gamma rays originating from the source or from neutron interactions in the materials are attenuated by neutron-transparent gamma shields (e.g. lead or bismuth). Typically in BNCT facilities, the beam intensity is measured and controlled by the use of relative monitors, e.g. $^{235}$U fission chambers or $\hbox {BF}_3$ detectors under cadmium or boron shield in order to filter out the thermal neutron component, to which such detectors are most sensitive. The possibility of an activation dosimetry technique providing absolute information on the neutron flux magnitude and sensitive specifically to the epithermal energy range is of significant importance in the context of BNCT research, as it would enable complementary experimental information to validate computational analyses and support the correlation between the incident radiation conditions and the exposure doses in the establishment of treatment procedures, as well as absolute monitoring and calibration of the incident neutron flux used for patient irradiation in BNCT facilities. It is also worth noting that activation dosimetry is insensitive to gamma radiation, which is generally not the case for on-line neutron detectors such as fission chambers or $\hbox {BF}_3$ detectors.

Various measurement techniques exist at a mature technological level by which thermal and fast neutrons can be detected and quantified. However, there is a general lack of measurement capabilities and suitable instrumentation sensitive specifically to the epithermal energy range. Neutron activation dosimetry is the reference neutron flux/fluence measurement technique and consists of irradiating material samples with a well-known composition and observing the photon emission due to the radionuclides generated. It has been widely used since the very beginnings of the development of nuclear energy. It has first been applied to quantify incident thermal neutrons, to characterize the radiation conditions during irradiations and to measure the power of a nuclear reactor during operation, and has subsequently been extended to fast neutrons, typically over 1 MeV, for material ageing validation and neutron radiation damage studies.

The need for a better understanding of the epithermal energy range has resulted in recent work aimed at improvements in neutron activation dosimetry⁵, however a general lack of measurement capabilities or suitable instrumentation still remains. This paper presents new research aimed at extending the sensitivity of neutron activation dosimetry to the epithermal energy region by the use of specific radiative capture reactions in conjunction with boron-based neutron filters. The lack of nuclear reactions applicable for neutron activation dosimetry sensitive specifically to the epithermal energy region is illustrated in Fig. 2. A representative neutron spectrum of a thermal fission reactor, corresponding to the Jožef Stefan Institute (JSI) TRIGA reactor, Pneumatic Tube (PT) irradiation facility (used in the present work), is plotted in lethargy representation. Overlaid onto the neutron spectrum are reaction rate color-maps for all nuclear reactions included in the latest release of the International Reactor Dosimetry and Fusion File (IRDFF-II) of the following types: $(n,\gamma )$, $(n,n')$, (n, p), $(n,\alpha),$ (n, t), (n, 2n), (n, 3n), (n, f). In the color-maps, the color at a particular energy indicates the magnitude of the reaction rate relative to the maximum. It is evident that for the majority of the reactions, their sensitivity lies either predominantly in the thermal neutron energy range or in the fast neutron energy range. In the graph in Fig. 2 the energy range from 1 eV to 100 keV is practically not covered at all—highlighted in yellow.

Fig. 2

Reaction rate color-maps for dosimetry reactions in the IRDFF-II⁶ library in a thermal reactor neutron spectrum (JSI TRIGA reactor, F24 irradiation channel—used in this work). The color maps indicate the magnitude of the reaction rates as a function of energy relative to their maximal values. The epithermal energy region (1 eV–100 keV) is practically not covered at all—highlighted in yellow.

Results

Candidate radiative capture reactions

In previous work⁷ we investigated the possibility of using boron nitride neutron filters to shift the sensitivity of $(n,\gamma )$ reactions to the epithermal energy range. We performed a systematic search of radiative capture reactions for which a pronounced sensitivity shift was observed, by irradiations under a boron nitride ($\hbox {B}\hbox {N}$) filter. Our search was based on the ENDF/B-VII.1 nuclear data library⁸ and a cylindrical boron nitride ($\hbox {B}\hbox {N}$) filter with a wall thickness of 4 mm. We classified the reactions by the following criteria: the energy $E_{50\%}$, i.e. the energy at which the cumulative reaction rate reaches 50% of its total, under $\hbox {B}\hbox {N}$, the reaction product half-life and gamma emissions, and finally assigned a verdict on the feasibility of their use. We excluded any reactions which were considered not measurable with gamma spectrometry, e.g. reactions producing stable products or radioactive products emitting only low intensity gamma rays, lower than the percent level. Several reactions were excluded on the basis of the very short half-life of the reaction products. Some of the identified reactions involved radioactive target isotopes, which were assigned a “possible” verdict. Although the usability of such reactions is made more difficult by the need to fabricate samples out of radioactive material, possibly by deposition from solution, we consider these cases as interesting, on account of the possibility of high precision monitoring of the starting target activity and product activity by means of gamma spectrometry. On the basis of the search results, we performed an experimental campaign with the objective to measure the reaction rates for the top 10 identified nuclear reactions which exhibited the most pronounced energy sensitivity shift between bare and $\hbox {B}\hbox {N}$-covered irradiations. In the experimental campaign we included several standard neutron dosimetry reactions for the characterization of the filter transmission function. The identified candidate reactions are listed in Table 1.

Table 1 Candidate $(n,\gamma )$ reactions measured in this work.

Filter transmission functions

In the present work we investigated the applicability of boron based filters with differing concentrations of the $^{10}$B isotope, which determines the shape of the filter transmission function. We considered three different materials: natural boron nitride ($\hbox {B}\hbox {N}$), natural boron carbide ($\hbox {B}_4\hbox {C}$) and boron carbide enriched in $^{10}$B ($^{10}\hbox {B}_4\hbox {C}$), with an enrichment level of $> 96\%$. We decided on the same filter geometry (wall thickness of 4 mm) in order to preserve the sample location during the irradiations.

Monte Carlo calculations

The transmission functions for the boron based filters employed in the present work, $t_f(E)$ were characterized via Monte Carlo calculations with the particle transport code MCNP6⁹ in conjunction with the ENDF/B-VIII.0 nuclear data library¹⁰ and the measured reaction rate ratios for the nuclear reactions $^{197}\hbox {Au}(n,\gamma ) ^{198}\hbox {Au}$ and $^{238}\hbox {U}(n,\gamma ) ^{239}\hbox {U}$. The experimental procedure for the measurement of reaction rate ratios is presented in section Sample irradiation and measurement. For the calculations, a detailed computational model of the JSI TRIGA Mark II reactor was used, based on the benchmark model featured in the International Criticality Safety Benchmark Experiment Project (ICSBEP) Handbook¹¹, which has been continuously upgraded and validated for the calculation of the effective multiplication factor, flux and reaction rate distributions^12,13, and kinetic parameters¹⁴. Boron based filters of the exact dimensions and compositions as used in the experiments were inserted into the PT irradiation position in the computational model; the neutron spectrum inside the filters was calculated by means of a track-length estimator of the neutron flux (an F4 tally in MCNP terminology), using the SAND-II 640 energy group structure. The unperturbed neutron spectrum was calculated in the exact same way, except that the filter material in the model was replaced by air. The calculated transmission function for the filters in groupwise form was obtained by dividing the groupwise values of the neutron flux from the calculation with the filters present ($\phi _f(E_i)$), by those from the unperturbed case ($\phi _b(E_i)$) (Eq. 1). The transmission functions are displayed in Fig. 3.

$$\begin{aligned} t_{f}(E_i) = \frac{\phi _{f}(E_i)}{\phi _b (E_i)} \end{aligned}$$

(1)

Filter transmission function parametrization

The filter transmission function was parametrized by the following two-parameter expression, assuming exponential attenuation of the neutron flux through the filter walls (Eq. 2):

$$\begin{aligned} t(E) = \exp \left[ -nd_{eff}(\sigma _a(E) + \xi \sigma _s(E))\right] , \end{aligned}$$

(2)

where:

• n is the atom number density in the filter material,

• $d_{eff}$ is the effective container thickness, the first parameter,

• $\sigma _a(E)$ is the energy dependent filter absorption cross-section,

• $\xi$ is the scattering fraction, the second parameter,

• $\sigma _s(E)$ is the energy dependent scattering cross section.

Cross sections for the filter materials

Cross sections were generated for the filter materials used in the experiments using the PREPRO2018¹⁵ nuclear data processing code package. Nuclear data for boron, carbon, nitrogen and oxygen isotopes were taken from the ENDF/B-VIII.0 library¹⁰. Both total ($\sigma _t$) and absorption (disappearance) cross sections ($\sigma _a$) were generated ($MT=1$ and $MT=101$ in ENDF terminology, respectively). The scattering cross-section $\sigma _s$ is calculated as the difference between the total and the absorption cross sections $\sigma _s = \sigma _t - \sigma _a$. The mixture cross sections were used in the determination of the transmission function, described in the following subsections.

Fitting the effective thickness $d_{eff}$

A first approximation for the effective thickness $d_{eff}$ of the filters was obtained by the bisection method, simply by fitting the transmission function as in Eq. (3) to the functions obtained with Monte Carlo calculations. Fine tuning of the effective thicknesses was then conducted with the bisection method, by fitting calculated reaction rate ratios using the transmission function given in Eq. (3), to measured ratios for the reactions $^{197}\hbox {Au}(n,\gamma ) ^{198}\hbox {Au}$ and $^{238}\hbox {U}(n,\gamma ) ^{239}\hbox {U}$, minimizing the average relative difference between the calculated and the measured reaction rate ratios.

Fitting the scattering fraction $\xi$

Neutron scattering affects the transmission function at higher neutron energies. In case of a pure 1/v absorber, the high energy limit of the transmission function is 1; the average value of the transmission function obtained from the Monte Carlo calculations from 500 keV to 3 MeV is 0.98. The scattering fraction $\xi$ was obtained with the bisection method by fitting the average value of the transmission function between the above energy limits to the average value of the function obtained with Monte Carlo calculations. The final result for the scattering fraction $\xi$ is 0.03. Table 2 reports the final parameter values, Fig. 3 compares the fitted transmission functions to the ones calculated with MCNP.

Table 2 Fitted filter transmission function parameters.

Fig. 3

Calculated and fitted filter transmission functions.

Comparison between experimental and calculated reaction rate ratios

We performed neutron irradiations of material samples in the JSI TRIGA reactor PT irradiation facility, bare and under boron filters, followed by gamma spectrometry measurements to determine the induced activities of the reaction products. The experimental reaction rate ratios were computed from the measurement data as per Eq. (3):

$$\begin{aligned} R_f= & \frac{\frac{N_{p,b}}{t_{m,b} m_b}}{\left( 1 - e^{-\lambda t_{irr,b}}\right) e^{-\lambda t_{cool,b}} \left( \frac{1 - e^{-\lambda t_{m,b}}}{\lambda t_{m,b}}\right) } \frac{\left( 1 - e^{-\lambda t_{irr,f}}\right) e^{-\lambda t_{cool,f}} \left( \frac{1 - e^{-\lambda t_{m,f}}}{\lambda t_{m,f}}\right) }{\frac{N_{p,f}}{t_{m,f} m_f}} \nonumber \\ b= & \hbox {bare} \nonumber \\ f= & \hbox {filtered (BN}, \hbox {B}_4\hbox {C or }^{10}\hbox {B}_4\hbox {C)}, \end{aligned}$$

(3)

where:

• $N_{p,b}$, $N_{p,f}$ are the fitted peak areas in the gamma spectra for the same energy $E_\gamma$ (in cases of multiple gamma lines emitted by the product isotope, multiple experimental results are reported per reaction),

• $m_b$ and $m_f$ are the sample masses,

• $\lambda$ are the activation product decay constants,

• $t_{irr,b}$, $t_{irr,f}$ are the irradiation times,

• $t_{cool,b}$, $t_{cool,f}$ are the cooling times,

• $t_{m,b}$, $t_{m,f}$ are the measurement (live) times.

Reaction rate ratios for the measured nuclear reactions were calculated using the GRUPINT code⁴ as per Eq. (4), where groupwise representations of the neutron spectrum ($\phi$), reaction cross-sections ($\sigma$) and filter cross-sections—absorption ($\sigma _{f,a}$) and scattering ($\sigma _{f,s}$) in the SAND-II 640 energy group structure were employed. The parameters in the denominator of Eq. (4) follow from Eq. (2).

$$\begin{aligned} R_f = \frac{\sum _{i=1}^{640} \sigma _i \phi _i}{\sum _{i=1}^{640} \sigma _i t_i \phi _i} = \frac{\sum _{i=1}^{640} \sigma _i \phi _i}{\sum _{i=1}^{640} \sigma _i \exp \left[ -n_f d_{f,eff}(\sigma _{f,a}^i + \xi _f \sigma _{f,s}^i)\right] \phi _i} , \end{aligned}$$

(4)

The ratios were computed using the neutron spectrum in the PT irradiation channel, previously characterized using the GRUPINT code on the basis of Monte Carlo calculations and measured reaction rate ratios⁴. Cross sections from the ENDF-B/VIII.0¹⁰ nuclear data library were used. The boron-based filter transmission functions were determined starting from Monte Carlo calculations with the MCNP v6.1 code⁹ and subsequent fitting on the basis of experimental data for the $^{197}$Au$(n,\gamma )$ and the $^{238}$U$(n,\gamma )$ reactions.

Table 3 reports the comparison of the experimental results from this work and the calculated values, and the relative differences observed (in %). The comparison for the $^{197}$Au$(n,\gamma )$ and the $^{238}$U$(n,\gamma )$ reactions is informative only, as the experimental data for these reactions was used for the determination of the filter transmission functions, used in the calculations of all reaction rate ratios, and are therefore reported in Bold in Table 3. The experimental reaction rate ratios were computed for the main gamma rays emitted by the product radioisotopes, hence there are multiple entries for some reactions (targets: $^{238}$U, $^{64}$Ni, $^{82}$Se, $^{94}$Zr and $^{130}$Te). All uncertainties are stated at the 1-$\sigma$ level.

Table 3 Comparison between experimental and calculated $\hbox {B}\hbox {N}$, $\hbox {B}_4\hbox {C}$ and $^{10}\hbox {B}_4\hbox {C}$ reaction rate ratios.

Discussion

Dosimetry reactions

In addition to the new candidate reactions reported in Table 1, measurements and calculations were performed for the $^{55}$Mn$(n,\gamma )$ and $^{232}$Th$(n,\gamma )$ reactions as well, as examples of neutron dosimetry reactions, included in the IRDFF-II library⁶, with cross-section evaluations deemed reliable. For the $^{55}$Mn$(n,\gamma )$ reaction, we observe agreement within 1 $\sigma$ only for the $\hbox {B}_4\hbox {C}$ ratio, for the $\hbox {B}\hbox {N}$ and $^{10}\hbox {B}_4\hbox {C}$ ratios there are discrepancies outside 3 $\sigma$. On the other hand, for the $^{232}$Th$(n,\gamma )$ reaction, the agreement between the experimental and calculated values is excellent, all three ratios being within 1–2 $\sigma$, strengthening the confidence in the cross-section evaluation for this reaction as well as the approach and methods used in this work.

New candidate reactions

In general, for the new candidate reactions we observe significantly larger discrepancies between the measured and calculated reaction rate ratios, indicating potential issues in the reliability of the cross section evaluations, in particular in the epithermal energy range. This is not unexpected, as the new candidate reactions in general do not play a critical role in nuclear reactor technology, and thus have not been considered of high importance in nuclear data evaluation efforts—although nuclear fuel and reactor structural components are commonly based on Al, Ni and Zr. Best agreement overall, for all three filters, was observed for the reaction rate ratios for $^{23}$Na (included in the IRDFF-II nuclear data library), $^{64}$Zn, $^{82}$Se, with discrepancies between experimental and calculated values ranging from the 2% to 3% level ($^{82}$Se, $^{10}\hbox {B}_4\hbox {C}$ ratio) up to the 20% level ($^{23}$Na, $^{10}\hbox {B}_4\hbox {C}$ ratio). Worst agreement overall was observed for the reaction rate ratios on $^{64}$Ni, $^{74}$Ge and $^{140}$Ce, ranging from the 20% level ($^{74}$Ge, $^{10}\hbox {B}_4\hbox {C}$ ratio) up to the 60% level ($^{64}$Ni, $^{10}\hbox {B}_4\hbox {C}$ ratio, $^{140}$Ce, all filters).

Figure 4 displays the bare and filtered neutron spectra as well as the reaction rate color-maps for the new candidate reactions. As in Fig. 2, the color at a given energy represents the magnitude of the reaction rate relative to the maximum. The color-maps clearly show a sensitivity shift to the energy region between $10^{-1}$ eV and 100 keV for the new candidate reactions. The reaction on $^{142}$Ce was not among the new candidate reactions, on account of its sensitivity shift not being as prominent, but as the reaction product was clearly measurable in the irradiated Ce samples, it was included in the present work. We consider Ce as an interesting target material on account of the possibility of simultaneous measurements of two reactions.

Fig. 4

Filtered neutron spectra and reaction rate color-maps for the new candidate reactions in a thermal reactor spectrum (JSI TRIGA reactor). The color maps indicate the magnitude of the reaction rates as a function of energy relative to their maximal values. Significant sensitivity shift to the epithermal energy region is clearly observable under boron-based filters.

Uncertainty analysis

To provide a better understanding of the observed differences in the experimental and calculated reaction rate ratios, a computational analysis of the impact of sources of uncertainty or bias was carried out, affecting the comparison between the experimental and calculated reaction rate ratios. The sources taken into account were the uncertainty in the filter wall thickness and the bias in the measured values due to the increased temperature of the samples in irradiations under filter. The impact on the reaction rate ratios due to different cross-section libraries was also investigated. Calculations were carried out using the MCNP6 code⁹ using a computational model comprising the polyethylene rabbit tube and the boron-based filters contained within, and a source neutron spectrum corresponding to the JSI TRIGA PT irradiation facility⁴. The filter wall thickness was varied by ± 0.1 mm from the nominal 4.0 mm. The temperature of the filter and sample material was varied from room temperature to $100^{\circ }\hbox { C}$, the maximal expected temperature during the irradiations, due to $\alpha$ heating in the filter material (see subsection $\alpha$ heating in neutron filters). This was accomplished by mixing cross-section data from the ENDF/B-VIII.0 library¹⁰ at room temperature (293.6 K) and next available data at 600 K. Mixing was done utilizing square root dependence, as described in¹⁶. In addition to the ENDF/B-VIII.0 library¹⁰, calculations were made using data from the ENDF/B-VII.1 library⁸ (the previous major release of the ENDF library), the JEFF3.2 library (the previous release of the JEFF library), the current JEFF3.3 library¹⁷ and the TENDL library¹⁸.

The variation in the reaction rate ratios for a varying wall thickness and for increased sample and filter temperature were mostly of the order of a few %; most observed differences were within $1\sigma$ (statistical uncertainty in the calculated values), and all differences were within $2\sigma$. However, substantial variations in the ratios were observed in the calculations using different cross section data. Relative variations between the reference ENDF/B-VIII.0¹⁰ library and ENDF/B-VII.1 library⁸ were typically a few %, mostly within $1\sigma$ (statistical uncertainty in the calculated values). This is expected in case the evaluations for the reactions of interest did not change between the two library releases, as is the case for most reactions, or the evaluations are similar. Relative variations in the reaction rate ratios between ENDF/B-VIII.0¹⁰ and JEFF3.2 libraries were up to 114% (in the case of $^{82}$Se) and decreased to a maximum of 45% for its newer evaluation JEFF3.3¹⁷. The highest differences in the calculated ratios between JEFF3.3 and ENDF/B-VIII.0 were observed for $^{27}\textrm{Al}$ (− 17%), $^{82}\textrm{Se}$ (− 48%), $^{74}\textrm{Ge}$ (+ 24%), $^{130}\textrm{Te}$ (+ 26%), $^{140}\textrm{Ce}$ (− 18%), $^{55}\textrm{Mn}$ (+ 29%). For other listed reactions, the differences were a few %, within $1\sigma$ of statistical uncertainty, again explained by the same or similar cross-section evaluations in the two libraries. The highest relative variations in the reaction rate ratios between the ENDF/B-VIII.0 and TENDL¹⁸ libraries were observed for $^{64}\textrm{Ni}$ (+ 25%), $^{82}\textrm{Se}$ (+ 188%), $^{26}\textrm{Mg}$ (+ 43%), $^{74}\textrm{Ge}$ (+ 20%), $^{140}\textrm{Ce}$ (− 21%), $^{142}\textrm{Ce}$ (+ 34%). This analysis provides a powerful indication on the comparatively poor quality of the cross-section evaluations for the new candidate reactions and the need for significant improvements in order for these reactions to be usable in the context of epithermal neutron dosimetry. Table 4 summarizes the observed relative variation the reaction rate ratios due to the listed sources of uncertainty/bias and different cross-section data.

Table 4 Observed relative variation in the reaction rate ratios due to multiple sources of uncertainty or bias.

Conclusions and future work—filtered beam configuration

This work demonstrates the applicability of particular radiative capture reactions in conjunction with boron based filters for epithermal neutron dosimetry. As the candidate reactions in this work have not been considered of high importance for neutron dosimetry, it was not unexpected to observe relatively high discrepancies between the experimental values obtained in this work and the calculated values, based on general purpose nuclear data. A recommendation can be made to the nuclear data community on the need for high quality experimental data, which will enable future improvements in the nuclear data evaluations, and possibly the inclusion of new candidate reactions in dosimetry nuclear data libraries. The approach used in this work may enable new research avenues. The use of filters with varying geometries or $^{10}$B concentrations open the possibility of reaction rate measurements in particular energy intervals–energy windows, to complement time-of-flight techniques and provide useful data to the nuclear data evaluation community. A filtered beam configuration is envisaged at the Jožef Stefan Institute TRIGA reactor, with multiple (several 10) $^{10}$B-bearing shutters, to achieve a higher energy resolution, and the possibility of prompt gamma-ray spectrometry, to infer ratios of reaction rates for reactions of interest vs. reference reactions. The energy resolution, i.e. the effective width of the energy intervals depends on the shutter geometry and the shutter material properties, in particular the $^{10}$B concentration. The highest resolution is achieved in theory with thin shutters with a low $^{10}$B concentration, however, this may not be favourable in practice due to the requirements of a well-known $^{10}$B concentration and a high degree of material homogeneity in order to minimize experimental uncertainties. The use of materials with no isotopic enrichment is envisaged, in particular boron nitride, with a comparatively higher cumulative shutter thickness required to achieve high effective cut-off energies in the neutron spectra.

Methods

Sample materials

Materials used for the preparation of metallic samples in this work were purchased from Goodfellow (UK) or the Joint Research Centre (JRC, Geel, Belgium), Institute for Reference Materials and Measurements (IRMM). Wherever possible, samples in disk/foil form were made, which was the case for Mg, Ce, Zr, Ni, Al. For samples of Se, Ge, Te it was not possible to create samples in disk form on account of the brittleness of the materials, and material fragments were used instead. In the case of Na, the sample material used was NaF powder, purchased from Sigma Aldrich, which was encapsulated in polyethylene foil. Table 5 reports the sample materials used in the present work, the nominal sample dimensions and the typical sample mass.

Table 5 Details of the samples irradiated in the experiments.

$\alpha$ heating in neutron filters

The boron based neutron filters used in the present work were manufactured by hot pressing ($\hbox {B}\hbox {N}$) and electron beam machining ($\hbox {B}_4\hbox {C}$ and $^{10}\hbox {B}_4\hbox {C}$). The filters were cylindrical with an internal cavity 5 mm in diameter and height. The filter wall thickness (top and bottom, as well as cylindrical) was 4 mm. Figure 5 displays the actual filters used in this work.

Fig. 5

Boron based neutron filters used in this work. From left to right: boron nitride ($\hbox {B}\hbox {N}$), natural boron carbide ($\hbox {B}_4\hbox {C}$) and enriched boron carbide ($^{10}\hbox {B}_4\hbox {C}$).

In this work, $\alpha$ particle heating originating from $^{10}$B$(n,\alpha )^7$Li reactions occurring in boron-based neutron filters posed an important constraint for the irradiations, as several sample materials had relatively low ignition temperatures (e.g. Ce, Te, Mg). In order to mitigate the risk of sample ignition during irradiation, prior to the experimental campaign we performed measurements of the temperature during irradiation inside a $^{10}\hbox {B}_4\hbox {C}$ neutron filter (most restrictive case). The filter was equipped with a small T-type thermocouple, made by silver-soldering 0.003 inch (approx. 0.08 mm) diameter teflon-insulated wires of copper and constantan. The filter was irradiated in the F26 irradiation channel of the JSI TRIGA reactor (close to the Pneumatic Tube, in position F24). Figure 6 displays plots of the measured temperature and reactor power vs. time, as well as a top view of the JSI TRIGA reactor core, highlighting the F24 irradiation channel used in the present work. Based on the measurements, we decided to limit the power level to 50 kW for the experimental campaign, resulting in a maximal expected temperature within the $^{10}\hbox {B}_4\hbox {C}$ filter between $80^{\circ }\hbox {C}$ and $100^{\circ }\hbox {C}$. No temperature-related issues were encountered in the experimental campaign.

Fig. 6

Left: 3D render of JSI TRIGA reactor core, highlighting the experimental locations used in the present work. Right: plots of the measured temperature in the $^{10}\hbox {B}_4\hbox {C}$ filter and reactor power vs. time.

Sample irradiation and measurement

Samples were weighed using an analytical balance with 10 $\upmu$g precision. For each material we irradiated 4 samples, one bare and three inside boron-based filters. Irradiations were performed in the F24 position in the core of the JSI TRIGA reactor, equipped with a pneumatic sample transfer system. The irradiation position is commonly denoted as Pneumatic Tube (PT). The irradiations were performed by placing the bare samples or samples contained within boron-based filters into standard polyethylene rabbit tubes. The filters were carefully wrapped in a small amount of paper to center them within the rabbit tubes.

The irradiations were performed using an electronically controlled pneumatic sample transfer system developed and manufactured in-house¹⁹. The irradiation, cooling and measurement times were chosen appropriately, depending of the half-lives of the reaction products. For the aluminium samples, the irradiation, cooling and measurement times were the shortest, of the order of a few minutes, as the measured reaction product ($^{28}$Al) has the shortest half-life −2.245 min. The longest irradiation, cooling and measurement times were, respectively, two hours, 107 days and 7 days in case of longer-lived activation products ($^{64}$Zn, with a half-life of 243.93 days, $^{95}$Zr, with a half-life of 64.032 days and $^{141}$Ce, with a half-life of 32.511 days). In order to compensate for the lower induced activities in samples irradiated under filter, longer irradiation times were specified, compared to irradiations of bare samples.

For the measurements, a p-type high purity germanium (HPGe) detector was used, manufactured by ORTEC (model GEM-P4 PLUS-S) with a relative efficiency of 54.1% at 1.33 MeV, operated by an ORTEC DSPEC 502 data acquisition system, located in the gamma spectrometry laboratory adjacent to the reactor.

Bare vs. filtered reaction rate ratios, as defined in Eq. (3) were computed from the fitted peak areas in the measured gamma spectra, the sample masses, and the timing information, using the JSI-developed SPCACT code. The code calculates the combined uncertainties in the reaction rate ratios by propagation of the uncertainties in all the input data: the sample masses, the irradiation, cooling and measurement times and the fitted peak areas.

In general, the main sources of uncertainty in the determination of absolute reaction rates/saturated activities through gamma spectrometry measurements are the uncertainties in the peak areas $N_p$ and the detection efficiency. Other correction factors may be significant and required, e.g. due to gamma self-absorption in the sample materials, coincidence correction factors; the uncertainties in these correction factors contributing to the uncertainty in the final result. In the present work, a pure relative method was used to determine the reaction rate ratios R, in order to minimize the uncertainty in the experimental results due to the numerous sources mentioned above. This approach is the same as adopted in (relative) Neutron Activation Analysis (NAA), a nondestructive analytical technique enabling measurements of wide ranges of concentrations for multiple elements, where the measured elemental concentrations in investigated materials are determined on the basis of measurements of irradiated material samples and specially prepared co-irradiated standards. Several conditions have to be met in order for the quantities needed in the determination of absolute reaction rates, to cancel out in the determination of reaction rate ratios. Corrections due to potentially different concentrations of the target isotope in the bare and filtered samples are assumed not to be required if all samples are prepared from the same batch of material. The neutron flux is assumed to be constant for the bare and filtered irradiations; this aspect was monitored during the experimental campaign. Several correction factors originate from the gamma spectrometry measurements. The detection efficiency (needed for absolute reaction rate/activity determination, usually calibrated by means of calibration sources with certified activity levels) can cancel out in Eq. (3) if the samples are measured with the same detector, using the same measurement geometry, and the ratios are computed for measured peak areas for the same gamma energy. It is worth noting that usually there are multiple gamma ray energies emitted by activation products. In the present work, ratios were computed for all the dominant gamma ray energies of the product isotopes, giving rise to multiple entries in Table 3 (one entry per gamma ray energy). Corrections due to coincidences in the measurements also cancel out if the same conditions are met. Corrections due to gamma self-absorption in the samples can also cancel out if the samples have the same macroscopic properties (density and thickness). If the above conditions are met, any uncertainty in the correction factors which cancel out in Eq. (3) does not propagate to the final result, the experimental reaction rate ratios R.

Neutron flux monitoring

Monitor samples of Al-0.1% Au alloy were used to monitor the neutron flux during the individual irradiations. Foils approximately 5 mm in diameter were prepared, weighted and packed in polyethylene film, and attached on the inside of the rabbit tube caps. The monitor samples were at approximately 5 cm from the neutron filters within the rabbit tubes. The measurements of the monitor samples for bare irradiations showed excellent consistency, the standard deviation of the reaction rates amounting to 1.3%. The measurements of the monitor samples for filtered irradiations also showed excellent consistency, the standard deviation being 2.3%, however the absolute reaction rate values were consistently lower than for the bare irradiations, on average around 4.3%. This is attributed to the presence of the neutron filter, causing a local depression in the neutron flux.

A miniature fission chamber was also used as an online relative monitor of the neutron flux. It was inserted in measurement position (MP) no. 10, in the vicinity of the F24 position highlighted in Fig. 6. The fission chamber was manufactured by the Instrumentation, Sensors and Dosimetry Laboratory of CEA—Cadarache (serial number 2289) and had a $^{235}$U deposit with an activity of 40 Bq. It was installed in an aluminium guide tube inserted into the reactor core from the platform level. The bottom of the guide tube was located 800 mm from the top of the top reactor grid plate, the fission chamber was lifted approximately 450 mm from the bottom in the guide tube, and its position was maintained throughout the campaign. The fission chamber was operated in current mode. The average measured currents during the irradiations at the reactor power level of 50 kW remained stable throughout the campaign, their standard deviation being 0.6%, demonstrating an excellent power stability. Figure 7 displays plots of the fission chamber current and reactor power vs. time during the experimental campaign, as well as the measured specific saturation activities for the $^{197}$Au$(n,\gamma )$ reaction used as a monitor, in units of reactions per second per target atom.

Fig. 7

Plots of the reactor power vs. time, obtained from the JSI TRIGA reactor instrumentation and the monitor fission chamber current vs. time for the whole experimental campaign.