Introduction

The KAMINI reactor is a 30 kW (th) 233U-fueled light-water moderated and cooled research reactor located at the Indira Gandhi Centre for Atomic Research (IGCAR) in Kalpakkam. KAMINI is the only operational pool-type reactor fuelled by 233U and serves as a test-bed for the three-stage nuclear energy program of India [1]. The KAMINI reactor is extensively used for neutron radiography, activation analysis, and radiation physics studies, primarily focusing on the thermal component of the neutron spectrum. Despite the extensive use of the reactor in a wide range of applications, fundamental research on fast neutron spectrum characterization at PFTS irradiation location need to be thoroughly investigated. The study of nuclear transmutations based on threshold neutron-induced reactions is crucial for providing an accurate approximation of the fast neutron component of the spectrum.

Characterizing the neutron energy spectrum is crucial not only for evaluating reactor parameters such as reactivity, burn-up, nuclear reaction rates, and temperature distribution, but also as a fundamental tool for experiments in various fields, including radio-analytical chemistry, radiation physics, radiobiology, and radiation damage studies. Several methods are used to characterize neutron spectra, such as foil activation, beam choppers, neutron Time-of-Flight (nToF), and Bonner sphere techniques. Foil activation, the most commonly employed method, stands out for its compact size and effectiveness across the spectrum, making it suitable for confined spaces like nuclear reactor cores. This method involves measuring the reaction rates of samples to neutron radiation, with the ease of measuring post-irradiation activity [2]. The Pneumatic Fast Transfer System (PFTS) of the KAMINI reactor is selected for irradiation due to its proximity to the reactor core.

In a multi-foil activation experiment, foil activation detectors that are sensitive to various energy ranges were exposed to a characteristic neutron spectrum at a specific irradiation location within the reactor. This exposure helps to determine reaction rates in the energy range of interest [3]. Various threshold foils are employed to measure the fast neutron component at the PFTS location. However, the number of foils used is significantly less than the number of energy groups, resulting in an underdetermined system of linear equations without a unique solution. Unfolding accuracy depends on the proximity of the input solution to the actual distribution and the effectiveness of the adjustment process [4]. Several spectrum adjustment/unfolding codes based on a wide range of algorithms have been developed, starting with the earliest one, SAND-II [5], followed by subsequent codes like STAY’SL [6], MAXED [7], MIEKE [8], and GAMCD [9]. These codes have proven successful in unfolding neutron spectra from measured reaction rates, relying on an input guess spectrum. SAND-II has been extensively utilized to characterize fast region spectra by employing threshold activation foils [10]. The code uses an iterative perturbation method to derive the 'best fit' neutron energy spectrum based on a set of infinitely dilute foil activities. The calculation process involves initially estimating the flux spectrum computationally and then iteratively refining it to achieve a suitable solution [11].

Recent years have seen a significant impact of radioisotope utilization on scientific domains, particularly in medicine, aiding in disease diagnosis and treatment. Carrier-free radioisotope production, crucial for ensuring high specific activity, primarily occurs in fast reactors. In our study, focusing on the PFTS irradiation site of KAMINI, we targeted energy levels beyond ~ 1 MeV, essential for producing specific radionuclides through (n, p) and (n, α) reactions. We specifically investigated four medically significant isotopes 32P, 89Sr, 64Cu, and 47Sc for their roles in alleviating bone pain and their diagnostic and therapeutic applications in various cancers [12].

The aim of the present study was to achieve an accurate model of the KAMINI reactor in MCNP, emphasizing an estimate of the neutron spectrum in a fine group in the fast energy range. The study utilized the SAND-II methodology, incorporating reaction cross-section data from the JENDL-A96 library and estimating saturated activities obtained from threshold foil activation measurements based on the MCNP-estimated flux. The unfolded spectrum was compared with similar available benchmarks. Subsequently, an estimate of radioisotope production at the PFTS was validated by comparing it to a previously published study on 32P production at the reactor location [13]. Finally, utilizing the validated MCNP simulation model, the paper sought to estimate the yields of 89Sr, 64Cu, and 47Sc at the PFTS location.

KAMINI reactor

The KAMINI reactor, detailed in reference [14], is a 30 kW thermal research reactor fuelled by 233U, with light water serving for both moderation and cooling. It utilizes beryllium oxide as a reflector and incorporates cadmium as the safety control plate. Operating with a core centre neutron flux of 8 × 1012 at 30 kW power, the reactor serves multiple purposes, including neutron activation analysis, shielding experiments, calibration/testing of neutron detectors and neutron radiography. Table 1 outlines the essential features of the core, while Fig. 1 provides a horizontal cross-sectional view of the reactor with irradiation sites. Among the designated irradiation sites within the KAMINI reactor, the PFTS location, north and south thimbles are allocated for activation analysis experiments. PFTS, located closest to the core focuses explicitly on neutron activation and is positioned approximately 14 m from the sample loading terminal with a sample transit time of less than 3 s. Samples, housed in polypropylene containers measuring 20 mm in diameter and 30 mm in length and weighing up to 1.7 g are pneumatically delivered to the irradiation site during reactor operation and promptly retrieved back post-irradiation [15]. Notably, the reactor's design facilitates sample irradiation without requiring reactor shutdown. Close to the reactor, an activation analysis laboratory equipped with a fume hood facilitates sample loading, preparation, and pre-or post-irradiation treatments. The facility also contains well-shielded high-resolution gamma spectrometry instruments for quick analysis of short-lived isotopes following irradiation.

Table 1 KAMINI reactor core
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Fig. 1
figure 1

Horizontal cross-sectional view of the KAMINI reactor with irradiation sites

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Methodology

The methodology adopted in this investigation facilitates a holistic comprehension of the neutron fast flux spectrum within the KAMINI reactor, combining theoretical modelling, experimental observations, and sophisticated data analysis techniques.

The spectrum unfolding is the solution of the homogeneous Fredholm integral equation of the first kind [3],

$$A_{i} = \int {\sigma_{i} (E)\phi (E){\text{d}}E}$$
(1)

where, \({\text{A}}_{\text{i}}\) is the induced saturated activity per atom for the ith activation foil, \({\upsigma }_{\text{i}}\left(\text{E}\right)\) is the energy dependent response function, and \(\upphi \left(\text{E}\right)\) is the differential flux (flux per unit energy). Solution flux \(\upphi \left(\text{E}\right)\) is deconvoluted from the set of measured induced activities by solving the energy discretized activation equation derived from Eq. (1) as given below in Eq. (2).

$$A_{i} = \sum\limits_{k} {\sigma_{i,k} } \phi_{k}$$
(2)

where the index ‘k’ runs over all energy bins, \({\upsigma }_{\text{i},\text{k}}\) is the average response function in the kth energy bin and \({\upphi }_{\text{k}}\) and the neutron flux in the energy bin. To ensure physical validity, constraints are applied, requiring all matrix elements to be non-negative. Typically, the resolution of the unfolded \({\upphi }_{\text{k}}\) vector in terms of energy groups exceeds the number of practical foil measurements, resulting in an underdetermined matrix problem with infinitely many solutions to Eq. (2). The objective of unfolding is to identify a single solution that closely approximates the true neutron energy spectrum [4].

This methodological framework integrates computational simulations with experimental measurements. Firstly, the neutron spectrum of the KAMINI reactor is generated using the MCNP-4B transport code. Concurrently, experimental measurements entail the acquisition of neutron flux spectra utilizing the foil activation technique. These empirical data serve as inputs for spectrum unfolding, facilitated by the SAND-II unfolding code. Notably, the MCNP-generated neutron spectrum serves as the ‘guess’ input for the spectrum unfolding process, ensuring seamless integration of computational predictions with experimental observations. The methodology is outlined in a flowchart (Fig. 2).

Fig. 2
figure 2

Flowchart to obtain energy neutron spectrum at PFTS location

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The total activity at the end of counting for the various foils can be calculated as follows,

$$A = N.[\int\limits_{{E_{th} }}^{\infty } {\sigma_{act} (E)\phi (E)dE} ].S.D.C$$
(3)

where, Activity \(A = \frac{cps}{{I_{\gamma } .\varepsilon }}\), cps—counts per second, Iγ -gamma intensity, \(\upvarepsilon\)—detector efficiency,\(\int\limits_{{E_{th} }}^{\infty } {\sigma_{act} (E)\phi (E)dE}\)—reaction rate for a nuclear reaction, N—number of target atoms, σact (E)- activation cross-section, ϕ(E)—neutron flux, \(S = [1 - {\text{e}}^{{ - \lambda t_{i} }} ]\), \(D = {\text{e}}^{{ - \lambda t_{d} }}\), \(C = \frac{{[1 - {\text{e}}^{{ - \lambda t_{c} }} ]}}{{\lambda t_{c} }}\), λ—decay constant, ti—irradiation time, td—decay time, tc—counting time.

The induced activity in the foil builds up over time and approaches saturation. Saturation activity Asat can be given by,

$$A_{sat} = N\sigma_{act} \phi$$
(4)

The activity reaches near saturation (~ 95%) when the foil is irradiated for 4–5 times the half-life of the sample [16].

Estimation of neutron spectrum by Monte-Carlo method

A realistic 3D Monte Carlo model for KAMINI was developed using the MCNP-4B [17] code to derive the initial spectrum for SAND-II calculations. The modelling intricacies are outlined in references [1, 18, 19]. Figure 3 illustrates the MCNP model representation of the KAMINI reactor. A constant initial source was employed using the SRCTR card in the KCODE calculations [20]. The simulation consists of 50 inactive cycles followed by 900 active cycles. Each cycle involves the simulation of 1,000,000 particles to minimise errors in flux estimation. For neutron flux and spectra calculation, F4 tally was used. F4 is a track length estimator that calculates the average flux over a cell volume. The Monte Carlo calculation employed ace-formatted ENDF/B-VIII.0 isotopic cross-section data processed through NJOY21 [21]. Various updated modules, including RECONR, BRODR, PURR, HEATR, GASPR, and ACER from NJOY21, were used to generate data, which were then validated against different IRPHEP and criticality ICSBEP [22, 23] benchmarks. To take care of the effect of the binding energies of the scattering nucleus at lower energies, thermal scattering law (TSL) data, denoted as S(α,β,T), was applied to H2O, Be, and graphite. The effective multiplication factor (keff) was determined to be 1.00348 ± 0.00009. Energy spectra were estimated in 104 energy groups in the fast region, ranging from 0.7 to 18 MeV.

Fig. 3
figure 3

KAMINI modelled in MCNP

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Multi-foil activation experiment using threshold foils

The neutron spectrum at the PFTS location within the KAMINI reactor was analysed using a multi-foil activation method. The PFTS location is primarily used for neutron activation analysis across the entire range of the spectrum i.e. thermal, epithermal and fast, this study explicitly targets the fast flux component. For the purpose, different foils were selected based on their sensitivity in the fast energy region.

Various threshold activation foils, such as titanium, indium, iron, cobalt and aluminium, with a purity exceeding 99.9%, were sourced from Good Fellow, UK. Additionally, Y2O3 powder with a purity of 99.999% was obtained from Alfa Aesar, UK. The mass of the foils and dimensions were precisely measured before being enclosed in polypropylene containers for the neutron irradiation. These foils underwent irradiation at the PFTS position with a power level of 20 kW. The duration of irradiation was decided based on the half-life of the resultant activated products and their corresponding activation cross-sections for the relevant nuclear reactions.

Following irradiation, the activated foils underwent sufficient cooling to reduce radiation exposure. Radioactive assessment employed at a distance of 20 cm using a 30% p-type co-axial High Purity Germanium (HPGe) detector. The detector offers energy resolution of 1.85 keV at FWHM for the prominent 1332 keV gamma energy line of 60Co, complemented by an associated 8 k multichannel analyser (MCA) system equipped with Aptec spectra software. Shorter half-life nuclides were analyzed at the Neutron Activation Analysis Laboratory within KAMINI, while longer half-life ones were assessed at the Radiochemistry Laboratory. Peak area analyses of these acquired gamma spectra were performed using the peak fitting program PHAST developed in Bhabha Atomic Research Centre (BARC), Mumbai, India [24]. The uncertainty associated with the peak areas corresponding to different gamma energies were found to be less than 2%. A typical gamma spectrum obtained for the neutron irradiated titanium foil, from the 30% p-type co-axial HPGe detector is shown in the Fig. 4.

Fig. 4
figure 4

Gamma spectrum of the neutron irradiated Ti foil using HPGe detector

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The reaction rate after irradiation in an activation foil can be estimated using an Eq. (5) established by ref [25].

$${\text{Measured reaction rate}},RR_{meas} = \frac{A}{N.S.D.C}$$
(5)

The detector efficiency calibration as shown in Fig. 5 was carried out using a multi-gamma emitter 152Eu reference standard source supplied by Amersham, Inc and fitted with the following Eq. (6).

$$\ln (\epsilon) = \mathop \sum \limits_{{{\text{i}} = 0}}^{3} {\text{A}}_{{\text{i}}} \left( {{\text{ln}}\left( {\text{E}} \right)} \right)^{{\text{i}}}$$
(6)
Fig. 5
figure 5

Efficiency Calibration curve for the 30% p type co-axial HPGe detector

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Tables 2 and 3 present comprehensive information on the foils, their related nuclear reactions, and various nuclear and irradiation parameters. Eight nuclear reactions were thoroughly analyzed, and the subsequent spectrum unfolding process was executed utilizing the gathered dataset.

Table 2 Data related to the activation of Foils
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Table 3 Comparison between experimentally determined and computationally predicted reaction rates
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Preparation of cross-section library

The determination of neutron spectra using activation analysis heavily relies on the accuracy of the activation cross-sections used in the spectrum unfolding. The required activation cross-sections for the present application are prepared from the evaluated activation library JENDL-A96 [26]. The data is represented in a tabular, linearly interpolable energy vs. cross-sections form as per ENDF-6 format conventions. Cross-sections are Doppler broadened and grouped into 620 bins SAND II structure using BROADR and GROUPR modules of NJOY-21 code. The multi-grouped activation cross-sections are retrieved and reformatted for spectrum unfolding using the SAND-II code. The energy-dependent multi group cross-sections are represented in Fig. 6.

Fig. 6
figure 6

Response function vs Energy for the various nuclear reactions of the activation foils

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SAND-II unfolding

Determining neutron flux spectrum from multiple foil activation measurements presents a mathematically ill-posed problem. The fundamental equations, which involve activation integrals, relate measured activities to neutron flux across a specified energy range. However, practical difficulties arise in solving the set of integral equations. These compel a discrete representation of response functions and flux averaged over several energy intervals. As a result, this leads to an underdetermined system of equations, where the number of unknowns (fluxes in each interval) significantly outnumbers the available equations (measured foil activities). Consequently, the solution neutron spectrum exhibits inherent non-uniqueness. Thus, it involves an estimate of guess spectra through the simulation of specific experimental contexts to arrive at a physically acceptable solution (Fig. 7).

Fig. 7
figure 7

Fast flux unfolding of PFTS irradiation channel using SAND-II and its comparison with fast benchmarks

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SAND II is a dedicated computational tool for estimating neutron spectrum from such an indeterminate system of equations. It employs an iterative approach to converge to a solution spectrum based on a set of foil activation measurements. Beginning with an initial guess spectrum, the code perturbs the spectrum through successive adjustments, aiming to reconcile calculated activities with measured ones within acceptable tolerances. SAND II uses a 620 fine group activation cross sections library encompassing a wide energy range (10–10–18 MeV) with varying resolution across decades. Further, it can account for flux attenuation by common foil cover materials such as cadmium, boron-10, and gold, refining the analysis. The SAND II algorithm for deriving flux spectra was further enhanced to improve consistency by limiting artificial structure. The method, detailed in reference [5], employs smoothing to remove spurious discontinuities, followed by modulation to reintroduce reactor physics features.

Monte-Carlo approach to radioisotope production yield

When a target undergoes irradiation within a reactor, it initiates a nuclear reaction, resulting in the production of isotopes. The rate of activation per second is given by,

$$\frac{dN}{{dt}} = N_{0} \sigma_{act} \phi$$
(7.0)

where, \(N_{0}\)-total no. of atoms present in target, \(\sigma_{act}\) is the activation cross-section and ϕ is the flux at that location.

Given that the radioisotope product decays with a distinct physical half-life, the overall rate of radioactive product atoms can be expressed as,

$$\frac{dN}{{dt}} = N_{0} \sigma_{act} \phi - \lambda N$$
(7.1)

where, λ → Decay constant (sec−1) of the isotope produced.

From (7.1),

$${\text{activity}} = \lambda N = N_{0} \sigma_{act} \phi (1 - e^{ - \lambda t} )$$
(7.2)

If A represents the mass number of the target element undergoing irradiation, then the equation above can be expressed in Curies as the specific activity,

$$S_{P} = \frac{{6.023 \times 10^{23} \times \sigma_{act} \varphi (1 - e^{{ - \frac{0.693t}{{T_{1/2} }}}} )}}{{A \times 3.7 \times 10^{10} }}Ci/g$$
(8)

where A is the mass number of the target, t1/2 is the half-life of the product (s), and t is the irradiation time (s) [27].

The MCNP code allows users to predict expected physical measurements by defining tally cards. The F4-tally is employed to determine the rate of neutron capture interactions/volume for a target exposed to neutron radiation, as outlined in [28],

F4: n a.

FM4 (C m R).

Here, n is particle type, which is neutron in our case, a is cell number respectively, C is the normalization constant, m is the material number for a pure dummy, and R is the reaction number, available at [29].

Equation (8) can be modified as,

$$S_{P} = \frac{{FM4result \times (1 - e^{{ - \frac{0.693t}{{T_{1/2} }}}} )}}{{\rho \times 3.7 \times 10^{10} }}Ci/g$$
(9)

Here, ρ represents the density of the target in g/cc. Following the calculation of FM4, additional factors can be multiplied using an EXCEL sheet.

Results and discussion

Spectrum unfolding

The primary objective of this study was to ascertain the high-energy neutron spectrum. Threshold activation foils were employed for this purpose, and the estimated spectrum was derived through a Monte Carlo calculation. The resulting unfolded spectrum lies in close proximity to the estimated spectra. The spectrum closely reproduced the activation measurements within an error margin of 15%, as given in Table 3. Spectral smoothing is employed to remove unwanted fluctuations. The precision of the spectra, however, is dependent upon the accuracy of measured activities, response functions, geometric model, composition, and cross-sections employed in the simulation. Figure 7 presents the unfolded fast neutron spectrum of the PFTS irradiation channel at KAMINI, closely aligning with the fast benchmark GODIVA and JEZEBEL-23 spectra.

Validation of the theoretical model generated

The MCNP model developed here has been validated using the data from reference [13]. 32P was produced via (n,p) reaction in the KAMINI reactor by irradiating Strontium sulphate (SrSO4) powder as the target material, followed by the separation and purification of 32P produced in the target. The details of the experiment and the outcomes are presented in Table 4.

Table 4 Irradiation details
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1 g SrSO4 as a target sample placed at the PFTS location were simulated, similar to those under the experimental conditions. The (n,p) reaction rate per unit volume was determined in the sample by F4-tally in conjunction with Fm4 cards, as previously outlined. The simulation employs the ENDF-VIII.0 data library, running through 50 inactive cycles preceding 500 active cycles. Each cycle simulates 1,000,000 particles to minimise errors in estimating flux and reaction rates. MatMCNP [30] is used to compute the number density of the compounds.

Table 5 illustrates that the MCNP-predicted value exceeds the observed value in the experiment by 5.72%. The disparity arises from various factors, including the target material's self-shielding effect, fluctuations in reactor power, flux attenuation caused by neighbouring samples within the reactor, the precision of theoretical models, and nuclear data. Hence, the theoretical model is suitable for predicting the production of various other radioisotopes at the PFTS location within an error range of approximately ± 6%.

Table 5 Comparison between Experiment and Theoretical model (MCNP) for producing 32P in KAMINI through (n,p) reaction
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Theoretical prediction for 89Sr, 64Cu, and 47Sc production at PFTS

Table 6 outlines the theoretical predictions for producing 89Sr, 64Cu, and 47Sc radioisotopes at the PFTS. 89Sr is produced through the 89Y(n,p)89Sr reaction utilizing Y2O3 powder as the target, resulting in a predicted yield of 10.7 nCi/g after 6 h of irradiation. The other threshold competing nuclear reaction like (n,2n) (n,α) gives the 88Y and 86Rb radioisotopes. Due to the high threshold energy and lower cross-section, the production yield of these radioisotopes will be much smaller than 89Sr. The production yield for the 88Y and 86Rb were also calculated and found to be 2.56 nCi/g and 0.86 nCi/g. 64Cu, generated via 64Zn(n,p)64Cu using metallic 64Zn as the target, shows a yield of 0.16 mCi/g under the same conditions. 47Sc is produced through 47Ti(n,p)47Sc using enriched 47TiO2 powder as the target, providing a yield of 18.81 µCi/g. However, the decay characteristics of each isotope, the composition of the target materials, irradiation time, and incident neutron flux greatly influence their respective yields. These theoretical predictions serve as valuable insights for potential isotope production in KAMINI. Figure 8 illustrates the activation cross-sections for 89Sr, 64Cu, and 47Sc, along with the unfolded spectrum at the KAMINI PFTS location.

Table 6 Theoretical predictions of 89Sr, 64Cu, and 47Sc production at the PFTS
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Fig. 8
figure 8

Activation cross-section of 89Sr, 64Cu, and 47Sc and unfolded spectrum of KAMINI PFTS location

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Conclusions

The neutron spectrum in the energy range of 0.7 to 18 MeV at the PFTS irradiation site in the KAMINI reactor was determined using multifoil activation measurements. This spectrum is vital for demonstrating capabilities in threshold (n,p), (n,α), (n,2n) reactions. Neutron energy spectrum determination relied on a numerically estimated guess spectrum using MCNP, followed by unfolding with the SAND-II code using foil activation measurements at the PFTS. The study assessed the viability of producing carrier-free radioisotopes utilizing threshold reactions. The spectrum is validated against the experimentally determined yield of 32P by transmutation of 32S. Comparison with experimental measurements showed an agreement within ± 6%, validating the theoretical model. Theoretical yields of 89Sr, 64Cu, and 47Sc were projected at the same location. Despite limitations on irradiation time in the KAMINI reactor, our findings suggest potential yields of 10.7 nCi/g, 0.16 mCi/g, and 18.81 µCi/g for 89Sr, 64Cu, and 47Sc, respectively, for irradiation of 6 h at an operating power of 20 kW. These results highlight the efficacy of our methodologies and insights into radioisotope production. However, a single study cannot fully establish experimental uncertainties and validate theoretical models. Therefore, forthcoming investigations are necessary to comprehend how the radioisotope yield varies under diverse conditions, such as neutron spectrum, irradiation duration, and target material for the irradiation.