1 Introduction

The Sc radioisotopes have good decay characteristics for using in various nuclear medicine applications [1,2,3,4,5,6] or for tracking oil and gas in pipelines because they can be easily identified and followed by detectors placed outside the systems [7]. According to previous publications, proton, deuteron and α-particle-induced nuclear reactions could be used for production of Sc radioisotopes with considerable yields [8,9,10]. 48V has long been used as radiotracer [11, 12], tumor imaging agent [13, 14] and laboratory positron source [6, 15]. Moreover, it recently attracts much attention regarding its production [17, 18] and utilization [19, 20].

The 46Sc and 48V radioisotopes are two isotopes that can be produced from the deuteron and alpha particle-induced reactions on Sc targets, respectively. As can be noticed in the previous reported data, there are very limited sets of experimental data that describe the excitation function within the low and high energy ranges [21,22,23,24,25,26,27]. It was found that the maximum cross section values for the two reactions 45Sc(d,p)46Sc and 45Sc(α,n)48V lie in the energy range 0–30 MeV. Therefore, the low energy MGC-20 cyclotron is suitable to study those reactions up to 10 MeV for deuteron and 20 MeV for α-particle incident energies. In this work, we performed experimental and theoretical evaluation of the cross section values for the deuteron and α-particle-induced reactions on 45Sc target and compared the results with the previously reported experimental data.

2 Experimental details

The excitation function of the radionuclides formed by irradiation of Sc targets with 10 MeV deuteron and 20 MeV α-particle incident energies were measured through stacked-foil irradiation technique [28, 29]. The samples were in the form of high-purity Sc foils (purity 99.9% and thickness 20 μm) purchased from Goodfellow. Deuteron and α-particle foil irradiations were done on the external beam line of the MGC-20 cyclotron in Debrecen, Hungary. The extracted beam energy is well identified using the calibrated acceleration parameters. Stacks of six Sc foils (8 × 8 mm), along with Cu monitor foils, were prepared in different arrangements to cover most of the studied energy range. The stacks were irradiated with a well-collimated beam in a dedicated target holder, which serves also as a Faraday cup to collect the charge of the incident particles. The mean energy was calculated with the help of the SRIM code [30]. The natTi(d,x)48V and natCu(α,x)66 Ga nuclear reactions were used as a current monitors, where three Ti or Cu foils were distributed between the irradiated samples. The IAEA recommended cross section values [31] were used to determine the real incident beam current on the samples. The targets were irradiated for 1 h at a beam current of about 100 nA. After a suitable cooling time from the end of irradiation, the targets and the monitor foils activity were measured with a high-resolution γ-rays spectrometer based on a HPGe detector of relative efficiency 50% and energy resolution (FWHM) 1.85 keV at γ-ray line 1332.5 keV of 60Co. The spectra were measured repeatedly in a cylindrical lead shield at a suitable distance from the detector to minimize pile-up and coincidence losses. Analysis of the spectra was carried out using Aptec program (version 6.31, by Aptec Instruments Ltd.). Table 1 presents the nuclear decay parameters of the measured radionuclides and the nuclear reactions under investigation using refs. [32, 33].

Table 1 Decay and spectrometric characteristics of the produced radioisotopes [32, 33]
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3 Model code calculations

The computer code EMPIRE-3.2 (Malta) [34] was used to evaluate the cross section of the investigated nuclear reactions. Additionally, the calculated cross section values on TALYS-based evaluated nuclear data library (TENDL) [35] were extracted for comparison. In this work we used the 11th version, TENDL-2021 [36], which is based on both default and adjusted TALYS code calculations and data from other sources. TALYS is based on the simulation of nuclear reactions by applying two-component exciton model [37].

4 Results and discussions

The values of the deuteron and α-particle beam current were determined through radioactivity measurements of 48V and 66 Ga radionuclides produced from irradiation of natTi and natCu monitors, respectively. For confirmation of the determined values, monitor reaction cross sections were calculated and compared with that of the IAEA for the reactions natTi(d,x)48V and natCu(α,x)66 Ga [31] as shown in Fig. 1. The estimated beam current on the samples was varied from 83 to 99 nA.

Fig. 1
figure 1

Cross section values for the monitor reactions in comparison with that recommended by IAEA [31]: (a) natTi (d,x)48V and (b) natCu(α,x)66 Ga

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The cross section values for the investigated reactions 45Sc(d,p)46Sc and 45Sc(α,n)48V were determined through the measurements of the characteristic gamma ray lines for the produced radioisotopes given in Table 1. Table 2 presents the calculated cross section values in the energy range from the reactions threshold up to 10 MeV for deuteron and 20 MeV for α-particle.

Table 2 The measured cross section values for the investigated nuclear reactions
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4.1 45Sc(d,p)46Sc

Figure 2 shows the measured cross section values as a function of incident deuteron energy for the 45Sc(d,p)46Sc nuclear reaction. There are only three sets of previously reported data for Skobelev et al. [21], Hermanne et al. [22] and Tsoodol et al. [23], which are presented in the same graph along with the calculated values using computer codes. The graph shows a good agreement between our data and that of Skobelev et al. [21] within the rising part of the excitation curve up to about 6 MeV. The number of cross section values for Hermanne et al. [22] is very limited in the low energy range and only two points around the 5 MeV peak are in agreement with our data. In general, all the experimental data showed a peak around deuteron energy of 5 MeV with maximum cross section value of about 400 mb with a continues decrease up to 30 MeV. The results of models calculation showed the same profile of the excitation curve but with lower cross section values by about 25% and 57% for EMPIRE and TANDEL-2021, respectively. A recognizable peak shift is found towards higher energy range for EMPIRE data.

Fig. 2
figure 2

The measured and calculated cross section values of the nuclear reaction 45Sc(d,p)46Sc in comparison with the previously reported data

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There are some difficulties in describing the common type of deuteron-induced reactions including (d,p) process due to incompatibility between the center of mass and the center of nuclear charge. The very low binding energy of the deuteron (2.226 MeV) may causes deformation of the incident particle, especially at low incident energy. This reveals that the interaction of the deuteron with the Coulomb field of the target nuclei leads to breakup of its p-n binding which is about four times smaller than the average nucleons binding energy in stable nuclei [38]. Furthermore, the lack of the experimental data on cross sections of such reactions as (d, p) and (d, t) on some light nuclei (Z = 21–23) led to inaccurate phenomenological input parameters of the nuclear models and hence a large disagreement with the experimental data.

4.2 45Sc(α,n)48V

Figure 3 shows the measured cross section values for the 45Sc(α,n)48V nuclear reaction as compared with the previously reported experimental results. The presented data revealed that the excitation function exhibits a peak around 12 MeV with maximum cross section value of 450 mb. There is a good agreement between our data and that presented by refs. [24,25,26,27] with exception of some points that seemed to be very far from the major trend of the data which were assigned by circles in Fig. 3. The presented theoretical data of TENDEL-2021 [36] are very close to the experimental results up to the peak position at about 12 MeV with narrower peak profile and slight lower values at higher energies. The EMPIRE [34] calculations showed a significant high values with respect to the major of the experimental results by about 200 mb at the peak position and ~ 50 mb for the other parts of the curve. The solid line presents an average curve describing the best fitting of the data obtained by using TableCurve-2D program [39] which can help to calculate the production yield.

Fig. 3
figure 3

Excitation function of the 45Sc(α,n)48V nuclear reaction in comparison with the previously reported data

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4.3 Integral yield for the 46Sc and 48V radioisotopes

Integral yields for the production of 46Sc and 48V radioisotopes formed through the deuteron and alpha particle reactions with natSc (100% 45Sc) were calculated from the evaluated excitation functions of the measured reactions and presented in Fig. 4. The calculated integral yields serve as a standard reference for the maximum achieved activity in (MBq/uAh) from an experiment.

Fig. 4
figure 4

Integral yields of the produced radionuclides

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Regarding the expected impurities for the produced radioisotope 48V, we can safely say that no impurities are expected to be found, since only 47 V (T1/2 = 32.6 min) can be formed in the present energy range which is very short as compared with 48V (T1/2 = 15.974 d). Considering the production of 46Sc, only 44Sc (T1/2 = 3.97 h) can be formed in this energy range which is also much shorter than that of 46Sc (T1/2 = 83.79 d). On the other hand, it is clear from the curves presented in Fig. 4 that an amount of 0.93 MBq/uAh of 48V can be obtained in the energy range 19.4 → 2.44 MeV. Regarding the 46Sc, an amount of 1.09 MBq/uAh can be produced in the energy range 8.5 → 0 MeV.

From the above results it is possible to estimate the thick target yield for the investigated radioisotopes in a real production run. Assuming a high-purity 45Sc target (100% natural abundance) needed for stopping a beam of deuteron and α-particle energies from 8.5 and 19.4 MeV down to the threshold energies for the two reactions used for producing 46Sc and 48V, respectively, one can calculate their yields at normal production conditions. For a beam current of 5 uA and irradiation time of 2 h, the estimated yields amount to be 10.9 MBq for 46Sc and 9.3 MBq for 48V, these values are corresponding to thick target activity before separation. Validation of these results needs further experimental measurements. There are no previously reported data to be compared with the estimated values.

5 Conclusions

The present study covers experimental and theoretical determination of the cross section data for the deuteron and α-particle-induced reactions on natSc targets as production routes of 46Sc and 48V radioisotopes. The validation of experimental results using EMPIRE-3.2 and TENDEL-2021 showed some deviation especially in the (d, p) reaction due to the instability nature of deuteron. Although the amounts of radioactivity obtained for both radioisotopes are of medium activities in the used energy ranges, they can be produced in a high-purity form. The obtained results fill some missing gapes of nuclear data in the low energy range due to the lack of experimental measurements. These results are a required addition to the IAEA and the Nuclear Cross Section Data Bank.