Optimized simulations of 50Ti(p,{\alpha}) and 49Ti(d,{\alpha}) reactions for hospital-cyclotron production of 47Sc

The production of 47Sc, a promising radioisotope for targeted radionuclide therapy, by means of hospital-cyclotron reactions is investigated. Two possible routes are considered: the proton-induced reaction on enriched 50Ti targets and the deuteron-induced reaction on enriched 49Ti targets. The cross-sections of the reactions are calculated using the TALYS code with optimized parameters and compared with the available experimental data. The optimal energy ranges for the production of 47Sc are determined by taking into account the thick-target yields and the purity of the product. The results show that both reactions can provide high yields and high purity of 47Sc. The feasibility of producing 47Sc with a hospital cyclotron is demonstrated by performing realistic simulations of the irradiation for both 50Ti(p,{\alpha}) and 49Ti(d,{\alpha}) reactions.


Introduction
Scandium-47 ( 47 Sc) is a radioisotope with potential applications in nuclear medicine, especially for targeted radiotherapy of cancer.It decays with a half-life of 3.349 days, emitting both β − particles and γ rays, which are suitable for therapy and imaging, respectively.Moreover, it can form stable complexes with various biomolecules, such as peptides, antibodies, and nanoparticles, that can deliver it to specific tumor sites [1].However, the production of 47 Sc is challenging, as it requires either neutron irradiation of 47 Ti targets in nuclear reactors [2] or cyclotron irradiation of protons on enriched targets (e.g., 48 Ca targets, see [3]).As of today none of the attempted production routes have proven feasibile in full.Therefore, finding a good production route for 47 Sc is important for making it more available and accessible for nuclear medicine applications.
In this paper, we first use a statistical description to visualize the trend and dispersion arising in the cross section when applying the variety of theoretical models included in massproduction nuclear reaction codes such as TALYS [4].For an outline on this statistical pathway to represent the model-trend and model-dispersion or variability, see Sect.6.1.2 of Ref. [5].Then, for an accurate evaluation of the production routes, we propose to use genetic algorithms (GAs) to optimize the parameters of nuclear reaction models that describe the production of 47 Sc from different reactions.GAs are a type of evolutionary computation that mimic the process of natural selection to find optimal solutions to complex problems [6].They can be used to optimize the parameters of nuclear reaction models [7], with the aim to describe production cross sections as accurately as possible [8].Nuclear reaction models are important for understanding various phenomena in nuclear physics, such as nuclear structure, nuclear astrophysics, nuclear fusion, nuclear fission, and can have a very important impact on nuclear medicine applications.However, finding the best parameters for these models is often challenging and time-consuming, as they depend on many factors and uncertainties.GAs can help overcome these difficulties by exploring a large and diverse search space of possible parameter values and selecting and combining the most promising ones based on their fitness or performance.In this work we optimize the parameters of nuclear reaction models for the production of 47 Sc from two different reactions: 50 Ti(p,α) 47 Sc and 49 Ti(d,α) 47 Sc.We compare the results of our optimization with experimental data.The first reaction considered for 47 Sc production involves the use of enriched 50 Ti targets and proton beams.Fig. 1 (panel A) describes the relevant cross sections calculated with TALYS and compares it to the available experimental data.The black dataset is the old measurements by Gadioli et al. [9].Newest data by Dellepiane et al. [10] and by De Dominicis et al. [11][12][13] are also reported with blue and red dots, respectively.The last two data sets are in contrast with the previous data and open new promising perspectives for this reaction.None of the TALYS models was able to reproduce the peak measured by Gadioli at around 25 MeV: the trend the TALYS models, expressed by the solid black line representing the medium between 1st and 3rd quartile of all the TALYS model calculations, indicates the peak occurring slightly before 20 MeV.Instead, the two new data sets are mutually consistent and show good agreement with the calculated cross sections with TALYS.Likely, the 1981 Gadioli measurements at low-energy (lower than 30 MeV) have an issue.The analysis has been extended to the cross section of 46 Sc production, one of the main contaminants.Fig. 1 (panel B) shows both the theoretical cross section and the experimental data.For both [10] and [11] only one energy point has been measured in correspondence of the threshold energy of the reaction.
While panels A and B of Fig. 1 provide an overall statistical picture of the trend and variation of TALYS model calculations, it is important to find a single, optimized calculation that describe accurately the data.Thus, it can be utilized to predict the irradiation parameters in nuclear medicine application.We have found that the most adequate combination of models corresponds to PE3 -LD4 with the following modification of the c and p level density parameters for the compound nucleus 47 Sc: c = 0.0 MeV −1/2 and p = 0.5 MeV.The corresponding results for 47 Sc and 46 Sc production are reported in panels C and D, respectively, with a solid line.The optimization of the level density of the compound 47 Sc nucleus improves also the cross section for 46 Sc production.Although in both cases the reproduction of the cross section at higher energies are not optimal, one should observe that at those energies only older data [9] are available and they might not be that precise to optimize the cross sections.In addition, this work is particularly focused on low energies, where the 46 Sc cross section remains negligible, preserving the purity of the 47 Sc production.The energy range of interest is limited to below 18 MeV.
Based on the optimized cross section, the evaluation of yields was conducted for an irradiation duration of 1 hour and a current of 1 µA.The comparison of 47 Sc yields obtained with the optimized cross-section modeling is presented in panel A of Fig. 2. The green area highlights the selected energy range, 8-18 MeV.The analysis of the yield has been performed also for the main contaminants, 46 Sc and 48 Sc.The red line refers to 47 Sc yield, the black curve to 46 Sc, and the blue one to 48 Sc.Clearly, the contribution from contaminants is suppressed within the highlighted window, and this affects positively the radionuclidic purity, which remains above 99% for several weeks.In panel B, its time evolution is reported.
A B An alternative nuclear reaction that employs enriched 49 Ti targets has been also investigated.
While we found that proton beams do not offer suitable energy ranges due to excessive contamination of both 46 Sc and 48 Sc, the use of deuteron beams on 49 Ti is an interesting and promising channel to examine.However, for this reaction, only one outdated experimental data set is available in the literature.This calls for new measurements to better understand the potential and efficacy of the production channel, providing an opportunity for a deeper investigation into the theoretical models used to describe this nuclear reaction.
To ensure the actual feasibility of the route it is necessary to perform a theoretical study considering the production yields of 47 Sc and contaminants, and the level of purity that can be obtained.Fig. 3 (panel A) illustrates the statistical cross section of the radionuclide 47 Sc (in blue) and its main contaminants, 46 Sc (orange) and 48 Sc (red).The variability described by the TALYS models is wide, especially for the 46 Sc cross section where the min-max range spans almost 100 mb.For these reactions the only available data are from Chen et al. [14].An evident poor agreement exists between measured and theoretical cross section for the 46 Sc case.However, focusing on the contaminant 46 Sc, the reaction starts at around 10 MeV and it is well described there by a thin band.If one trusts the 46 Sc result at least around 10 MeV it could be possible to limit the production of this contaminant.By restricting the energy range up to a maximum of 10 MeV, one will be in the condition where the peak of 47 Sc occurs, ensuring maximum production of 47 Sc minimal contamination of 46 Sc.Thus, low-energy deuterons on enriched 49 Ti targets is a promising route, with a significant 47 Sc production potentially pure from contaminants.Hence, the possibility of using hospital cyclotrons providing 10 MeV deuterons is quite interesting.
To improve the reproduction of the cross sections and achieve a good agreement with the measurements, enabling a more accurate prediction of yields and activities, it is essential to rely on the limited information gathered from the preliminary analysis.An optimization strategy by means of GA has been carried out.The TALYS combination of models PE3-LD6 has been identified as the most convenient to define the new optimized curves, since without any change in the free level-density parameters the cross sections were closest to the Chen data.Using GA, the optimized level density parameters were set to c = 1.573MeV −1/2 and p = 0.390 MeV for 46 Sc compound nucleus, and c = -0.029MeV −1/2 and p = 1.327MeV for the 47 Sc one.The resulting cross sections are shown in panel B of Fig. 3, and they closely reproduce the experimental data.
Finally, the evaluation of the radionuclidic purity (panel D in Fig. 3) indicates a value higher than 99% for almost 20 days, an outcome quite adequate for nuclear medicine applications.In addition, the isotopic purity has been computed, revealing that it reaches and maintains a high value within 10 days.This suggests that this production route is essentially carrier-free, as it shows no significant presence of contaminants, including the long-lived or stable ones.
Since the 5 -10 MeV window is below the rise in 46 Sc cross section and in correspondence of 47 Sc peak, it has been selected as an optimal energy-range for target irradiation.Panel C of that figure shows the calculated integral yields obtained from the optimized cross section considering the standard irradiation conditions of T irr = 1h and I = 1 µA, and the green band delimits the selected energy to optimize the production.The curves in that panel denote the yields of 47 Sc and of the two main contaminants.It is evident that the contamination by 46 Sc and 48 Sc can be considered negligible in the selected range.
To conclude this Section, the nuclear reaction 49 Ti(d,x) is a promising route thanks to the possibility to produce the radionuclide 47 Sc almost pure with a very minimum contamination by 46 Sc.Indeed, the theoretical results indicate a radionuclidic purity above the Pharmacopoeia's recommended threshold of 99%.In order to improve the initial agreement of the measured and calculated cross sections, further analysis should be carried out.To this purpose the need of new experimental data is clear and this would validate the models and would allow to refine their tuning parameters.

Limitations and perspectives
As mentioned earlier, this reaction has been studied experimentally by Chen and Miller in 1964 [14], who measured the cross sections for different deuteron energies.However, their data have some limitations that need to be addressed by future research.
Their target was not fully enriched in 49 Ti, but contained a significant amount of 48 Ti as well.This means that the cross sections they obtained are not pure for the 49 Ti(d,α) 47 Sc reaction, but include contributions from other reactions involving 48 Ti, such as 48 Ti(d,α) 46 Sc.These reactions may affect the accuracy and precision of the cross-section measurements.Therefore, it would be desirable to repeat the experiment with a target that has a higher enrichment of 49 Ti, or to correct the data for the presence of 48 Ti.
Another limitation is that the nuclear reaction models used to describe this reaction do not properly account for the deuteron break-up contribution, which is an important process in deuteron-induced reactions.The deuteron break-up contribution refers to the possibility that the deuteron splits into a proton and a neutron before or after interacting with the target nucleus, resulting in different contributions to final states, compared to the direct reaction.However, most of the nuclear reaction codes used to calculate the cross sections for this reaction do not include this contribution by default.Therefore, further work is needed to improve the nuclear reaction models and include the deuteron break-up contribution in a more realistic way, as suggested by Avrigeanu [15].
To sum, the production route: 49 Ti(d,α) 47 Sc to produce 47 Sc is a feasible and attractive option for obtaining this radioisotope, but it requires more experimental and theoretical investigation to overcome some of the limitations of the existing data and models.A new experiment with a highly enriched 49 Ti target and a more accurate measurement of the cross sections would be valuable, as well as a better understanding and modeling of the deuteron break-up contribution in this reaction.

Results and conclusive comments
In Table 1 the integral yield values are reported for the two production routes, comparing 47 Sc and the two contaminants.Considering that 47 Sc has an half-life of 3.349 d, the yield could be enhanced by increasing significantly the irradiation time before arriving at saturation, and/or the current.
Both production routes are suitable for production of this radionuclide with purity suitable for medical applications.The production with deuterons require a 10-MeV beam, a clear advantage compared with the required 18-MeV proton beam for the 50 Ti(p,α) reaction.However, both productions can be performed with hospital-type cyclotrons.The reaction with protons, on the other hand, performs better in yield (almost three-times) and purity.

2Figure 1 .
Figure 1.Statistical description of 47 Sc and 46 Sc cross sections, in panels A and B, respectively.The dashed lines are the min-max values of the Talys models and the gray area denotes the interquartile band, measuring the model variability.The solid black line, i.e. the centerline of the band, represents the "trend" of the cross section, averaged over the models.In panels C and D, the corresponding optimized curves are compared with the measured cross sections.

Figure 2 .
Figure 2. Panel A denotes the integral yields of 47 Sc, 46 Sc, and 48 Sc, and the shaded area highlights the production energy window.The time evolution of the radionuclidic purity is given in panel B.

Figure 3 .
Figure 3.Comparison of 47 Sc (blue), 46 Sc (orange), and 48 Sc (red) cross sections using the statistical representation (panel A), in the case of deuteron beams on 49 Ti target.The cross sections determined with GA optimization are shown in panel B. Integral yields determined from the GA-optimized cross sections are given in panel C.The time evolution of the corresponding radionuclidic purity is given in panel D.