Next Article in Journal
Open Source Completely 3-D Printable Centrifuge
Previous Article in Journal
First Operation of a Resistive Shell Liquid Argon Time Projection Chamber: A New Approach to Electric-Field Shaping
Previous Article in Special Issue
Vortex Target: A New Design for a Powder-in-Gas Target for Large-Scale Radionuclide Production
Article Menu

Export Article

Instruments 2019, 3(2), 29; https://doi.org/10.3390/instruments3020029

Communication
Can We Extract Production Cross-Sections from Thick Target Yield Measurements? A Case Study Using Scandium Radioisotopes
1
Heavy Ion Laboratory, University of Warsaw, 02-093 Warszawa, Poland
2
Faculty of Physics, University of Warsaw, 02-093 Warszawa, Poland
3
Groupement d’Intérêt Public ARRONAX, 44817 Saint-Herblain Cedex, France
4
Institute of Physics, Department of Nuclear Physics and Its Applications, University of Silesia, 41-500 Chorzów, Poland
*
Author to whom correspondence should be addressed.
Received: 27 March 2019 / Accepted: 11 May 2019 / Published: 14 May 2019

Abstract

:
In this work, we present an attempt to estimate the reaction excitation function based on the measurements of thick target yield. We fit a function to experimental data points and then use three fitting parameters to calculate the cross-section. We applied our approach to 43Ca(p,n)43Sc, 44Ca(p,n)44gSc, 44Ca(p,n)44mSc, 48Ca(p,2n)47Sc and 48Ca(p,n)48Sc reactions. A general agreement was observed between the reconstructions and the available cross-section data. The algorithm described here can be used to roughly estimate cross-section values, but it requires improvements.
Keywords:
medical Sc radioisotopes; radioisotope production; thick target yield measurements; cross-section reconstruction; numerical analysis

1. Introduction

The interest in three scandium radioisotopes, 43Sc, 44g/mSc and 47Sc, in nuclear medicine has already been acknowledged and discussed in [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] (the selected properties of these radioisotopes are summarized in Table 1). Both positron emitters 43Sc and 44gSc are promising PET radioisotopes that can compete with the commonly used 68Ga [1,2,3,4,5], while 44gSc offers unique possibilities in the three-photon PET technique [6,7,8]. Additionally, 44mSc can be used as a 44mSc/44gSc long-lived in-vivo generator as it decays mainly by a low energy transition to the ground state [9,10,11,12]. Meanwhile, 47Sc is a β-emitter suitable for both therapeutic purposes and SPECT imaging [13], which is emphasized also within the IAEA Coordinated Research Project [14,15]. As mentioned in [16,17], this radioisotope is a matched pair for diagnostic 43Sc and 44gSc radioisotopes.
In our recent papers [19,20], we have reported on the production routes of medical scandium radioisotopes as well as extending this data with scandium formed in natural and enriched thick CaCO3 targets (from around 50 up to 1000 mg/cm2) irradiated with α particles up to 30 MeV, deuterons up to 8 MeV and protons up to 30 MeV. The thick targets were used because we found that it was not feasible to prepare thinner (in the order of 1 mg/cm2) self-supporting CaCO3 as a homogeneously thick target for our experimental set-up. The significant stopping-power of our targets allowed us to obtain experimental thick target yield (TTY) values for scandium production.
In this work, we want to complement our research by evaluating the 43Ca(p,n)43Sc, 44Ca(p,n)44gSc, 44Ca(p,n)44mSc, 48Ca(p,2n)47Sc and 48Ca(p,n)48Sc cross-sections based on reported TTY measurements (the latter is not medically relevant, but 48Sc production is important as it is a radioactive impurity). A similar attempt has already been proposed in [21] for the study of 34mCl production. In this work, we verify this approach for above-mentioned reactions while employing a different, straight-forward numerical algorithm (our Python code is submitted in the Supplementary Materials to this paper).

2. Materials and Methods

In our recent work [20], we reported TTY for 43Ca(p,n)43Sc on 43CaCO3 (90% 43Ca) targets, 44Ca(p,n)44gSc and 44Ca(p,n)44mSc on 44CaCO3 (94.8% 44Ca) as well as 48Ca(p,2n)47Sc and 48Ca(p,n)48Sc on 48CaCO3 (97.1% 48Ca). Those TTY values are directly related to cross-sections by the following formula [22,23]:
T T Y ( E ) = H   N A Z   e   m   τ   E m i n E m a x σ ( E ) d E / d x ( E ) d E
where H is target enrichment, NA is Avogadro’s number, τ is the mean lifetime of a radioisotope, Z is the ionization number of the projectile, e is the elementary charge, m is the atomic mass of the target, Emax and Emin are the maximal and minimal energy of the projectile penetrating the target (in case of TTY, Emin <= reaction threshold), respectively, σ is the cross-section for the nuclear reaction, and dE/dx is the stopping-power of the projectile according to the aerial density of the target. Here, we describe the attempt to obtain the energy dependence of the cross-section (the excitation function) based on the experimental TTYexp(E) [MBq/µAh] values for different projectile energies E. These data are supplemented by an assumption TTYexp(Ethr) = 0, where Ethr denotes the energy threshold for this reaction.
The crucial factor is the choice of the function used to describe the TTY energy dependence. The number of parameters of the function used to fit the data should be restricted, as the number of the experimental data points is usually limited. Therefore, we propose a simple shape,
T T Y f i t ( E ) = d + a c 2 ( π   ( b E t h r )   e r f { E b a } a   e x p { ( E b ) 2 a 2 } )
which fulfils several important criteria. This function is monotonically increasing, as TTY(E) should be. Most importantly, its derivative is a modified q-Weibull distribution [24],
d T T Y f i t d E [ M B q μ A h ] = MAX [ 0 ;   c   ( E E t h r )   e x p { ( E b ) 2 a 2 } ]
which reflects the global shape of the (p,n) and (p,2n) excitation functions, commonly used in the field of the production of medical radioisotopes. The request TTYexp(Ethr) = 0 provides the condition
d = a 2 c 2   e x p { ( b E t h r ) 2 a 2 }
and limits the number of TTYfit parameters to 3: a, b and c. Once those parameters are obtained, the cross-section values can be estimated as
σ ( E ) [ m b ] = τ [ h ] Z e [ C ] m [ u ] N A H · d T T Y f i t d E [ M B q μ A h ] · d E d x [ M e V m g / c m 2 ] · 10 42
In our case, TTY measurements were obtained on CaCO3 targets instead of metallic Ca. Therefore, we used dE/dx(E) values corresponding to the energy loss in calcium carbonate (provided by SRIM software [25]), m = 100 u to address the mass of CaCO3, and H as the level of enrichment of employed material. We have also calculated the 95% confidence band for TTYfit(E) fit and reconstructed the cross-section. Details of our calculations are shown and explained in the Python code attached to this paper.
Alternatively, in [21], the cross-section was reconstructed after fitting the TTY curve by calculating target yields (TY) for thicknesses corresponding to 0.1 MeV projectile energy loss each 1 MeV and multiplied by projectile range. This method assumes the constant stopping-power in each layer. In our approach, this simplification was not necessary.

3. Results and Discussion

In Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5, we show the TTY data and the reconstructed cross-sections for 43Ca(p,n)43Sc, 44Ca(p,n)44gSc, 44Ca(p,n)44mSc, 48Ca(p,2n)47Sc and 48Ca(p,n)48Sc reactions (the fit parameters are shown in Table 2 while the reconstructed cross-section values are listed in Table 3). We compare them with the experimental cross-section in [26,27,28,29,30,31,32,33,34,35], with the recommended values from [36], with the predictions of the EMPIRE [37] evaporation code (version 3.2.2 Malta) and with the TENDL-2017 cross-section library [38]. All reconstructions exhibit a similar shape to the model predictions and measured cross-section values, indicating the validity of modified q-Weibull distribution in estimating the global shape of the (p,n) and (p,2n) excitation functions.
We have also checked our reconstruction method by implementing the approach in [20]. We obtained similar values (marked on the plots) with a visible correction near the threshold in the 44mSc case (Figure 3) but also with the discontinuity fragments due to the numerical approach. Since the mentioned paper does not provide the recommended TTYfit function, we adopted ours.
In the case of 43Sc data (Figure 1), the recent experimental results [34] are significantly lower than other measurements (by a factor of 2 around 10 MeV proton energy). The experimental results for TTY are quite linear in the measured proton energy range and do not reach the expected saturation, so the resulting excitation function is relatively flat and does not reproduce any of the previous measurements. This reaction might require further validation, as with the extension of TTY measurements up to 30 MeV proton energy.
A general agreement is observed for 44gSc (Figure 2), both with the theoretical models and experimental results, although again the data by [34] are lower than the measurements. More discrepancies are observed in the case of 44mSc (Figure 3). The excitation function obtained from TTY measurements does not show the peak seen in the experiments and in model calculations and overestimates the values near the reaction threshold. We suspect that the problem with this reconstruction might be related to the offset of TTY data, as only in case of 44mSc are the TTY values below model predictions at low energies and above them at higher energies, which causes the reconstructed excitation function to be flatter.
For 47Sc (Figure 4), the shape of the reconstruction reflects the shape predicted by both model calculations. While our results provide about 10% lower values compared to the models, recent measurements [35] indicate similar values at low energies but about 20% higher values at maximum.
Finally, we decided to adopt the arbitrary value of Ethr = 3.0 MeV as a parameter for 48Sc fit (Figure 5) to satisfy the visible and significant TTY build-up at this energy rather than the actual threshold (0.51 MeV). This might be explained by the fact that the shape of the function used for the fit does not adequately describe the behavior of the cross-section at energies much below the Coulomb barrier. Since the cross-section values far below the Coulomb barrier are very small, they do not contribute significantly to the TTY values. The extracted cross-section values are in line with the data in [30] at lower energies and in [35] at higher energies.

4. Conclusions and Summary

We have presented an attempted numerical method for cross-section evaluation based on the thick target yield (TTY) measurements obtained from the irradiation of thick targets (in which the energy of a projectile is reduced to the reaction threshold). This method is based on fitting a function with three free parameters to TTY data points and using its analytical derivative to obtain the cross-section. The fitting requires the knowledge of the reaction threshold and a sufficient number of experimental points to represent the shape of the TTY curve, including the saturation region.
Using this approach, we were able to obtain a useful estimation of cross-sections for the production of medically important 43Sc, 44gSc, 44mSc, 47Sc, and 48Sc radioisotopes via (p,n) and (p,2n) reactions on Ca. The results were compared to the already measured cross-sections and to the model predictions. General agreement is observed; however, not all experimental results confirm our reconstructions, particularly those near the reaction threshold. In conclusion, our algorithm can provide good insights for the (p,xn) excitation function, but improvements are necessary.

Supplementary Materials

The following are available online at https://www.mdpi.com/2410-390X/3/2/29/s1.

Author Contributions

M.S.: formal analysis, software, methodology, writing—original draft, writing—review & editing; J.J.: conceptualization; F.H.: supervision, writing—review & editing; T.M.: conceptualization, methodology, supervision, writing—review & editing; K.S.: supervision, writing—review & editing; W.Z.: conceptualization, supervision, writing—review & editing.

Funding

Part of this work was performed within the framework of the EU Horizon 2020 project RIA-ENSAR2 (654 002). This research was also partly supported by the Polish Funding Agency NCBiR grant No. DZP/PBS3/2319/2014 and by a grant from the French National Agency for Research called “Investissements d’Avenir”, Equipex Arronax-Plus noANR-11-EQPX-0004, Labex IRON noANR-11-LABX-18-01, and ISITE NEXT no. ANR-16-IDEX-0007.

Acknowledgments

The authors sincerely thank Anna Stolarz and Agnieszka Trzcińska (from Heavy Ion Laboratory, Warsaw) as well as Aleksander Bilewicz (from Institute of Nuclear Chemistry and Technology, Warsaw) for valuable discussions and constructive suggestions regarding this work. The PhD cotutelle scholarship from the French Government for Mateusz Sitarz is acknowledged.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Koumarianou, E.; Pawlak, D.; Korsak, A.; Mikolajczak, R. Comparison of receptor affinity of natSc-DOTA-TATE versus natGa-DOTA-TATE. Nucl. Med. Rev. 2011, 14, 85–89. [Google Scholar] [CrossRef]
  2. Walczak, R.; Krajewski, S.; Szkliniarz, K.; Sitarz, M.; Abbas, K.; Choiński, J.; Jakubowski, A.; Jastrzębski, J.; Majkowska, A.; Simonelli, F.; et al. Cyclotron production of 43Sc for PET imaging. EJNMMI Phys. 2015. [Google Scholar] [CrossRef] [PubMed]
  3. Bunka, M.; Müller, C.; Vermeulen, C.; Haller, S.; Türler, A.; Schibli, R.; van der Meulen, N.P. Imaging quality of 44Sc in comparison with five other PET radionuclides using Derenzo phantoms and preclinical PET. Appl. Radiat. Isot. 2016, 110, 129–133. [Google Scholar] [CrossRef] [PubMed]
  4. Domnanich, K.A.; Müller, C.; Farkas, R.; Schmid, R.M.; Ponsard, B.; Schibli, R.; Türler, A.; van der Meulen, N.P. 44Sc for labeling of DOTA- and NODAGA-functionalized peptides: Preclinical in vitro and in vivo investigations. EJNMMI Radiopharm. Chem. 2016. [Google Scholar] [CrossRef]
  5. Domnanich, K.A.; Eichler, R.; Müller, C.; Jordi, S.; Yakusheva, V.; Braccini, S.; Behe, M.; Schibli, R.; Türler, A.; van der Meulen, N.P. Production and separation of 43Sc for radiopharmaceutical purposes. EJNMMI Radiopharm. Chem. 2017. [Google Scholar] [CrossRef] [PubMed]
  6. Grignon, C.; Barbet, J.; Bardiès, M.; Carlier, T.; Chatal, J.F.; Couturier, O.; Cussonneau, J.P.; Faivre, A.; Ferrer, L.; Girault, S.; et al. Nuclear medical imaging using β+ γ coincidence from 44Sc radio-nuclide with liquid xenon as detection medium. Nucl. Instrum. Meth. A 2017, 571, 142–145. [Google Scholar] [CrossRef]
  7. Lang, C.; Habs, D.; Parodi, K.; Thirolf, P.G. Sub-millimeter nuclear medical imaging with reduced dose application in positron emission tomography using β+ γ coincidences. JINST 2013, 9, P01008. [Google Scholar] [CrossRef]
  8. Thirolf, P.G.; Lang, C.; Parodi, K. Perspectives for Highly-Sensitive PET-Based Medical Imaging Using β+γ Coincidences. Acta Phys. Pol. A 2015, 127, 1441–1444. [Google Scholar] [CrossRef]
  9. Huclier-Markai, S.; Kerdjoudj, R.; Alliot, C.; Bonraisin, A.C.; Michel, N.; Haddad, F.; Barbet, J. Optimization of reaction conditions for the radiolabeling of DOTA and DOTA-peptide with 44m/44Sc and experimental evidence of the feasibility of an in vivo PET generator. Nucl. Med. Biol. 2014, 41, e36–e43. [Google Scholar] [CrossRef] [PubMed]
  10. Alliot, C.; Audouin, N.; Barbet, J.; Bonraisin, A.C.; Bossé, V.; Bourdeau, C.; Bourgeois, M.; Duchemin, C.; Guertin, A.; Haddad, F.; et al. Is there an interest to use deuteron beams to produce non-conventional radionuclides? Front. Med. 2015. [Google Scholar] [CrossRef]
  11. Alliot, C.; Kerdjoudj, R.; Michel, N.; Haddad, F.; Huclier-Markai, S. Cyclotron production of high purity 44m,44Sc with deuterons from 44CaCO3 targets. Nucl. Med. Biol. 2015, 42, 524–529. [Google Scholar] [CrossRef]
  12. Duchemin, C.; Guertin, A.; Haddad, F.; Michel, N.; Métivier, V. Production of scandium-44m and scandium-44g with deuterons on calcium-44: Cross-section measurements and production yield calculations. Phys. Med. Biol. 2015, 60, 17. [Google Scholar] [CrossRef]
  13. Domnanich, K.A.; Müller, C.; Benešová, M.; Dressler, R.; Haller, S.; Köster, U.; Ponsard, B.; Schibli, R.; Türler, A.; van der Meulen, N.P. 47Sc as useful β- emitter for the radiotheragnostic paradigm: A comparative study of feasible production routes. EJNMMI Radiopharm. Chem. 2017. [Google Scholar] [CrossRef]
  14. International Atomic Energy Agency. Call for Coordinated Research Project “Therapeutic Radiopharmaceuticals Labelled with New Emerging Radionuclides (67Cu, 186Re, 47Sc)”. 2015. Available online: https://www.iaea.org/projects/crp/f22053 (accessed on 13 May 2019).
  15. International Atomic Energy Agency. 2015. Available online: http://cra.iaea.org/cra/stories/2015-09-30-F22053-New_Emerging_Radionuclides.html (accessed on 13 May 2019).
  16. Müller, C.; Bunka, M.; Haller, S.; Köster, U.; Groehn, V.; Bernhardt, P.; van der Meulen, N.P.; Türler, A.; Schibli, R. Promising Prospects for 44Sc-/47Sc-Based Theragnostics: Application of 47Sc for Radionuclide Tumor Therapy in Mice. J. Nucl. Med. 2014, 55, 1658–1664. [Google Scholar] [CrossRef]
  17. Müller, C.; Domnanich, K.A.; Umbricht, C.A.; van der Meulen, N.P. Scandium and terbium radionuclides for radiotheranostics: Current state of development towards clinical application. Br. J. Radiol. 2018. [Google Scholar] [CrossRef]
  18. International Atomic Energy Agency. Live Chart of Nuclides. Available online: https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html (accessed on 12 May 2019).
  19. Szkliniarz, K.; Sitarz, M.; Walczak, R.; Jastrzębski, J.; Bilewicz, A.; Choiński, J.; Jakubowski, A.; Majkowska, A.; Stolarz, A.; Trzcińska, A.; Zipper, W. Production of medical Sc radioisotopes with an alpha particle beam. Appl. Radiat. Isot. 2016, 118, 182–189. [Google Scholar] [CrossRef]
  20. Sitarz, M.; Szkliniarz, K.; Jastrzębski, J.; Choiński, J.; Guertin, A.; Haddad, F.; Jakubowski, A.; Kapinos, K.; Kisieliński, M.; Majkowska, A.; et al. Production of Sc medical radioisotopes with proton and deuteron beams. Appl. Radiat. Isot. 2018, 142, 104–112. [Google Scholar] [CrossRef]
  21. Nagatsu, K.; Fukumura, T.; Takei, M.; Szelecsényi, F.; Kovács, Z.; Suzuki, K. Measurement of thick target yields of the natS(α,x)34mCl nuclear reaction and estimation of its excitation function up to 70 MeV. Nucl. Inst. Meth. Phys. Res. B 2008, 266, 709–713. [Google Scholar] [CrossRef]
  22. Phelps, M.E. PET: Molecular Imaging and Its Biological Applications; Springer: New York, NY, USA, 2004. [Google Scholar]
  23. Pedroso de Lima, J.J. Nuclear Medicine Physics Series in Medical Physics and Biomedical Engineering, Cyclotron and Radionuclide Production, Series in Medical and Biomedical Engineering; CRC Press: Boca Raton, FL, USA, 2010. [Google Scholar]
  24. Jose, K.K.; Naik, S.R. On the q-Weibull Distribution and Its Applications. Com. Stat. Th. Meth. 2009, 38, 912–926. [Google Scholar] [CrossRef]
  25. Ziegler, J.F.; Ziegler, M.D.; Biersack, J.P. SRIM Code, Version 2008.04. Available online: http://www.srim.org/ (accessed on 12 May 2019).
  26. de Waal, T.J.; Peisach, M.; Pretorius, R. Activation cross sections for proton-induced reactions on calcium isotopes up to 5.6 MeV. J. Inorg. Nucl. Chem. 1971, 33, 2783–2789. [Google Scholar] [CrossRef]
  27. Kennett, S.R.; Switkowski, Z.E.; Paine, B.M.; Sargood, D.G. Yield Measurements in the Reactions 48Ca(p,γ)49Sc and 48Ca(p,n)48Sc. J. Phys. G 1979, 5, 399. [Google Scholar] [CrossRef]
  28. Zyskind, J.L.; Davidson, J.M.; Esat, M.T.; Spear, R.H.; Shapiro, M.H.; Fowler, W.A.; Barnes, C.A. Cross Section Measurements and Thermonuclear Reaction Rates for 48Ca(p,γ)49Sc and 48Ca(p,n)48Sc. Nucl. Phys. A 1979, 315, 430–444. [Google Scholar] [CrossRef]
  29. Mitchell, L.W.; Anderson, M.R.; Kennett, S.R.; Sargood, D.G. Cross-sections and thermonuclear reaction rates for 42Ca(p,γ)43Sc, 44Ca(p,γ)45Sc, 44Ca(p,n)44Sc and 45Sc(p,n)45Ti. J. Nucl. Phys. A 1982, 380, 318–334. [Google Scholar] [CrossRef]
  30. Singh, G.; Kailas, S.; Saini, S.; Chatterjee, A.; Balakrishnan, M.; Mehta, M.K. Reaction 48Ca(p,n)48Sc from E(p) = 1.885 to 5.1 MeV. Pramana 1982, 19, 565–577. [Google Scholar] [CrossRef]
  31. Levkovskij, V.N. Cross-section of medium mass nuclide activation (A=40-100) by medium energy protons and alpha-particles (E=10-50 MeV); Inter-Vesi: Moscow, Russia, 1991. [Google Scholar]
  32. Krajewski, S.; Cydzik, I.; Abbas, K.; Bulgheroni, A.; Simonelli, F.; Holzwarth, U.; Bilewicz, A. Cyclotron production of 44Sc for clinical application. J. Radiochim. Acta 2013. [Google Scholar] [CrossRef]
  33. Carzaniga, T.S.; Auger, M.; Braccini, S.; Bunka, M.; Ereditato, A.; Nesteruk, K.P.; Scampoli, P.; Türler, A.; van der Meulen, N. Measurement of 43Sc and 44Sc production cross-section with an 18 MeV medical PET cyclotron. Appl. Radiat. Isot. 2017, 129, 96–102. [Google Scholar] [CrossRef] [PubMed]
  34. Alabyad, M.; Mohamed, G.V.; Hassan, H.E.; Takács, S.; Ditrói, F. Experimental measurement and theoretical calculations for proton, deuteron and α-particle induced nuclear reactions on calcium: Special relevance to the production of 43,44Sc. J. Radioan. Nucl. Chem. 2018, 316, 119–128. [Google Scholar] [CrossRef]
  35. Carzaniga, T.S.; Braccini, S. Cross-section measurement of 44mSc, 47Sc, 48Sc and 47Ca for an optimized 47Sc production with an 18 MeV medical PET cyclotron. Appl. Radiat. Isot. 2019, 143, 18–23. [Google Scholar] [CrossRef]
  36. Tárkányi, F.T.; Ignatyuk, A.V.; Hermanne, A.; Capote, R.; Carlson, B.V.; Engle, J.W.; Kellett, M.A.; Kibédi, T.; Kim, G.N.; Kondev, F.G.; et al. Recommended nuclear data for medical radioisotope production: diagnostic positron emitters. J. Radioan. Nucl. Chem 2019, 319, 533–666. [Google Scholar] [CrossRef]
  37. Herman, M.; Capote, R.; Carlson, B.V.; Obložinský, P.; Sin, M.; Trkov, A.; Wienke, H.; Zerkin, V. EMPIRE: Nuclear Reaction Model Code System for Data Evaluation. Nucl. Data Sheets 2007, 108, 2655–2715. [Google Scholar] [CrossRef]
  38. Koning, A.J.; Rochman, D. Modern Nuclear Data Evaluation with The TALYS Code System. Nucl. Data Sheets 2012, 113, 2841–2934. [Google Scholar] [CrossRef]
Figure 1. Reconstruction of 43Ca(p,n)43Sc cross-section (bottom) based on the fit to TTY data on 43CaCO3 enriched in 90% 43Ca (top). The cross-section data points are taken from [26,31,33,34].
Figure 1. Reconstruction of 43Ca(p,n)43Sc cross-section (bottom) based on the fit to TTY data on 43CaCO3 enriched in 90% 43Ca (top). The cross-section data points are taken from [26,31,33,34].
Instruments 03 00029 g001
Figure 2. Reconstruction of 44Ca(p,n)44gSc cross-section (bottom) based on the fit to TTY data on 44CaCO3 enriched in 94.8% 44Ca (top). The cross-section data points are taken from [26,29,31,32,33,34,36].
Figure 2. Reconstruction of 44Ca(p,n)44gSc cross-section (bottom) based on the fit to TTY data on 44CaCO3 enriched in 94.8% 44Ca (top). The cross-section data points are taken from [26,29,31,32,33,34,36].
Instruments 03 00029 g002
Figure 3. Reconstruction of 44Ca(p,n)44mSc cross-section (bottom) based on the fit to TTY data on 44CaCO3 enriched in 94.8% 44Ca (top). The cross-section data points are taken from [31,32,34,35].
Figure 3. Reconstruction of 44Ca(p,n)44mSc cross-section (bottom) based on the fit to TTY data on 44CaCO3 enriched in 94.8% 44Ca (top). The cross-section data points are taken from [31,32,34,35].
Instruments 03 00029 g003
Figure 4. Reconstruction of 48Ca(p,2n)47Sc cross-section (bottom) based on the fit to TTY data on 48CaCO3 enriched in 97.1% 48Ca (top). The cross-section data points are taken from [35].
Figure 4. Reconstruction of 48Ca(p,2n)47Sc cross-section (bottom) based on the fit to TTY data on 48CaCO3 enriched in 97.1% 48Ca (top). The cross-section data points are taken from [35].
Instruments 03 00029 g004
Figure 5. Reconstruction of 48Ca(p,n)48Sc cross-section (bottom) based on the fit to TTY data on 48CaCO3 enriched in 97.1% 48Ca (top). Here, we adopted an arbitrary threshold of 3 MeV. The cross-section data points are taken from [26,27,28,30,35]. The results from [27,28,30] are averaged.
Figure 5. Reconstruction of 48Ca(p,n)48Sc cross-section (bottom) based on the fit to TTY data on 48CaCO3 enriched in 97.1% 48Ca (top). Here, we adopted an arbitrary threshold of 3 MeV. The cross-section data points are taken from [26,27,28,30,35]. The results from [27,28,30] are averaged.
Instruments 03 00029 g005
Table 1. Nuclear data [18] of medically interesting scandium radioisotopes (43Sc, 44g/mSc, 47Sc). 48Sc, as a radioactive impurity, is also listed here with reference to the analysis in this paper.
Table 1. Nuclear data [18] of medically interesting scandium radioisotopes (43Sc, 44g/mSc, 47Sc). 48Sc, as a radioactive impurity, is also listed here with reference to the analysis in this paper.
Radio-NuclideT1/2Eaverage β- or β+Branching or TransitionMain γ-Lines [keV] and Intensities
43Sc3.89 hβ+ 476 keVβ+ 88%373 (22.5%)
44gSc3.97 hβ+ 632 keVβ+ 95%1157 (99.9%)
44mSc58.61 hN/AIT 99%271 (86.7%), 1002 (1.2%),
1126 (1.2%), 1157 (1.2%)
47Sc3.35 dβ- 162 keVβ- 100%159 (68.3%)
48Sc43.67 hβ- 220 keVβ- 100%175 (7.5%), 984 (100%), 1038 (97.6%), 1213 (2.4%), 1312 (100%)
Table 2. Parameters of the TTYfit (for Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5) obtained with least square method for different nuclear reactions and the χ2/dof values for each fit. Parameter d is calculated from a, b, c and Ethr.
Table 2. Parameters of the TTYfit (for Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5) obtained with least square method for different nuclear reactions and the χ2/dof values for each fit. Parameter d is calculated from a, b, c and Ethr.
Parameter43Ca(p,n)43Sc44Ca(p,n)44gSc44Ca(p,n)44mSc48Ca(p,2n)47Sc48Ca(p,n)48Sc
Ethr [MeV]3.074.544.818.93theory: 0.51 adopted: 3.0
a [MeV]10(2)8.8(6)13.7(7)14.7(9)8.0(8)
b [MeV]4.5(6)4.8(1.0)7.0(1)9.05(14)4.2(7)
c [MBq(μAh)−1 (MeV)−2]7.1(9)24.5(1.2)0.075(3)1.57(6)2.5(2)
d [MBq/μAh]3489526.8216979.4
χ2/dof1.300.576.111.051.79
Table 3. Cross-section values for different nuclear reactions deduced from the thick target yield data from [20].
Table 3. Cross-section values for different nuclear reactions deduced from the thick target yield data from [20].
E [MeV]σ [mb]
43Ca(p,n)43Sc44Ca(p,n)44gSc44Ca(p,n)44mSc48Ca(p,2n)47Sc48Ca(p,n)48Sc
5145(20)115(6)2.11(8)0552(48)
6187(26)314(13)11.7(5)0692(66)
7214(29)450(20)19.2(8)0761(77)
8228(28)534(26)25.1(1.1)0744(78)
9231(24)572(31)29.6(1.3)14.2(6)740(71)
10225(18)572(32)32.9(1.4)199(7)674(58)
11211(12)543(30)35.0(1.4)353(14)586(43)
12193(10)493(25)36.2(1.3)478(18)490(29)
13172(15)431(19)36.4(1.2)576(20)393(20)
14148(21)363(15)35.9(1.0)647(20)304(18)
15125(26)297(14)34.7(8)698(20)228(21)
16104(29)235(15)33.1(7)729(19)164(22)
1784(30)180(16)31.0(7)739(18)115(21)
1866(30)134(16)28.7(8)734(18)78(19)
19 97(16)26.1(1.0)716(21)51(15)
20 68(14)23.4(1.1)684(26)32(12)
21 47(12)20.8(1.3)647(31)20(9)
22 31(10)18.2(1.4)600(35)12(6)
23 20(7)15.7(1.4)550(40)7(4)
24 13(6)13.5(1.4)499(43)4(3)
25 8(4)11.3(1.4)445(46)2.0(1.6)
26 5(3)9.5(1.4)393(47)1.0(9)
27 2.7(1.8)7.8(1.3)343(48)0.5(5)
28 1.5(1.1)6.4(1.2)297(47)0.3(3)
29 0.8(7)5.1(1.1)253(45)0.12(16)
30 0.4(4)4.0(9)213(43)0.05(8)

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Instruments EISSN 2410-390X Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top