Upgrade of recommended nuclear cross section data base for production of therapeutic radionuclides

The IAEA Nuclear Data Section has coordinated several actions to setup and improve a database for recommended cross sections and nuclear decay data for various charged-particle reactions that can be used for medical radionuclide production. Some of the earlier evaluations did not provide uncertainties for the recommended cross sections. Updated evaluations with uncertainty quantification for 25 reactions relevant for production of 67Cu, 103Pd, 102mgRh, 114mIn, 125I, 169Yb, 177gLu, 186Re, 192Ir and 210,211At therapeutic radioisotopes are presented. Recommended cross-section data and their uncertainties for production of therapeutic radionuclides are available on the Web page of the IAEA Nuclear Data Section at https://nds.iaea.org/radionuclides and also at the IAEA medical portal ﻿https://nds.iaea.org/medportal.


Introduction
Optimization of radionuclide production for those isotopes of interest in medical applications are of considerable interest to IAEA. The IAEA Nuclear Data Section has hence coordinated several actions to set up a database for recommended cross-sections and associated nuclear decay data for various charged-particle reactions used for medical radionuclides production over the last 25 years. The results of these evaluations were published in webpages of the IAEA-NDS and documented in [1][2][3][4][5][6][7] and at numerous conferences. For most of the reactions studied these evaluations resulted in recommended cross section data with uncertainties and production yield data. For few earlier evaluations the uncertainties of the recommended cross section data are missing. Over the last 2 years an upgrade of these evaluations to include an uncertainty quantification was carried out. The results are presented in this work for 25 reactions relevant for production of 67 Cu,103 Pd, 102m,g Rh, 114m In, 125 I, 169 Yb, 177m,g Lu, 186 Re,192 Ir and 210,211 At therapeutic isotopes.

Methods of compilation, correction, selection and data fitting
The main steps of this upgrading evaluation process are: • Survey of new or missing literature for experimental data of studied production routes. • Correction of the published datasets for up-to-date monitor cross sections or nuclear decay characteristics. • Selection of the data sets for fitting of all available corrected datasets considering the earlier evaluations and the results of model calculations. • Fit of the selected experimental data using Padé approach (approximant by rational function) [8,9]. • Deducing recommended data with uncertainties. • Calculation of integral production yields based on recommended cross-section data.
Some additional, important comments should be repeated related to above mentioned steps: • The experimental circumstances and the nuclear decay data used are often not documented properly in the original publications. In those cases, corrections for nuclear data are practically impossible, when the only information available is the year of publication to estimate the values of the used decay data. • Without detailed experimental description decay data can only be corrected for the linearly contributing parameters (intensities) and correction for half-life is, in most cases, impossible. • Systematic differences of cross sections often exist between the different publications. One of the main reasons is an improper estimation of the number of incident particles that can be determined by direct measurement of collected charge (or secondary particles) or indirectly by using monitor reactions. The proper technical base and equipment for direct charge measurement are available only at a limited number of experimental sites. To determine the beam intensity by using monitor reactions requires in principle exact knowledge of the incident energy on the monitor foils. In most cases the energy of the extracted beams is not well defined and by using only one monitor foil, especially in an energy region where the excitation function is rapidly changing, improper estimation of the beam intensity can be obtained. • It is a well-known experimental fact that cross section data deduced from spectra measured at different times and different sample-detector distances may be systematically different (within usual 3-4% uncertainties), due to uncertainties in the efficiency of the detector and different dead-time corrections during measurements. To reduce uncertainties hence in principle the monitor and target foils should be measured practically simultaneously, which in most cases is not possible. • The estimation of the target thickness and hence number of target atoms present, is also improper in many cases, especially for targets made by sedimentation, pressing, electro-deposition etc. Improper target preparation can result in systematic errors of the measured data, but also can be the source of scattering of the obtained data. • An important factor in data selection is the experience of the research group in data measurement and data evaluation. Some laboratories have a proper technical background and large expertise in data measurement and reporting, proved by several earlier publications. Usually, more weight is given to results measured in these laboratories when only limited number of discrepant data points are available. • In the evaluations the weight of each experiment is determined by the reported uncertainties, which hence deserve special attention. In reported data uncertainties difference by a factor of two are seen for laboratories having the same level of technical background and expertise. Evaluations based only on original data, without critically considering uncertainties, will often result in erroneous recommended data. • Theoretical data and systematics can be helpful for selection of experimental data especially for decisions on very outlying data points, on overall shape of the excitation function and for systematic energy shifts. This is especially true near the threshold of the reaction as the theoretical calculations are reliable and depend only on the well-measured masses. During the data selections, these outlying data points are mostly neglected, and systematic energy shift can be only partly corrected when the data set covers a large energy range. • The fitting process requires often additional de-selection of outlying data points, or to introduce additional "guessed" points in energy ranges not covered or represented by the reported experimental results. • Uncertainties in the fitted results were estimated via a least-squares method with an addition of a 4% systematic uncertainty which is an expert estimate of overall unrecognized uncertainties as discussed in Ref. [10].
Detailed information on the method of collection and selection of experimental data including extensive discussion of the Padé fitting methodology and obtaining uncertainties of the fit, can be found in the introductory chapters of the IAEA related publications: [1][2][3][4][5][6][7].

Evaluated nuclear reactions
The summary of the evaluated reactions in the present report is collected in the Table 1 that contains the list of reactions, the number of available experimental data sets, the maximal energy of the experimental data, the number of selected data series and the parameters of the final Padé fit. The main decay data used in the evaluation of the reported radionuclides and the parameters showing their applicability in nuclear medicine are collected in Table 2.
For each radionuclide of interest, we mention shortly the possible medical applications in separate subsections. They were discussed in detail in the IAEA TRS 473 [2] and specially dedicated paper [6]. After presentation of the decay data of the reaction product the evaluation and the results for each of the reactions studied (multiple reactions possible for one medical radioisotope) are illustrated in two figures: the first figure shows all available experimental data (corrected if necessary), the second figure contains only the selected experimental data with their uncertainties and the Padé fit that defines the recommended cross sections for the evaluated reaction. The uncertainties defined for the recommended cross sections are expressed as percentages on the secondary axis of the figure. The theoretical predictions taken from the TENDL 2017 [11] and TENDL 2019 libraries [12], based on TALYS-model code calculations, are also shown for comparison in the first figure. Integral yields for every reaction (integrated yield for a given incident energy down to the reaction threshold) are calculated from the recommended cross section data, as shown in a separate figure at the end of each subsection. The results represent the physical yields (obtained in an instantaneous irradiation time) [13,14]. 67 Cu production 67 Cu is the longest-lived radioisotope of copper, is ideally suited for both radionuclide therapy and imaging. Along with 100% β − emission, 67 Cu emits gamma photons of 92 and 184 keV that are suitable for gamma scintigraphy (Fig. 1).
Only one data point at 200 MeV was reported in Mirzadeh et al [22] that was not considered in the evaluation process. The data of McGee [21] were adjusted in order to account for improved IAEA monitor data. Data of Levkovskij [23] were corrected by 0.8 to adjust to the new monitor data. No correction was done for the small contribution of the reactions on 70 Zn for data measured on nat Zn.
Two data sets were deselected. Cohen [18] data were rejected because the authors state a very high uncertainty for their 67 Cu cross-sections; Schwarzbach [28] published relative data that showed a very large scatter. Twelve data points in the energy range 35-45 MeV of Stoll [24] were  Table 2 Decay data of investigated reaction products taken from ENSDF [15]. ENSDF nuclear structure and decay data can be easily extracted, understood and studied in an attractive user-friendly manner by means of LiveChart of Nuclides [16] and NuDat [17] Product or isomer, excitation energy, isomer spin J π Half life and decay mode (%) E α,max (keV) <E β− > or <E β+ > (keV)

Main electrons auger (AE), conversion (CE) E e (keV) and I e (%) in parentheses
Main gamma lines E γ (keV) and I γ (%) in parentheses X-ray are indicated 67  excluded due to systematic errors in that energy range (information from authors). The selected data vs the Padé fit are shown in Fig. 3.

70
Zn(p,α) 67 Cu reaction A total of 3 data sets were found in literature: [23,28,30] ( Fig. 4). None of these sets are new and were already evaluated in TRS 473 [2]. The data in Schwarzbach [28] are only relative and were normalized at low energies, but as the resulting values are very different from the TENDL predictions they were excluded.  67

Cu reaction
This reaction on natural targets was not evaluated earlier. A total of four data sets can be derived from literature: [23,25,28,30] and are compared with TENDL evaluations in Fig. 6.
Schwarzbach [28] data (see remark on normalisation above) were deselected as they are scattered and contradicting the Bonardi [25] data.
Levkovskij [23] and Kastleiner [30] data, measured on 70 Zn, were normalised to nat Zn below the (p,2p) threshold and were included. Levkovskij [23] data were corrected due to outdated monitor reaction data. The selected and corrected data vs the Padé fit are shown in Fig. 7.     67 Cu reaction A total of 2 data sets were found in literature: Tárkányi [31] and Khandaker [32] and are compared with TENDL evaluations in Fig. 8. Both sets were selected and fitted (Fig. 9). This reaction was not evaluated earlier.

Integral yields for production of 67 Cu
The integral yields calculated on the basis of fitted crosssections for production of 67 Cu are collected in Fig. 10.

Pd and 102 Rh production
Palladium-103 (T 1/2 = 16.991 d) decaying 100% by electron capture, accompanied by emission of Auger electrons and low energy X-rays, is extensively used in the treatment of prostate cancer and ocular melanoma. Applied mostly in brachytherapy form.
Rhodium-102 (metastable and ground state) is an important radioisotopic impurity generated during production of 103 Pd.
The simplified decay schemes of 103 Pd and 103m Rh are shown in Fig. 11, and those for the co-produced 102m Rh and 102g Rh in Fig. 12.
Cross sections for production of 103 Pd and 102m,g Rh 103 Rh(p,n) 103 Pd reaction A total of 9 data sets were found in literature: [33][34][35][36][37][38][39][40][41], which are compared to TENDL evaluations in Fig. 13. The work by Bramblett [36] is to be considered new as it was not included in the previous evaluation.
The set of Mukhammedov [39] was de-selected because of the differences in shape compared with all other excitation functions just above the threshold energy.
The highest energy point of Albert [34] is outlying and was not considered for the fitting.
It was mentioned in an earlier publication [2] that a systematic difference in cross sections was found depending on if X-lines, or γ-lines were used for the activity measurement. This discrepancy could not be explained by a recent unpublished review of 103 Pd decay data although for X-lines absolute intensities are calculated, while γ-ray abundances are measured. For the present report we used cross sections derived from X-ray measurement, except for the datasets of [34,35,38] that rely on neutron measurements.
The uncertainty for data of Sudar [41] was increased up to 10% (selected data vs. Padé fit are shown in Fig. 14).

Rh(p,x) 102m,g Rh reaction
For formation of the ground and metastable state of 102 Rh by proton induced reactions on 103 Rh, the two data sets found in literature were used for fitting: [40,42]. The data

Rh(p,x) 102g Rh reaction
Two data sets were found in the literature published by [40] and are compared with TENDL evaluations in Fig. 17. Tárkányi 40 data have large uncertainties in the overlapping high energy region and were normalized to Hermanne [42] data by a factor of 0.7 before the fit was undertaken. Corrected data are shown in Fig. 18 versus the Padé fit.

Rh(d,2n) 103 Pd reaction
For formation of 103 Pd by deuteron induced reactions on 103 Rh, the two data sets found in literature were used for fitting: [43][44][45] (Fig. 19). The set of Tárkányi [45] is new and was not considered in the earlier evaluation. The data reported in Ditrói [46] are identical to those in Tárkányi [45] and were excluded from the compilation. In the earlier evaluation the X-ray data were selected. In the last unpublished review of decay data, a small change was made for γ-ray probability. The Tárkányi data [45] relying on γ-measurements are systematically lower than the Hermanne [43,44] values based on X-ray measurements and were hence multiplied by 1.2 according to ratio shown in case of protons for the 103 Rh(p,n) 103 Pd reaction.
Hermanne [43,44] X-ray data and the Tárkányi [45] corrected gamma data were selected and used for fitting as shown in Fig. 20.

Rh(d,x) 102m Rh, 102g Rh reactions
A total of 3 data sets were found in literature for formation of the ground and metastable state of 102 Rh by deuteron irradiation of 103 Rh: [43,44,46,47]. The values reported in Hermanne [47] and Ditrói [46] data are new.
A few low energy points of Ditrói [46] below the threshold were deselected.
The collected and the selected data vs the Padé fit for production of 102m Rh are shown in Figs. 21 and 22, and for production of 102g Rh in Figs. 23 and 24, respectively.

Rh and 102g Rh
The deduced integral yields for the (p,n) and (d,2n) reactions leading to 103 Pd are shown in Fig. 25.

In production
The radionuclide 114m In (T ½ = 49.51 d), being a longer-lived analogue of 111 In, is of potential interest in Auger and conversion electron therapy for longer lasting therapeutic studies with use of its compounds of appropriately slow kinetics.
The decay scheme and the decay data are shown in Fig. 27 and Table 2.

Cd(d,2n) 114m In reaction
A total of 5 data sets were found in literature: [56,[63][64][65] (Fig. 30). No new data were found since the last evaluation. The set of Tárkányi [65] was corrected by a factor of 0.9 after re-analysing and using the Cu + d monitor reactions instead of the Fe + d reactions. The data of Mirzaei [56] were deselected. The absolute cross-section values are too small comparing to Tárkányi [65] and to Nassiff [63]. The absolute cross-section values are also too small for the simultaneously measured 111 In. Two data points of Nassiff [63] above 17 MeV were deselected. The data measured on nat Cd target of Tárkányi [60] contains the contribution from the 113 Cd(d,n) 114m In reaction. According to the Alice IPPE calculation this contribution can be neglected (estimated 113 Cd(d,n) 114m+g In is around 5-10% in the important low energy range, for 114m In alone is even smaller). No correction was done for this contribution considering that the data measured on 114 Cd targets and derived from nat Cd targets show excellent agreement and the uncertainty on the absolute values is in both cases in the 12-15% range.
As the threshold for 116 Cd(d,4n) 114 In is 19.6 MeV, we used normalized data obtained on nat Cd up to 20.7 MeV. The collected and the selected data vs the Padé fit for the

Cd(p,3n) 114m In reaction
A total of 3 data sets were found in literature: [51,64,66]. The sets of Nieckarz [51] and Hermanne [66] are new and were not used in the previous evaluation as shown in Fig. 32. All data were selected and fitted and are shown vs the Padé fit in Fig. 33.

In yields
Calculated integral yields of the 114 Cd(p,n) 114m In, 114 Cd(d,2n) 114m In and 116 Cd(p,3n) 114m In reactions are shown in Fig. 34.

I production
The long-lived iodine isotope 125 I (T½ = 59.41 d) is an intense Auger electron emitter. It is commonly used in radio-immunoassay.  The decay scheme and the decay data are shown in Fig. 35 and Table 2.
The 125 Te(p,n) 125 I and 124 Te(d,n) 125 I production routes were evaluated.
The single discrepant data point of Zweit [68] was deselected due to its low cross-section value.
The lowest energy outlying data point of Al-Azony [70] was removed. The selected data and the Padé fit are shown in Fig. 37.

Te(d,n) 125 I reaction
Three data sets measured by Bastian [72] on highly enriched 124 Te and by Zaidi [73] and Hermanne [74] on tellurium target with natural isotopic composition were found in literature (Fig. 38). Zaidi [73] and Hermanne [74] data were not considered relevant here due to the low threshold (3.2 MeV) of the contaminating 125 Te(d,2n) 125 I reaction, so those data are not shown in Fig. 38. Selected data are shown vs the Padé fit in Fig. 39.

Integral yields for production of 125 I
Calculated integral yields of the 125 Te(p,n) 125 I and 124 Te(d, n) 125 I reactions are shown in Fig. 40.   169g Yb production 169 Yb emits a low-energy photon spectrum, evaluated for use in high dose rate brachytherapy.
The decay scheme and the decay data are shown in Fig. 41 and Table 2.

Tm(p,n) 169 Yb reaction
Four data sets measured by [75][76][77][78] were found in literature. Two of them are new and were not considered in the  previous evaluation: [77,78]. All data sets were selected and compared with TENDL predictions in Fig. 42.
The data in Spahn [76] were normalized considering the systematic trend of the other selected datasets. Two outlying data points of Birattari [75] near the maximum were excluded from the figure and uncertainties were increased up to 10%. The fitted data versus the Padé fit are shown in Fig. 43.

Tm(d,2n) 169 Yb reaction
A total of four data sets were found in literature: [79][80][81][82][83] and are compared to TENDL libraries in Fig. 44. The results of [80][81][82][83] are new as they were not considered in the earlier evaluation. All data sets were selected for fitting without changes and are shown vs the Padé fit in Fig. 45.

Lu production
The ground state of 177 Lu is one of the most important novel therapeutic β − emitters that also emits low energy gammas for imaging and localization with gamma cameras (a   theranostic radioisotope).
The simplified decay scheme and the decay data are shown in Fig. 47 and collected in Table 2.

Yb(d,p) 177 Yb reaction
A total of 4 data sets were found in literature for formation of the parent radionuclide 177 Yb: [84][85][86][87] and are compared to TENDL evaluations in Fig. 48. The data sets of Tárkányi [85] and Khandaker [87] are new. All data series were selected for fitting and are compared versus the Padé fit in Fig. 49.

3
The data sets of Tarkanyi [85,86] are deselected as they are significantly different within the uncertainty limits of the three other datasets that agree very well. The selected data are compared with the Padé fit in Fig. 51.

Integral yields for production of 177 Yb and 177g Lu
Calculated integral yields of the 176 Yb(d,p) 177 Yb and 176 Yb(d,x) 177g Lu reactions are shown in Fig. 52.

Re production
The radionuclide 186g Re provides both high-abundance β − particle emissions to deliver high doses, and low-energy γ-rays suitable for imaging.
The simplified decay scheme and the decay data are presented on Fig. 53 and Table 2.
The reason of large systematic disagreements was not found during detailed investigation of the reported experimental methods and data evaluation methods. Systematic behavior of the excitation functions in the same atomic mass range was also studied. The data by Shigeta [90], Zhang [92], Khandaker [98], and Tarkanyi [94] were deselected as they show too high or too low cross-section values, respectively. Lapi data [97] were normalized at the maximum to get more data points to fit near the maximum. Selected data vs the Padé fit are compared in Fig. 55.
The too low cross-section point at 15.7 MeV of Zhenlan [105] was not taken into account for fitting. The selected data and the Padé fit are shown in Fig. 57.

Integral yields for production of 186 Re
Calculated integral yields of the 186 W(p,n) 186g Re and 186 W(d,2n) 186g Re reactions are shown in Fig. 58.

Ir production
The 192 Ir has good decay properties for therapy (high intensity beta radiation and long half-life), but it emits undesirable high-energy gammas difficult for shielding. It is commonly used in brachytherapy. The simplified decay scheme and the decay data are presented in Fig. 59

Os(p,n) 192m1+g Ir reaction
A total of four data sets were found in literature: [115][116][117][118] and were compared with TENDL evaluations in Fig. 60. The two sets by Szelecsenyi and Hermanne [117,118] are new since the last evaluation. All data sets were selected and fitted and are compared vs the Padé fit in Fig. 61.

Os(d,2n) 192m1+g Ir reaction
Two experimental data sets were published and compared to TENDL evaluations in Fig. 62. Both datasets were selected for fitting: [119,120] Fitted data versus the Padé fit are shown in Fig. 63.
The data series of Hermanne [120] is new and was not included into the earlier evaluation.

Integral yields for production of 192m1+g Ir
Calculated integral yields of the 192 Os(p,n) 192m1+g Ir and 192 Os(d,2n) 192m1+g Ir reactions are shown in Fig. 64.  At production 211 At is one of the most promising α-particle emitting radionuclides for targeted radionuclide therapy using short penetration, high linear energy transfer and great biological effectiveness of the α-particles. 210 At is an impurity that leads to production of radio-toxic 210 Po. The decay schemes of 211 At and 210 At are shown in Figs. 65 and 66 and their decay data are collected in Table 2.

Bi(α,2n) 211 At reaction
A total of seven data sets were found in literature: [121][122][123][124][125][126][127] (in Refs. [126] and [127] two data sets were reported: by direct measurement and through decay of 211 Po). Comparison of available data versus TENDL evaluations is shown in Fig. 67. No new data were reported since the last evaluation in [2]. The data by Stickler [124] were deselected, due to significantly lower cross-section values. Fitted data versus the Padé fit are shown in Fig. 68.

Integral yields for production of 211 At and 210 At
Calculated integral yields of the 209 Bi(α,2n) 211 At and 209 Bi(α,3n) 210 At reactions are shown in Fig. 71.

Summary
New evaluations were performed on 25 reactions for production of 67 Cu,103 Pd, 102mg Rh, 114m In, 125 I, 169 Yb, 177g Lu, 186 Re,192 Ir and 210,211 At therapeutic radioisotopes by upgrading the compilations with new experimental data and to get uncertainties of the recommended data. The experimental data were compared with theoretical predictions taken from the TENDL-2017 and TENDL-2019 libraries. A Padé fitting method was applied for the selected evaluated datasets to deduce recommended data and their uncertainties. Based on recommended production data integral yields were calculated. Recommended cross-section data and their  uncertainties for production of therapeutic radionuclides are available on the Web page of the IAEA Nuclear Data Section at https:// nds. iaea. org/ radio nucli des and also at the IAEA medical portal https:// nds. iaea. org/ medpo rtal. These data have importance for radionuclide production and can be used to validate nuclear reaction models.
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