Investigation of activation cross-sections of deuteron induced reactions on ruthenium up to 50 MeV Applied Radiation and Isotopes

The activation cross sections of deuteron induced reactions on natural ruthenium have been measured up to 50 MeV for production of radioisotopes of rhodium ( 105 Rh, 102m Rh, 102g Rh, 101m Rh, 101g Rh, 100g Rh, 99m Rh, 99g Rh), ruthenium ( 105 Ru, 103 Ru (cum), 102 Ru (cum), 97 Ru (cum), 95 Ru (cum)) and of technetium ( 99m Tc, 96g Tc (m + ), 95m Tc (cum), 95g Tc (cum), 94g Tc, 93g Tc (m + )). The results are compared with the predictions of the most common theoretical nuclear reaction model codes (ALICE-D, EMPIRE-D and TALYS (TENDL)). From the measured cross section physical yields have been calculated for all measured radioisotopes. The medically important radioisotopes are discussed from the point of view of production routes by charged particle methods and other alternatives.


Introduction
We are performing a systematic investigation on activation cross sections of deuteron induced nuclear reactions in all elements. The investigation up till now covered around 1200 excitation functions for reactions on 61 elements (natural targets or enriched stable isotopes). The investigation is connected to projects in a wide range of subjects as activation analyses, medical isotope production, radiation safety of accelerator elements, nuclear reaction theory, etc. In the present work we investigated the activation cross sections of deuteron induced reactions on ruthenium up to 50 MeV incident energy. In literature only one experimental study by Mito et al., (1969) (Mito et al., 1969) was found, presenting the cross sections up to 14 MeV for (d,p) reactions on individual stable 96 Ru, 102 Ru and 104 Ru isotopes, although natural ruthenium targets were used, and an unpublished PhD work  providing data for some radioisotopes below 20 MeV. The fission products 103 Ru (39.35 d) and especially 106 Ru (368 d) are considered troublesome in the PUREX reprocessing process of spent nuclear fuel, but also have, together with some light ion induced reactions (direct or decay) products applications in nuclear medicine ( 106 Ru brachytherapy, 105 Rh therapeutic, 103 Ru/ 103m Rh Auger-electron therapy, 101 Rh brachytherapy, 97 Ru SPECT, 99m Tc SPECT, 94m Tc PET).

Experiment and data evaluation
For measurement of the cross-section data the well-established activation method, using stacked-foil target technique and off-line gamma-ray spectroscopy, was used. The preparation of the thin samples used for the performed cross section measurements was achieved using the sedimentation technique (Rosch et al., 1993). In this process salt of ruthenium, namely RuCl 3 (99,9%, Carl-Roth Karlsruhe) was suspended in wet ethanol and transferred into Teflon sedimentation cells equipped with aluminum foils of 0.05 mm thickness and 13 mm diameter as backing for the sediments. After evaporation of the liquid the dried samples were each covered with aluminum foils of 0.01 mm thickness. The target was covered by a 10 μm Al foil for protection. The thickness of the sediment layer was 5-45 mg/cm 2 RuCl 3 . Reactions on the Al backing and the Al cover served as monitor.
The target stack was irradiated in a Faraday cup-like target holder equipped with a 5 mm collimator. The details of the experimental technique, spectra evaluation and cross section determination are collected in Table 1. The used decay data are collected in Table 2. Effective beam intensities and the energy scale were determined by using the excitation functions of the 24 Al (d,x) 24 Na reaction, simultaneously re-measured over the whole energy range. For illustration, the excitation functions of this monitor reaction, in comparison with the IAEA recommended data (Tárkányi et al., 2001) are shown in Fig. 1. The final energy scale was adjusted to the fitted monitor reaction.
For estimation of the uncertainty of the effective beam energy in the target foils, cumulative effects of possible uncertainties in primary energy and target thickness were taken into account together with the effect of the energy straggling and of the correction for the monitor reaction. The uncertainties of cross sections were obtained from the sum in quadrature of all individual contributions (beam current (7%), beamloss corrections (maximum 1.5%), target thickness (3%), detector efficiency (5%), photo peak area determination and counting statistics 1-20%) (International-Bureau-of-Weights-and-Measures, 1993). The uncertainty of the non-linear contributing processes like irradiation, cooling and measuring time, and half-life was not considered.
When complex particles are emitted instead of individual protons and neutrons the Q-values have to be decreased by the respective binding energies of the compound particles: np-d, +2.

Nuclear model calculation
The cross sections of the investigated reactions were calculated using the modified pre-compound model codes (versions D) ALICE-IPPE (Dityuk et al., 1998) and EMPIRE-II (Herman et al., 2007). The experimental data are also compared with the cross section data in the TENDL-2019 (Koning et al., 2019) nuclear reaction data library. The TENDL-2019 is based on both default and adjusted TALYS (Koning and Rochman, 2012) calculations. Also the TENDL-2017 (Koning et al., 2017) results are shown that are only marginally different.
During the recent analyses of the (d,p) reactions on many elements we were confronted with a large underestimation of the measured cross sections. We come to the conclusion that the experimentally observed cross sections of the (d,p) reaction cannot be reproduced below 20-30 MeV with the available statistical model codes. It is well known that for the (d,p) reactions at low energies the direct stripping process plays a very important role.
To achieve now a better description of available data, the versions ALIC-IPPE-D and EMPIRE-II-D are used where a phenomenological enhancement factor K in these relations was taken as energy dependent and was estimated to describe the whole set of the observed (d,p) cross sections for medium and heavy nuclei. The direct (d,p) channel is strongly increased through this adaptation and this is reflected in changes for all other reaction channels in both codes.
As ALICE-IPPE calculates only the total cross section, for estimation of isomeric states from the ALICE code the isomeric ratios calculated by EMPIRE-D were applied.

Results
The measured experimental cross-section data are shown in Figs. 2-19 together with the predictions of the theoretical models and the results of the earlier measurement found in Mito et al. (1969). The calculated data are presented up to 70 MeV to illustrate the tendencies and the predictivity of the model calculations. The numerical values of the new experimental results are presented in Tables 3 and 4.

Cross sections of residual radionuclides of rhodium
The radioisotopes of rhodium are produced only by direct (d,xn) reactions. The contributing reactions and the reaction Q-values are presented in Table 2.   Fig. 2, together with theoretical estimations. Above 18 MeV the best estimation is given by the EMPIRE-D, but it strongly overestimates around the maximum. The cross section peak could not be reconstructed by our measurement but the prediction of ALICE-D is the best around the peak energy. Both TENDL versions strongly underestimate in the whole energy region and they give the same result. The only experimental results at low energies are obviously lower than ours.

The nat Ru(d,xn) 102m Rh process
The 3.742 y half-life isomeric state decays for 0.233% by IT to the   207.3 d half-life ground state and for the rest by EC to stable 102 Ru. The production cross sections of the 102m Rh are shown in Fig. 3together with theoretical estimations. Now the best estimation is given by the ALICE-D in the whole energy region. Both TENDL versions give identical results, mostly overestimate the experimental data and fail in giving the peak positions. The EMPIRE-D overestimates the experimental data.

The nat Ru(d,xn) 102g Rh process
The 102g Rh (T 1/2 = 207.3 d) decays with ε: 78% and β − : 22% to stable 102 Ru. The experimental data were obtained by subtracting the small contribution of the isomeric state, i.e. direct production cross sections are presented (Fig. 4). Now the best results are given by EMPIRE-D, both ALICE-D and the TENDL underestimate the experimental results.

The nat Ru(d,xn) 101m Rh process
The radionuclide 101 Rh has two states: a high spin isomer ( 101m Rh, T 1/2 = 4.34 d, IT: 7.20% ε: 92.8%) and the longer-lived ground state ( 101g Rh, T 1/2 = 3.3 y, ε: 100%). We obtained the production cross section of the isomeric state as can be seen in Fig. 5. None of the theoretical model codes give an acceptable estimation now, except the EMPIRE-D predictions between 40 and 50 MeV. The single dataset at low energies (Sitarz, 2019) is slightly lower than our new data.

The nat Ru(d,xn) 101g Rh (m+) process
The cross section for the ground state formation of 101g Rh (T 1/2 = 3.3 y), after the complete decay of the isomeric state, is shown in Fig. 6. The experimental data are a bit more scattered here, but one can state that the EMPIRE-D gives the best approximation above 25 MeV while ALICE-D below, which runs almost together with the both TENDL versions under 20 MeV.

The nat Ru(d,xn) 100g Rh(m+) process
The experimental and theoretical results for production of ground state of 100 Rh (T 1/2 = 20.8 h, ε: 100%), obtained after complete decay of short-lived isomeric state (T 1/2 = 4.6 min, IT: 98.3%, ε: 1.7%) are shown in Fig. 7. All theoretical model codes overestimate the experimental results, only the approximation of ALICE-D is acceptable between 43 and 50 MeV. The only literature data (Sitarz, 2019) is slightly lower than ours.

The nat Ru(d,xn) 99m Rh process
The radionuclide 99 Rh has two long-lived states decaying independently: a shorter-lived, high spin isomer (T 1/2 = 4.7 h, ε: 100%) and the longer-lived ground state (T 1/2 = 16.1 d, ε > 99.84 %IT < 0.16%). We could measure the cross section data for both states separately. The experimental and theoretical results for direct production of the isomeric state are shown in Fig. 8. The theoretical model codes overestimate our experimental data and some of them produce even local maxima, which could not be confirmed by the experiment. A single literature dataset at low energies (Sitarz, 2019) is proved to be lower than ours.

The nat Ru(d,xn) 99g Rh process
The experimental and theoretical results for direct production of the ground state (T 1/2 = 16.1 d) are shown in Fig. 9. The theoretical model codes again overestimate the experiment and produce strange local maxima and minima. The available experimental literature data (Sitarz, 2019) is lower than ours.

Cross sections of residual radionuclides of ruthenium
The radioisotopes of ruthenium are produced by direct (d,pxn) reactions and through the decay of parent radioisotopes. The contributing reactions and the reaction Q-values are presented in Table 2.

The nat Ru(d,x) 105 Ru process
The 105 Ru (T 1/2 = 4.44 h, β − : 100%) is produced via the 104 Ru (d,p) reaction. The new data are shown in Fig. 10, together with the earlier experimental data (Mito et al., 1969). These literature data, expressed in the original publication as reaction cross sections on single target isotopes, are normalized to natural isotopic contribution. The agreement with the present experiment is satisfactory. Good approximation is given above 20 MeV by ALICE-D, EMPIRE-D and systematics. All theoretical model codes fail in estimation of the peak cross section peak value, while       the TENDL versions underestimate the experimental results in the whole energy region. The low energy experimental literature data of (Sitarz, 2019) are lower than ours.

The nat Ru(d,x) 103 Ru process
The 103 Rh (T 1/2 = 39.247 d, IT: 100%) is produced directly and through the decay of short-lived 103 Tc (54.2 s, β − : 100%). The measured cumulative cross sections, the normalized (d,p) literature data (Mito et al., 1969;Sitarz, 2019) and the theoretical results are shown in Fig. 11. The low energy data of (Mito et al., 1969) are 20% higher than our data and the data of (Sitarz, 2019) are much lower than our values at the same energy. The theoretical codes agreements are varying: above

Cross sections of residual radionuclides of technetium
The radioisotopes of technetium are produced by direct (d, 2pxn) reactions (possibly clustered into α-emission) and through the decay of parent ruthenium radioisotopes. The contributing reactions and the reaction Q-values are presented in Table 2.

The nat Ru(d,x) 99m Tc process
We have obtained cross sections for direct (d, 2pxn) production of the 99m Tc isomeric state (T 1/2 = 6.0072 h, β − : 0.0037%, IT: 99.9963%) (Fig. 14). Due to the very long half-life of 99g Tc (T 1/2 = 2.111 × 10 5 y, β − : 100%) it is practically impossible that any significant amount is contributed by the mother decay. EMPIRE gives a good approximation above 32 MeV but overestimates the peak around 22 MeV. All other theoretical models fail in a great amount.

The nat Ru(d,x) 96g Tc process
The ground state 96g Tc (T 1/2 = 4.28 d, ε: 100%) is produced directly and by the decay of its short-lived isomeric state 96m Tc (T 1/2 = 51.5 min, ε: 2.0%, IT: 98%). Due to the several hours of cooling time between EOB and the first spectra measurement the isomeric state practically decayed out and its activity was not detected. The cross sections of the 96g Tc (m+) are shown in Fig. 15. The best prediction for the experimental results is given by the ALICE-D in the whole energy region. The approximation of the TENDL-2019 is also acceptable, and in this figure the improvement from TENDL-2017 to 2019 is clearly seen.

The nat Ru(d,x) 95m Tc process
The radionuclide 95 Tc has two isomeric states: a longer-lived metastable state 95m Tc (T 1/2 = 61 d, ε: 96.12%, IT: 3.88%) and the ground state 95g Tc (T 1/2 = 20.0 h, ε: 100%). Both states are populated by decay of the 95 Ru (T 1/2 = 1.643 h, ε: 100%) parent. The cross section data of 95m Tc represent cumulative cross sections, obtained from spectra measured after the complete decay of 95 Ru parent (Fig. 16). The estimation of the EMPIRE-D is the best again, ALICE-D and both TENDL versions underestimate above 25 MeV.

The nat Ru(d,x) 95g Tc process
The cumulative cross section data for 95g Tc (T 1/2 = 20.0 h) were deduced from the second series of spectra measurements (21.7-29.0 h) after EOB, where 95 Ru (T 1/2 = 1.643 h) decayed out and the contribution of the decay of longer-lived 95m Tc (T 1/2 = 61 d, ε: 96.12%, IT: 3.88%) can be practically neglected according to our calculation. The measured 95g Tc cross sections hence represent the direct production plus the decay of 95 Ru (Fig. 17). In this case the approximation of the TENDL versions is acceptable.

The nat Ru(d,x) 94g Tc process
Out of the two listed isomers of 94 Tc we can deduce cross sections only for production of the ground state 94g Tc (T 1/2 = 293 min, ε: 100%), as the rather short half-life of the metastable 94m Tc (T 1/2 = 52.0 min, ε: 100%) and the time schedule of our gamma spectra measurement did not allow assessment of its activity. The measured cross sections are cumulative containing the complete decay of 94 Ru (T 1/2 = 51.8 min, ε: 100%) (Fig. 18). In this case the approximations of the 4 model codes/ versions run together from 20 to 40 MeV and show also acceptable agreement with our new results. Above 40 MeV the TENDL-2019 estimation gives acceptable results.

The nat Ru(d,x) 93g Tc process
The 93g Tc (2.75 h, ε: 100%) is produced directly, from the decay of its isomeric state ( 93m Tc, 43.5 min, ε: 22.6%, IT: 77.4%) and through the decay of the 93m Ru (10.8 s, IT: 22.0%, ε: 78%) and 93g Ru (59.7 s, ε: 100%) parent isotopes. The measured and calculated cross sections are shown in Fig. 19. The experimental data have large uncertainties, due to the low statistics and it can be a reason why the comparison with the theoretical model calculations only shows a general underestimation of the experimental results.

Integral yields
The integral yields calculated from spline fits to our experimental excitation functions are shown in Figs. 20-22. The integral yields represent so called physical yields i.e. activity for instantaneous production rates (Bonardi, 1987;Otuka and Takacs, 2015). No experimental thick target yield data were found in the literature for comparison.

On application for production of medical radioisotopes
We shortly summarize the possible role of the deuteron induced reactions on ruthenium for production of medical radioisotopes, by comparing integral production yields of charged particle production routes for 105 Rh, 103 Ru/ 103m Rh, 101m Rh, 101 Rh, 97 Ru, 99m Tc and 95g Tc. In practice of course also many other factors play an important role in the selection of an optimal production route (available accelerator, radionuclide purity and specific activity, target preparation and recovery, required chemical separation, etc.). We compare the production yield on natural targets as deduced from cross section results of our group or from the activation database, if a reaction was not studied by us, with the aim to indicate the production power of deuterons. For real production of medical isotopes, the comparison has to be more specific as often using nuclear reactions on highly enriched monoisotopic targets is required, especially to ensure better purity and specific activity of the end product.

Production of 105 Rh
The radionuclide 105 Rh is considered as a low-energy β − emitter for therapy in small tumors. 105 Rh radionuclide can be produced by nuclear reactors using an enriched 104 Ru target via the indirect 104 Ru (n,γ) 105 Ru  → 105 Rh processes. It is also possible to obtain 105 Rh as a fission product of uranium and thorium. 105 Rh can also be produced using cyclotrons through the proton and deuteron irradiations on palladium targets or deuteron induced reactions on ruthenium. The corresponding integral yields for charged particle routes are shown in Fig. 23. The integral yields are based on experimental cross sections Tarkanyi 2016(Tárkányi et al., 2016 for nat Pd(p,x) 105 Rh and of (Ditrói et al., 2012a) and  for nat Pd(d,x) 105 Rh and our present data for nat Ru(d,xn) 105 Rh reaction.
Additional cross section data from r (Khandaker et al., 2010) also exist but were not exploited here. From Fig. 23 it is obvious that the highest yield can be reached by irradiation of ruthenium targets with deuterons. Even the energy range is within the deuteron energy of the compact cyclotrons. The proton and deuteron reactions on Pd have lower, but very similar yields.

103
Pd is a parent isotope (EC decay) of 103m Rh (T 1/2 = 56.1 min), an isotope of interest for Auger electron therapy. The integral yield data for production of 103 Pd using proton or deuteron induced reactions on 103 Rh via the 103 Rh(p,n) 103 Pd and 103 Rh(d,2n) 103 Pd reactions were taken from the IAEA recommended database (Qaim et al., 2011).
Another route to produce 103m Rh is the β − decay of parent 103 Ru (T 1/ 2 = 39.35 d). The 103 Ru can be obtained as fission products of 235 U (n, f) 103 Ru or 232 Th (p,f) 103 Ru (not exploited here), by alpha induced reactions on molybdenum ( (Graf and Munzel, 1974), (Esterlund and Pate, 1965), (Abe et al., 1984), (Ditrói et al., 2012b) and (Tarkanyi et al., 2017)) and via proton (in progress) and deuteron induced reactions (this work) on ruthenium. The integral yields deduced from cross section measurements of our group ([26] and this work) are shown in Fig. 24. For production of 103m Rh the proton and deuteron induced reactions on  F. Tárkányi et al. 103 Rh (through parent 103 Pd) are the favorites. All the routes through 103 Ru mother are less productive.

Production of 101g Rh
Long-lived 101g Rh (T 1/2 = 3.3 y) is proposed as an alternative to the existing High Dose Rate sources used in brachytherapy. This radionuclide can be produced indirectly through 101 Pd (see 101m Rh above) and  directly via nat Pd(p,x) 101g Rh ((Tárkányi et al., 2016), (Hien et al., 2018)), nat Pd(d,x) 101g Rh ((Ditrói et al., 2012a), ), nat Ru(d,x) 101 Rh (this work). Integral yields of charged particle induced reactions, based on results of our group, are collected in Fig. 26. The deuteron induced reaction on Ru has the highest yields for production of 101g Rh (Fig. 26).

Production of 99m Tc
Technetium-99 m is the worldwide most used radioactive tracer for SPECT. It can be produced directly or through the decay of its 99 Mo   Fig. 27. Integral yields of charged particle induced reactions for production of 97 Ru. Fig. 28. Integral yields of charged particle induced reactions for production of 99m Tc.

Summary and conclusions
We have measured the excitation functions on natural ruthenium for production of 105 Rh, 102m Rh, 102g Rh, 101m Rh, 101g Rh, 100g Rh, 99m Rh, 99g Rh, 105 Ru, 103 Ru (cum), 102 Ru (cum), 97 Ru (cum), 95 Ru (cum), 99m Tc, 96g Tc (m+), 95m Tc (cum), 95g Tc (cum), 94g Tc, 93g Tc (m+) up to 50 MeV and presented cross section results for the first time in the whole energy range. The experimental cross sections are compared with our calculations using the ALICE-D and EMPIRE-D theoretical codes and with TALYS (from TENDL database) theoretical results, showing in many cases significant disagreements.
In several of our earlier studies we have shown that deuteron induced reactions are competitive with protons, especially for targets above the middle mass region. This opens also the possibility to produce additional products, not reachable with proton reactions on the same targets, by using (d,n), and (d,p) reactions. For production of isotopes the widely used H + cyclotrons can, if the option is foreseen, also assure high intensity deuteron beams. To illustrate the production power of deuteron induced reactions we have compared the production yields of the presently studied reactions with other light charged particles for production of a few medical isotopes. The comparison shows that the deuteron induced nuclear reactions, from point of view the production yields, are in many cases promising.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.