Investigation of the deuteron induced nuclear reaction cross sections on lutetium up to 50 MeV: review of production routes for 177Lu, 175Hf and 172Hf via charged particle activation

In a systematic study of light charged particle induced nuclear reactions we investigated the excitation functions of deuteron induced nuclear reactions on natural lutetium targets. Experimental excitation functions up to 50 MeV on high purity natLu were determined using the standard stacked foil activation technique. High resolution off-line gamma-ray spectrometry was applied to assess the activity of each foil. From the measured activity direct and/or cumulative elemental cross-section data for production of 171,172,173,175Hf, 171,172,173,174g,176m,177m,177gLu and 169Yb radioisotopes were determined. The experimental data were compared to results of the TALYS theoretical code taken from the TENDL databases and results of our calculations using the ALICE-IPPE-D and the EMPIRE-D codes. No earlier experimental data were found in the literature. Thick target yields for the investigated radionuclides were calculated from the measured excitation functions.


Introduction
Presently, the proton induced reactions play major role in different applications due to simpler production of high energy/intensity proton beams, to low stopping-power, and to the relatively high cross sections of the reactions. The second most important light charged particle is deuteron, due to simple production of high intensity beam, the moderate stopping compared to heavier particles, relatively high cross sections, and to production of high intensity neutrons via break up. The activation cross sections of deuteron induced reactions are important for a wide variety of applications: isotope production, accelerator technology and material studies, thin layer activation (TLA) for wear studies.
A few decades ago the status of the database for deuteron induced reactions was relatively poor compared to that was available for proton induced reactions, and the quality of the theoretical descriptions was, even after several attempts for improvement, far from being acceptable. Therefore, we have started systematic study of activation cross sections of deuteron induced reactions in a broad international cooperation. The already reported, peer reviewed, investigations include around 640 reactions induced on 61 target elements: Be, B, C, N, Ne, Mg, Al, Si, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, Kr, Sr, Y, Zr, Nb, Mo, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, Xe, Cs, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Er, Tm, Yb, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl and Pb. A significant part of the cross section data was reported for the first time. A systematic comparison with the results calculated with theoretical models allows conclusions on the predictivity of the different codes (ALICE-IPPE, EMPIRE, GNASH, TALYS, PHITS). The database was especially poorly populated for rare earths, due to more limited applications (compared to metals) and to the more complicated target preparation. In the present work we report on cross section data on natural lutetium (missing in our rare earth list), for which no experimental data are available in the literature.
Preliminary results were presented in the RANC-2016 conference [1]. The activation cross section data for production of 172 Hf on natural hafnium were published in our paper investigating production routes of the 172 Hf/ 172 Lu generator and 169 Yb [2].

Target preparation
Due to limited beam time only one stack was prepared containing 25 high purity lutetium foils (Goodfellow) with natural isotopic composition and nominal thickness of 110 µm interleaved with 27 µm aluminum beam monitor foils (Goodfellow). The aluminum foils were evenly distributed in the stacks to cover the full energy range. The number of target atoms was determined by measuring the surface and weight of the individual foils.

Irradiation
The stacks were irradiated at the Cyclone 90 cyclotron of Université Catholique in Louvain la Neuve (LLN) Belgium using our standard Faraday-cup type target holder. Irradiation took place with a constant 100 nA beam current for 40 min. The primary beam energy was determined by the settings of the cyclotron. Both the beam energy and intensity were corrected on the basis of the detailed re-measured and analyzed excitation function of the nat Al(d,x) 22,24 Na monitor reactions compared to the latest recommended values [3]. The recoil fragments from the Al targets were corrected by 22,24 Na activities measured in the Lu samples positioned behind Al in the stack ("corrected" in Fig. 1), but the results without recoil correction are also presented for comparison ("uncorrected" in Fig. 1). As can be seen in Fig. 1 for the 27 Al(d,x) 24 Na monitor reaction, the agreement is very good over the whole energy range without any correction in energy or beam current. The main parameters of the experiment and the methods of data evaluations with references are summarized in Table 1.
The activity produced in the target and monitor foils was measured non-destructively (without chemical separation) at VUB-Brussels cyclotron laboratory with a high resolution off-line HPGe gamma-ray spectrometer coupled to a Canberra-GENIE acquisition system. The evaluation of the measured spectra and the determination of the net counts in the gamma-ray peaks were made by the peak fitting algorithm included in the GENIE software package and by the interactive Forgamma software [4]. The irradiated foils were measured at three different times after the EOB (End of Bombardment). The first acquisition started 7.4 h after the EOB due to the initial high activity and transport from the irradiation to the measurement site.
Direct and/or cumulative elemental cross section data were determined from the measured activity of the reaction products. Some of the radionuclides formed are the result of cumulative processes where decay of parent nuclides or metastable state contributes to the production process. The used nuclear data (half-lives and gamma branching ratios), the possible contributing reactions and their Q-values are shown in Table 2. The listed Q-values refer to formation of the ground state. The energy degradation as a function of penetration of the bombarding particles in the stack was determined by a stopping calculation and based on incident energy according to the monitor reaction. The uncertainty Fig. 1 Application of monitor reactions for determination of deuteron beam energy and intensity on each experimental cross section data point was estimated by taking the square root of the sum in quadrature of all individual contributing error components, supposing equal sensitivities for the linearly contributing different parameters appearing in the formula: counting statistics 1-18%, detector efficiency 5-7%, gamma intensities 1-3%, effective target thickness 5% and beam current 7%. The contributions on the uncertainties of non-linear parameters were neglected (time, half-life, etc.). Taking into account the cumulative effects of possible uncertainties of the primary incident energy, of the thickness and homogeneity of the different targets and of the energy straggling the uncertainty on the median energy in each foil varies between ± 0.3 and ± 1.1 MeV from the first to the last.

Model calculations
The updated ALICE-IPPE-D [14] and EMPIRE-D [15] codes were used to analyse the experimental results. As described in detail in our earlier publications, Tárkányi et al. [19] and Hermanne et al. [20], these modified codes were developed to assure a better description of deuteron induced reactions. In the standard versions of the codes a simulation of direct (d,p) and (d,t) phenomena is included through an energy dependent enhancement factor for the corresponding transitions. The parameters were taken as described in Belgya et al. [21]. The theoretical data from the TENDL-2017, Koning 2017 [22] and the TENDL-2019 [17] libraries (based on the modified TALYS 1.9 code, Koning 2017 [23] and standard input parameters) was also used for a comparison. For most activation products also the values for the TENDL-2015, calculated with an earlier TALYS version are shown in order to demonstrate only marginal differences between them.

Cross sections
The cross sections for all the reactions studied are shown in Figs. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and 13 and the numerical values are collected in Tables 3, 4 and 5. For completeness we have included also the cross section data for production of 172 Hf, measured in present study and reported earlier in [2]. Although all activation products except 177 Lu are formed in reactions on both stable Lu isotopes, remarkable surplus of 175 Lu over 176 Lu (97.4/2.6) results in dominance of the reactions on 175 Lu and in presence of a single peak in the measured excitation functions.    Table 2) should be multiplied by 0.055 to get absolute intensities if one makes an assumption that the ground state of Lu is not fed by β +decay. According to the present data the ground state is fed by 0.007% β + -decay, hence the multiplication factor should be a little less.
We have used factor of 0.04 (see values in Table 2) in the cross section evaluation process (which can be corrected according to new valuations in the future) to get a similar difference between our values and the EMPIRE prediction (good threshold) as for 171 Lu (Fig. 12), where the contribution of parent 171 Hf is dominating. The multiplication factor has been normalized to 100% for the 469.3 keV γ-line. The TENDL and ALICE-D curves are shifted to lower energy (Fig. 5). There is large difference in magnitude between the theoretical data sets near the maximum. Our experimental data can be adapted when more precise decay data are agreed on, but with the present values our experimental results are between the EMPIRE-D and the ALICE-D calculations.   (Fig. 6).
The 177g Lu was identified through its 208.3662 keV γ-line. This line is also present in the β − decay of 177m Lu, but its contribution can be neglected due to the low cross section for its production and the low activity because of its long half-life. Although, in principle the measured cross sections for 177g Lu are cumulative, the formation through the limited IT (24.1%) of the low induced activity 177m Lu is negligible under our measuring conditions (cooling time for measurement of ground state is short compared to the long-half-life of metastable state) (Fig. 7).
The underestimation of the 177m Lu experimental data by the standard EMPIRE-D and ALICE-D prediction is very significant, while the TENDL is about 40% lower. It is remarkable that the ALICE-D and EMPIRE-D can give an acceptable prediction for the (d,p) reaction leading to 177g Lu while the predicted values of the TENDL libraries are significantly lower (Figs. 6, 7).

nat Lu(d,x) 176m Lu reaction
The cross sections for formation of 176m Lu, (3.635 h, 99.905% β − , 1 − ) were obtained through its 88.361 keV γ-line (Fig. 8). The contribution from same energy γ-line of the quasi-stable 176g Lu (3.76 × 10 10 y) can be neglected and it is also the case for the low abundance γ-line with similar energy of 177m Lu (160.44 d, 88.4 keV, 0.037%). As for the previous reaction the TENDL data for the process where emission of a proton is involved, are very low (Fig. 8). The best approximation is given by the ALICE-D. In Fig. 8 also the results of systematics based on the TENDL-2011 on-line library, which was involved in the FENDL-3 database, is presented. This prediction gives also a good approximation of the experimental data, especially from the point of view of the maximum value.

nat Lu(d,x) 174g Lu reaction
The 174 Lu has two long-lived states, the 174m Lu (142 d, (6-) IT: 99.38%) metastable state and the 174g Lu (3.31 y) ground state. We obtained cross section data for direct production of the ground state (Fig. 9). Taking into account the predicted cross sections for formation of 174m Lu, the decay data and the time of the irradiation and the measurements of the 174g Lu spectra (see Table 1), the contribution from the decay of the metastable state is very low compared with the actual uncertainties, but the experimental curve was corrected with it. Agreement with the TENDL results is acceptable, but in  (Fig. 9).

Lu(d,x) 173 Lu reaction
The 173 Lu (1.37 y) is produced directly and through the decay of its 173 Hf parent (23.6 h). We measured cumulative production cross section of 173 Lu from spectra collected after nearly complete decay of the parent. We deduce cross section data also for direct production by subtracting the contribution of the 173 Hf decay (Fig. 10). The magnitudes of theoretical results are very different both for the direct and for the cumulative production (Fig. 10), only the ALICE-D direct prediction agrees very well with our experimental data corrected for the 173 Hf decay.

nat Lu(d,x) 172 Lu reaction
The ground-state of 172 Lu (6.70 d) is produced directly, through the decay of its short-lived metastable state (3.7 min, IT: 100%) and through the decay of its long-lived 172 Hf parent (1.87 y, ε: 100%). The cross sections were measured from spectra measured a few hours after EOB, in which the effect of decay of 172 Hf for production of 172 Lu is very low, but has been taken into account. The measured cumulative cross sections for the direct production cross section (m + g)  Fig. 11. The agreement with description of the theoretical codes is moderate, but disagreement especially in shape and energy shift of the effective threshold can be noted, especially the TALYS calculations are more consistent with our experimental data than the both other codes.

Lu(d,x) 171 Lu(cum) reaction
The cross sections for cumulative production of the groundstate of 171 Lu (8.24 d) are shown in Fig. 12. It includes the direct production, the decay of the short lived isomeric state (79 s, IT: 100%) and the decay of the 171 Hf parent (12.1 h, ε: 100%). The TENDL-2017, 2019 (and TENDL-2015 with slightly larger values above 43 MeV) and ALICE-D cumulative data are shifted to lower energy because of the contribution of 171 Hf that already showed this difference between experiment and theory (Fig. 5). The 171 Hf contribution has not been subtracted because of the uncertain intensity data of 171 Hf. The shape, the effective threshold and the magnitude of the results of the different theoretical codes differ significantly. The best agreement is seen with the prediction of the EMPIRE-D code.

nat Lu(d,x) 169 Yb reaction
The practical threshold of 36 MeV indicates that clustered emission is involved in formation of 169 Yb and that in the investigated energy range (up to 50 MeV) the predominant reaction is nat Lu(d,αxn) (see Table 2). The experimental data are significantly higher than the TENDL-2017, 2019 prediction, as well as significantly lower compared to ALICE-D and EMPIRE-D (Fig. 13).

Integral yields
Integral yields were calculated from excitation functions constructed by an analytical fit to our experimental cross section data points (Fig. 14). The so-called physical integral yield [12]. Otuka [13] was calculated (yield at EOB for an instantaneous irradiation, i.e. no decay corrections).

Review of production options of 177 Lu, 175 Hf and 172 Hf with charged particle nuclear reactions
The new experimental data provide a basis for improved model calculations and for optimization various charged particle production routes. Concerning applications in nuclear medicine among the investigated radioisotopes the 177 Lu (variety of therapeutic procedures, theranostic), 176m Lu (in SPECT, to image the distribution of lutetium), 175 Hf for nuclear-medical investigations and for off-line chemical studies of Group IV homologs, 172 Hf-172 Lu (radionuclide generator for industrial radiotracer applications and for pre-clinical bio-distribution studies), 169 Yb (brachytherapy, as an alternative to 125 I) have established practical applications. In the following chapters we compare the production yields of the deuteron induced reactions with other charged particle production routes. Of course for production of the above mentioned radioisotopes many other parameters should be taken into account.

177
Lu production

Non-charged particle production routes
The widely used, non-charged particle production routes use nuclear reactors and high intensity gamma sources [25]. In case of 176 Yb(n,γ)-177 Yb-177 Lu indirect route the product has high specific activity and it is close to carrier free. In case of direct production 177 Lu(n,γ) 177 Lu the product is not carrier free, but may still be produced in very high specific activity. By using the nat Hf(γ,x) 177 Lu reaction via high energy bremsstrahlung photons hundreds of mCi of 177 Lu activity can be obtained on targets from 10 g enriched hafnium-oxide [26].
As it is seen from Fig. 15, the best way to produce 177 Lu is the Yb + d reaction, if a high energy accelerator is available.   (Fig. 16).
The product in all cases is no carrier added, in case of 175 Lu(p,n) reaction the product is of high specific activitz. By using natural Lu target the deuteron route is much more productive. By using highly enriched targets the yield of the 176 Lu(p,2n) is higher. Comparing the proton and deuteron induced reactions on Lu one can conclude that the deuteron reaction has much higher cross sections, but at higher energies, which excludes compact cyclotrons with deuteron option under 10 MeV.

Hf production
We have compared the charged particle production routes for 172 Hf/ 172 Lu generator in our previous paper [2]. Here we reproduce the figure of production yields completed with Lu + d reaction. In accordance with Fig. 17 in the low energy range the Yb + α, at high energies the Lu + p reactions are

Summary and conclusions
In the frame of a systematic study of activation cross sections of deuteron induced reactions we report experimental cross sections for the nat Lu(d, Concerning the use of deuteron induced nuclear reactions for production of medically relevant 177 Lu, 175 Hf and 172 Hf, in case of 177 Lu the product is carrier added. Yield calculations based on excitation functions for production of the 175 Hf show that the nat Lu + d yield is the highest comparing to nat Lu + p and Yb + α routes, but in the case of enriched 176 Lu target the proton induced reaction gives higher yield. By comparing the production routes of 172 Hf via Lu + p, Lu + d, Yb + α, Ta + p and W + p reactions up to 70 MeV, we clearly see that the Lu + d yields are also high and at higher energies almost as high as those for the Lu + p route. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/.