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 172Hf on natural hafnium were published in our paper investigating production routes of the 172Hf/172Lu generator and 169Yb [2].

Experiment and data evaluation

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 natAl(d,x)22,24Na monitor reactions compared to the latest recommended values [3]. The recoil fragments from the Al targets were corrected by 22,24Na 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 27Al(d,x)24Na 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.

Fig. 1
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Application of monitor reactions for determination of deuteron beam energy and intensity

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Table 1 Main parameters of the experiment and the methods of data evaluation
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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 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.

Table 2 Decay characteristics of the investigated activation products (primary evaluation peaks are bold) [8, 18]
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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.

Results

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 172Hf, measured in present study and reported earlier in [2]. Although all activation products except 177Lu are formed in reactions on both stable Lu isotopes, remarkable surplus of 175Lu over 176Lu (97.4/2.6) results in dominance of the reactions on 175Lu and in presence of a single peak in the measured excitation functions.

Fig. 2
figure 2

Experimental and theoretical excitation functions for the natLu(d,x)175Hf reaction

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Fig. 3
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Experimental and theoretical excitation functions for the natLu(d,x)173Hf reaction

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Fig. 4
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Experimental and theoretical excitation functions for the natLu(d,x)172Hf reaction

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Fig. 5
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Experimental and theoretical excitation functions for the natLu(d,x)171Hf reaction

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Fig. 6
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Experimental and theoretical excitation functions for the natLu(d,x)177mLu reaction

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Fig. 7
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Experimental and theoretical excitation functions for the natLu(d,x)177gLu reaction

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Fig. 8
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Experimental and theoretical excitation functions for the natLu(d,x)176mLu reaction

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Fig. 9
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Experimental and theoretical excitation functions for the natLu(d,x)174gLu reaction (corrected for 174mLu contribution)

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Fig. 10
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Experimental and theoretical excitation functions for the natLu(d,x)173Lu reaction

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Fig. 11
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Experimental and theoretical excitation functions for the natLu(d,x)172Lu reaction

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Fig. 12
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Experimental and theoretical excitation functions for the natLu(d,x)171Lu(cum) reaction

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Fig. 13
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Experimental and theoretical excitation functions for the natLu(d,x)169Yb reaction

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Table 3 Cross sections of deuteron induced reactions on lutetium for production of 171Hf,172Hf, 173Hf and 175Hf radionuclei
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Table 4 Cross sections of deuteron induced reactions on lutetium for production of 171(m+g)Lu, 172(m+g)Lu, 173Lu and 174gLu radionuclei
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Table 5 Cross sections of deuteron induced reactions on lutetium for production of 176mLu, 177mLu, 177gLu and 169Yb radionuclei
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natLu(d,x)175Hf reaction

The radionuclide 175Hf has a long, 70-day half-life and only one intense gamma-line at Eγ = 343.4 keV (Iγ = 84%). 175Hf is produced directly in (d,xn) reactions. Data are shown in Fig. 2 together with the result of TALYS calculation taken from TENDL-2017, -2019 data libraries (marginally difference with TENDL-2015) and results of ALICE-D and EMPIRE-D calculations. Our experimental data points fit well on the TENDL curves, except the maximum. Both EMPIRE and ALICE fail to give an acceptable approximation.

natLu(d,x)173Hf reaction

The radionuclide 173Hf (T1/2 = 23.6 h) can be produced directly in (d,xn) reactions. This radionuclide has several intense independent gamma-lines. The cross sections were determined by using the Eγ = 123.7 keV (Iγ = 83%) gamma-line considered to be interference free and confirmed by the results of the other three intense gamma-lines (Iγ > 10%). Data are shown in Fig. 3 together with the result of the TALYS, ALICE-D and EMPIRE-D calculations. Some energy shifts of the two TENDL predictions can be observed but the prediction of the energy dependent behavior and maximum cross section value are good. The ALICE-D and EMPIRE-D codes overestimate almost twice the experimental data.

natLu(d,x)172Hf reaction

The long-lived 172Lu (1.87 y) radioisotope is produced via 175Lu(d,5n) and 176Lu(d,6n) reactions. The cross sections were determined by using the most abundant 125.81 keV line among the few strong gamma lines. Comparing with TENDL predictions the agreement in magnitude is good, but the excitation functions (the 2017 and 2019 results are marginally different from the 2015 values) are shifted systematically by 2–3 MeV to the low energy (Fig. 4). The ALICE-D and EMPIRE-D codes overestimate the experiment twice at the maximum, and the ALICE-D predictions are shifted to lower energy.

natLu(d,x)171Hf reaction

The measured cross sections of 171 Lu (12.1 h) are based on the 347.20 keV (6% per decay) gamma-line. The absolute intensities of gamma-lines following the decay of 171Hf are still under question. The gamma-ray intensities of this reaction product available in different references are all relative. The latest recommendation found in the Nuclear Data Sheets [24] says that the relative intensities (see 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 171Lu (Fig. 12), where the contribution of parent 171Hf 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.

natLu(d,x)177mLu and natLu(d,x)177gLu reactions

The 177mLu (160.44 d, 23/2-, IT: 21.4%) and 177gLu (6.647 d) states are produced only via the 176Lu(d,p) reaction but results are expressed for natLu. For calculation of the cross section of the 177mLu the highest energy (lowest background) independent γ-line (418.5388 keV) was used, but under our measuring circumstances only poor statistics could be obtained (Fig. 6).

The 177gLu was identified through its 208.3662 keV γ-line. This line is also present in the β− decay of 177mLu, 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 177gLu are cumulative, the formation through the limited IT (24.1%) of the low induced activity 177mLu 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 177mLu 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 177gLu while the predicted values of the TENDL libraries are significantly lower (Figs. 6, 7).

natLu(d,x)176mLu reaction

The cross sections for formation of 176mLu, (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 176gLu (3.76 × 1010 y) can be neglected and it is also the case for the low abundance γ-line with similar energy of 177mLu (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.

natLu(d,x)174gLu reaction

The 174Lu has two long-lived states, the 174mLu (142 d, (6-) IT: 99.38%) metastable state and the 174gLu (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 174mLu, the decay data and the time of the irradiation and the measurements of the 174gLu 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 case of ALICE-D and EMPIRE-D the underestimation is significant (Fig. 9).

natLu(d,x)173Lu reaction

The 173Lu (1.37 y) is produced directly and through the decay of its 173Hf parent (23.6 h). We measured cumulative production cross section of 173Lu 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 173Hf 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 173Hf decay.

natLu(d,x)172Lu reaction

The ground-state of 172Lu (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 172Hf 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 172Hf for production of 172Lu is very low, but has been taken into account. The measured cumulative cross sections for the direct production cross section (m + g) are shown in 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.

natLu(d,x)171Lu(cum) reaction

The cross sections for cumulative production of the ground-state of 171Lu (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 171Hf 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 171Hf that already showed this difference between experiment and theory (Fig. 5). The 171Hf contribution has not been subtracted because of the uncertain intensity data of 171Hf. 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.

natLu(d,x)169Yb reaction

The practical threshold of 36 MeV indicates that clustered emission is involved in formation of 169Yb and that in the investigated energy range (up to 50 MeV) the predominant reaction is natLu(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).

Fig. 14
figure 14

Integral thick target yields for the formation of the investigated radioisotopes of hafnium, lutetium and ytterbium as a function of incident energy

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Review of production options of 177Lu, 175Hf and 172Hf 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 177Lu (variety of therapeutic procedures, theranostic), 176mLu (in SPECT, to image the distribution of lutetium), 175Hf for nuclear-medical investigations and for off-line chemical studies of Group IV homologs, 172Hf-172Lu (radionuclide generator for industrial radiotracer applications and for pre-clinical bio-distribution studies), 169Yb (brachytherapy, as an alternative to 125I) 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.

177Lu 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 176Yb(n,γ)-177Yb-177Lu indirect route the product has high specific activity and it is close to carrier free. In case of direct production 177Lu(n,γ)177Lu the product is not carrier free, but may still be produced in very high specific activity. By using the natHf(γ,x) 177Lu reaction via high energy bremsstrahlung photons hundreds of mCi of 177Lu activity can be obtained on targets from 10 g enriched hafnium-oxide [26].

Charged particle induced reactions

The production yields of natYb(d,x)177Lu, natHf(p,x)177Lu, natHf(d,x)177Lu, natLu(p,x) 177Lu, natLu(d,x)177Lu and natYb(α,x)177Lu routes are collected together for comparison (Fig. 15), The calculated integral yields are based on experimental data in the literature except natLu(p,x) where experimental data are missing therefore the TENDL-2019 data were used

Fig. 15
figure 15

Integral yields for production of 177Lu

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The production yield of natYb(d,x)177Lu reaction is based on experimental data reported by Manenti [27], Hermanne [28], Tarkanyi [29] and Tarkanyi [30], Khandaker [31], the natHf(p,x) on [32], the natHf(d,x) on [33], natLu(d,x) [this work] and the natYb(α,x) on [34, 35].

As it is seen from Fig. 15, the best way to produce 177Lu is the Yb + d reaction, if a high energy accelerator is available. In the case of a compact cyclotron with deuteron energies not higher than 10 MeV the Lu + d reaction (this work) gives an acceptable alternative.

175Hf production

The 175Hf can be produced via (p,xn) and (d,xn) reaction on natLu or on enriched 175Lu(97.41%) and 176Lu(2.59%) or on (α,xn) reaction on natYb. Experimental data are available for natLu(p,x)175Hf [36] (only cross section), natLu(d,x)175Hf (this work) and natYb(α,xn)175Hf [34] reactions (Fig. 16). The product in all cases is no carrier added, in case of 175Lu(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 176Lu(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.

Fig. 16
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Integral yields for production of 175Hf

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172Hf production

We have compared the charged particle production routes for 172Hf/172Lu 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 the more productive routes. The calculated integral yields are based on experimental data Tarkanyi 2017 [37], Michel 2002 [38], Titarenko 2011 [39].

Fig. 17
figure 17

Integral yields for production of 172Hf

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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 natLu(d,x) 171,172,173,175Hf, 171,172,173,174g,176m,177m,177gLu and 169Yb reactions up to 50 MeV. No earlier experimental data were found in the literature. The experimental data were compared with the results of a priori model calculations performed with the EMPIRE-D, ALICE-IPPE-D and TALYS codes (available in TENDL-2015, TENDL-2017 and TENDL-2019 on-line libraries) using reference input parameters. The descriptions of the shape and the absolute values of the excitation functions by the theoretical calculations is only partly successful, especially observed energy shifts, shape and magnitude disagreements underline the importance of the experimental data. There are only marginal differences on data of predictions of the applied latest versions.

Concerning the use of deuteron induced nuclear reactions for production of medically relevant 177Lu, 175Hf and 172Hf, in case of 177Lu the product is carrier added. Yield calculations based on excitation functions for production of the 175Hf show that the natLu + d yield is the highest comparing to natLu + p and Yb + α routes, but in the case of enriched 176Lu target the proton induced reaction gives higher yield. By comparing the production routes of 172Hf 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.