Optimization of Deuteron Irradiation of 176Yb for Producing 177Lu of High Specific Activity Exceeding 3000 GBq/mg

The irradiation of 176Yb with deuterons offers a promising pathway for the production of the theranostic radionuclide 177Lu. To optimize this process, calculations integrating deuteron transport, isotope production, and decay have been performed. In pure 176Yb, the undesired production of 174g+mLu occurs at higher deuteron energies, corresponding to a distribution slightly shallower than that of 177Lu. Hence, 174g+mLu can be effectively filtered out by employing either a low-energy deuteron beam or stacked foils. The utilization of stacked foils enables the production of 177Lu using a high-energy linear accelerator. Another unwanted isotope, 176mLu, is produced roughly at the same depth as 177Lu, but its concentration can be significantly reduced by selecting an appropriate post-irradiation processing time, owing to its relatively short half-life. The modeling approach extended to the mapping of yields as a function of irradiation time and post-irradiation processing time. An optimized processing time window was identified. The study demonstrates that a high-energy deuteron beam can be employed to produce 177Lu with high specific activity exceeding 3000 GBq/mg. The effect of different purity levels (ranging from 98% to 100%) was also discussed. The impurity levels have a slight impact. The modeling demonstrates the feasibility of obtaining 177Lu with a specific activity > 3000 GBq/mg and radionuclidic purity > 99.5% when using a commercially available 176Yb target of 99.6% purity.


Introduction
Theranostics is an emerging approach that combines therapeutic and diagnostic elements for effective cancer treatment [1].In this approach, radionuclides emitting low-energy gamma rays are used for diagnostic purposes, while those emitting charged particles such as beta rays and alpha particles are utilized for therapy.This fusion of diagnostics and therapy represents a significant advancement in personalized cancer treatment [2,3]. 177Lu has garnered considerable interest as a theranostic radionuclide due to its emission of beta rays with an energy of 134 keV and low-energy gamma rays at 208 keV [4,5].Combining 177 Lu with other therapeutic radionuclides, such as 90 Y/ 177 Lu and 67 Cu/ 177 Lu, has shown great promise in cancer treatment [6,7].The efficacy of 177 Lu in neuroendocrine tumors has been acknowledged by the US Food and Drug Administration (approved in 2018) and the European Medicines Agency (approved in 2017) [8].
The term "carrier-free" is used to describe radionuclides with the highest specific activity.This means that the final product has 100% isotopic abundance and is not contaminated with stable isotopes. 177Lu, which has a high specific activity, is particularly important in certain radiation therapies, although it may not be necessary for all types.For instance, in peptide receptor radionuclide therapy, the limited concentration of different cellular cognate receptors expressed on the tumor cell surface necessitates the use of 177 Lu with high specific activity.
Currently, the production of 177 Lu relies primarily on reactors using two production routes [9,10]: the "direct" route and the "indirect" route.In the direct route, the 176 Lu target is subjected to neutron irradiation via 176 Lu(n, γ) 177 Lu reactions.In comparison, the indirect route involves the use of a 176 Yb target via 176 Yb(n, γ) 177 Yb → 177 Lu reactions.Each route has its advantages and disadvantages.
The direct route benefits from the high thermal neutron capture cross-sections of 176 Lu, which is as high as 2090 barn [11,12].However, a drawback of the direct route is the production of 177m Lu as an impurity of concern.177m Lu has a relatively long halflife of 160.5 days, leading to an increasing ratio of 177m Lu/ 177 Lu over time.This poses challenges in hospital preparations, as the presence of 177m Lu triggers concerns regarding radioactive waste management.Currently, the average specific activity of the direct route is approximately 740 to 1100 GBq/mg, which needs further improvement.
The indirect production route is based on the 176 Yb(n, γ) 177 Yb → 177 Lu reactions.This route offers the advantage of producing high specific activity, approximately 2960 GBq/mg, as it does not generate 177m Lu as an impurity.Furthermore, the product obtained via the indirect route can be carrier-free.However, there are some disadvantages associated with the indirect production route.It has low production yields due to the low cross-section of 176 Yb, which is only 2.5 barns.Additionally, the chemical properties of Yb and Lu are very similar, posing challenges in the separation of Yb and Lu [13].For more information on the various methods under development for Yb/Lu separation, a comprehensive review can be found in reference [13].
Previous studies have modeled the utilization of deuteron irradiation on a Yb target for 177 Lu production [22,23].Kambali compared the production yields between (d,n) and (d,p) reactions [22].Nagai et al. systematically modeled the activities and specific activities of 177 Lu using deuteron beams of different energies and Yb targets of varying purities [23].Both studies suggested the feasibility of the overall processes.The present study aims to accomplish two objectives: firstly, to assess the feasibility of producing 177 Lu using a high-energy linear accelerator (LINAC); secondly, to optimize both the irradiation time and the post-irradiation processing time to attain the highest achievable specific activity.
LINAC is a unique type of accelerator that can achieve very high beam energy at a relatively low cost.However, both the ion species and beam energies are fixed characteristics determined by the beam design.In other words, if it is designed at high energy, it cannot be operated at low energies.A high-energy LINAC provides opportunities for isotope production that requires high threshold beam energies.Conversely, a high-energy beam may be less suitable for isotope production that necessitates low threshold energies.An example of such a high-energy accelerator is the LINAC, located in Denton, Texas.Originally manufactured as part of the superconducting supercollider project, it was designed to operate at a beam energy close to 70 MeV for isotope production.This LINAC utilized a design that originated from Los Alamos National Laboratory in the 1980s, specifically tailored for an energy range of 70 to 90 MeV for the nuclear medicine program at that time [24,25].Therefore, exploring the applications of high-energy LINACs for isotope production holds commercial value.It is worthwhile to investigate the feasibility of utilizing high-energy accelerators as versatile instruments capable of accommodating a wide range of isotopes requiring thermal energy at different energy levels, both low and high.
The current study utilized 80 MeV as an illustrative example of a high-energy LINAC.However, the proposed methodology is applicable to various high-energy LINACs, regardless of whether they operate at 80 MeV or not.The multiple foil target configurations, as proposed in the present study, can be adjusted based on the specific beam energy of any LINAC, making the approach versatile and not limited to Denton LINAC.For the same reason, the beam current was chosen to be typical of the Denton LINAC.Nevertheless, the obtained yields can be readily converted for other LINACs.Hence, the impact of this study extends to general high-energy LINACs and is not specific to the Denton LINAC.

Modeling Procedure
The modeling approach employed in this study consists of the following steps: (1) a Monte Carlo simulation code was utilized to determine the energy of deuterons at different penetration depths; (2) the localized energy is converted into localized isotope production using energy-dependent activation functions; (3) the effects of continuous ion bombardment (gain) and decay (loss) are calculated as functions of irradiation time and post-irradiation processing time; and (4) the amount of produced isotopes is integrated over the region of interest to calculate activity and specific activity.
The Stopping and Range of Ions in Matter (SRIM) code has been widely used in materials science for irradiation studies [26].However, SRIM does not directly provide detailed information about the local beam energy at different penetration depths as an output.Nevertheless, this information can be estimated reasonably well by analyzing the projected range of ions at various incident energies.Figure 1 plots the projected ranges of deuterons as a function of incident energy.For instance, at an incident energy of 80 MeV, the projected range of deuterium in Yb is approximately 9.2 mm.Conversely, at a lower energy of 60 MeV, the projected range reduces to 8 mm.This difference of 1 mm in range suggests that, in order for an 80 MeV beam to stop at 9.2 mm, its energy at a depth of 1 mm must be around 60 MeV.In other words, if we denote the projected range curve as R(E), where E is the incident energy as a variable, then for a selected incident energy E 0 , the energy at a depth of R(E 0 ) − R(E) from the surface is E. Figure 2 plots the local energy as a function of depth for different incident energies, calculated using the procedure described.
configurations, as proposed in the present study, can be adjusted based on the specific beam energy of any LINAC, making the approach versatile and not limited to Denton LINAC.For the same reason, the beam current was chosen to be typical of the Denton LINAC.Nevertheless, the obtained yields can be readily converted for other LINACs.Hence, the impact of this study extends to general high-energy LINACs and is not specific to the Denton LINAC.

Modeling Procedure
The modeling approach employed in this study consists of the following steps: (1) a Monte Carlo simulation code was utilized to determine the energy of deuterons at different penetration depths; (2) the localized energy is converted into localized isotope production using energy-dependent activation functions; (3) the effects of continuous ion bombardment (gain) and decay (loss) are calculated as functions of irradiation time and post-irradiation processing time; and (4) the amount of produced isotopes is integrated over the region of interest to calculate activity and specific activity.
The Stopping and Range of Ions in Matter (SRIM) code has been widely used in materials science for irradiation studies [26].However, SRIM does not directly provide detailed information about the local beam energy at different penetration depths as an output.Nevertheless, this information can be estimated reasonably well by analyzing the projected range of ions at various incident energies.Figure 1 plots the projected ranges of deuterons as a function of incident energy.For instance, at an incident energy of 80 MeV, the projected range of deuterium in Yb is approximately 9.2 mm.Conversely, at a lower energy of 60 MeV, the projected range reduces to 8 mm.This difference of 1 mm in range suggests that, in order for an 80 MeV beam to stop at 9.2 mm, its energy at a depth of 1 mm must be around 60 MeV.In other words, if we denote the projected range curve as R(E), where E is the incident energy as a variable, then for a selected incident energy  , the energy at a depth of ( ) − () from the surface is . Figure 2 plots the local energy as a function of depth for different incident energies, calculated using the procedure described.The utilization of Figure 2 to convert local beam energy into isotope production, based on energy-dependent cross-sections, assumes that straggling can be neglected.As a result, for a given incident energy, the energy values at each depth point are precise and have minimal uncertainty.This approximation holds true for protons and deuterons because their collisions with target atoms are primarily influenced by glancing angle collisions.Consequently, the ion trajectory remains a straight line for most of the penetration, except towards the very end, where low-energy collisions favor the creation of small damage cascades.
The available cross-section data for deuterium bombardment of Yb and other Yb isotopes are quite limited.Khandaker et al. conducted measurements on natural Yb and reported cross-section data for (d,x) reactions up to 24 MeV [27].Nagai et al. fitted these cross-section data and experimentally validated the integrated yields [23].Figure 3 plots the experimental activation functions for producing Lu in pure Yb [27], along with the fitted functions [23].Two reactions result in the production of 177  Yb undergoes β emission followed by gamma transitions in Lu , with a relatively short half-life of 1.88 h.Therefore, Lu can be approximated as the direct product of deuteron irradiation.It is important to note that the available experimental data is limited to energies up to 24 MeV.Further validation is required to assess the accuracy of the data at higher energies.The utilization of Figure 2 to convert local beam energy into isotope production, based on energy-dependent cross-sections, assumes that straggling can be neglected.As a result, for a given incident energy, the energy values at each depth point are precise and have minimal uncertainty.This approximation holds true for protons and deuterons because their collisions with target atoms are primarily influenced by glancing angle collisions.Consequently, the ion trajectory remains a straight line for most of the penetration, except towards the very end, where low-energy collisions favor the creation of small damage cascades.
The available cross-section data for deuterium bombardment of 176 Yb and other Yb isotopes are quite limited.Khandaker et al. conducted measurements on natural Yb and reported cross-section data for (d,x) reactions up to 24 MeV [27].Nagai et al. fitted these cross-section data and experimentally validated the integrated yields [23].Figure 3 plots the experimental activation functions for producing 177 Lu in pure 176 Yb [27], along with the fitted functions [23].Two reactions result in the production of 177 Lu.The first reaction is 176 Yb(d, n) 177 Lu, and the second reaction is 176 Yb(d, p) 177g+m Yb → 177 Lu .The cross-section of the 176 Yb(d, p) 177g+m Yb → 177 Lu reaction is higher than that of the 176 Yb(d, n) 177 Lu reaction. 177Yb undergoes β emission followed by gamma transitions in 177 Lu, with a relatively short half-life of 1.88 h.Therefore, 177 Lu can be approximated as the direct product of deuteron irradiation.It is important to note that the available experimental data is limited to energies up to 24 MeV.Further validation is required to assess the accuracy of the data at higher energies.
To maximize the specific activity of 177 Lu, minimizing the production of other isotopes is crucial.This is why purified 176 Yb is preferred over natural Yb.Natural Yb consists of seven stable isotopes: 176 Yb, 174 Yb, 173 Yb, 172 Yb, 171 Yb, 170 Yb, and 168 Yb, with 174 Yb being the most abundant at 31.8% of natural abundance.Figure 4a-f presents the fitted cross-sections for producing isotopes other than 177 Lu in 176 Yb, 174 Yb, 173 Yb, 172 Yb, 171 Yb, and 170 Yb, respectively. 168Yb is not included due to its very low abundance (0.126%).It is observed that almost all cross-sections of (d,x) reactions are higher than that for producing 177 Lu in 176 Yb (Figure 3).Therefore, utilizing purified 176 Yb instead of natural Yb is the most effective approach to avoid the generation of unwanted isotopes.[26] and fitting [23].
Table 1 summarizes Lu isotopes (only relevant ones are selected) and their half-lives and decay modes [28,29].As for specific isotope products in Figure 4, 173 Lu produced from the bombardment of 174 Yb or 173 Yb decays into 173 Yb via electron capture (EC) with a half-life of 1.37 years.For 172g+m Lu produced from both 173 Yb and 172 Yb, 172 Lu decays into 172 Yb via β+ decay with a half-life of 6.7 days.172m Lu decays into 172 Lu via isomeric transition (IT) with a half-life of 3.7 min.For 171g+m Lu produced from 172 Yb and 171 Yb, 171 Lu decays to 171 Yb via b β + decay with a half-life of 8.24 days.171m Yb decays to 171 Lu via IT decay with a half-life of 79 s.For 170g+m Lu produced from 171 Yb and 170 Yb, 170 Lu undergoes β+ decay into 170 Yb with a half-life of 2 days.170m Lu decays rapidly into 170 Lu via IT decay with a half-life of 670 milliseconds.For 169 Lu produced from bombarding 170 Yb, it decays into 169 Yb with a half-life of 34 h.Yb , (e) Yb , and (f) Yb , as a function of deuteron energy [23].
Table 1 summarizes Lu isotopes (only relevant ones are selected) and their half-lives and decay modes [28,29].As for specific isotope products in Figure 4, 173 Lu produced from the bombardment of 174 Yb or 173 Yb decays into 173 Yb via electron capture (EC) with a halflife of 1.37 years.For 172g+m Lu produced from both 173 Yb and 172 Yb, 172 Lu decays into 172 Yb via β+ decay with a half-life of 6.7 days.172m Lu decays into 172 Lu via isomeric transition (IT) with a half-life of 3.7 min.For 171g+m Lu produced from 172 Yb and 171 Yb, 171 Lu decays to 171 Yb via b β + decay with a half-life of 8.24 days.171m Yb decays to 171 Lu via IT decay with a half-life of 79 s.For 170g+m Lu produced from 171 Yb and 170 Yb, 170 Lu undergoes β+ decay into 170 Yb with a half-life of 2 days.170m Lu decays rapidly into 170 Lu via IT decay with a half-life of 670 milliseconds.For 169 Lu produced from bombarding 170 Yb, it decays into 169 Yb with a half-life of 34 h.
Figure 4a is important in minimizing the presence of unwanted isotopes when using a purified 176 Yb target.176m Lu, in particular, undergoes β − decay into 176 Hf (99.9%) and EC decay into 176 Yb (0.095%).With a relatively short half-life of 3.664 h, it is feasible to wait for a sufficient time period for 176m Lu to decay before initiating the chemical separation process.By optimizing the timing, the specific activity of 177 Lu can be maximized while minimizing the presence of 176m Lu and its decay products.  17Yb, (c) 173 Yb, (d) 172 Yb, (e) 171 Yb, and (f) 170 Yb, as a function of deuteron energy [23].
Figure 4a is important in minimizing the presence of unwanted isotopes when using a purified 176 Yb target.176m Lu, in particular, undergoes β − decay into 176 Hf (99.9%) and EC decay into 176 Yb (0.095%).With a relatively short half-life of 3.664 h, it is feasible to wait for a sufficient time period for 176m Lu to decay before initiating the chemical separation process.By optimizing the timing, the specific activity of 177 Lu can be maximized while minimizing the presence of 176m Lu and its decay products.
174g Lu, with a half-life of 3.31 years, decays into 174 Yb via β + decay.The long half-life of 174g Lu poses a challenge in achieving a high specific activity of 177 Lu.However, the reactions leading to its production start above 15 MeV and become significant above 20 MeV.Therefore, the concentration of 174g Lu can be minimized by optimizing the beam energy (E < 20 MeV).Regarding 174m Lu, it undergoes IT decay into 174 Lu (99.38%) and EC decay into 174 Yb (0.62%).Its relatively long half-life of 142 days presents concerns about quality control.However, since 174m Lu has a higher threshold energy at 20 MeV, its concentration can also be minimized via beam energy optimization (E < 20 MeV).
The distinctive energy dependence of the production of 177 Lu and other isotopes in pure 176 Yb leads to the difference in their isotope distribution profiles, as shown in Figure 5 for the case of 80 MeV deuteron irradiation.The dashed line in Figure 5 represents the local deuteron energy as a function of penetration depth.The symbols represent the cross-section of producing 177 Lu, 176m Lu, 174g Lu, and 174m Lu.At shallow depths, where the deuteron energy is high, the production of isotopes is relatively low.As the deuteron energy decreases to approximately 40 MeV, corresponding to a depth of around 6 mm, the cross-section for producing 174g+m Lu increases (as shown in Figure 4a).At an energy of approximately 30 MeV, corresponding to a depth of about 7.5 mm, 177 Lu production starts to increase.At an energy of around 20 MeV and a corresponding depth of 8.3 mm, the cross-section for 176m Lu production begins to rise.The 174m Lu cross-section reaches its peak at a depth of approximately 7.7 mm and then decreases to almost zero at a depth of 8.3 mm.For 174g Lu, its cross-section reaches its peak at a depth of around 7.9 mm and drops to almost zero at a depth of 8.5 mm.For both 177 Lu and 176m Lu, they exhibit increasing cross-sections and peak at a depth of approximately 8.8 mm.The corresponding deuteron energy at this depth is approximately 13 MeV.Both 177 Lu and 176 Lu cross-sections decrease and approach zero at a depth of approximately 9 mm.As to be discussed shortly, the differences in in-depth profiles of different isotopes are important in maximizing the specific activity of 177 Lu.The depth-dependent cross-sections are used to calculate the quantity of isotope products at different depths for specific bombardment time and processing time.The change of isotopes per unit volume (N) is determined by the following equation [30], with the solution where t is time, t b is the end of irradiation time, R is the reaction rate per unit volume, λ is the decay constant, N 0 denotes the atomic density (which is 2.422 × 10 22 atoms/cm 3 for Yb), and Φ the number of deuterons arriving on the surface per unit area per unit of time.
For Φ, a value of 1 × 10 16 deuterons/cm 2 /s is used, which is typical for a high-performance plasma source.Note that 1 × 10 16 deuterons/cm 2 /s corresponds to 1.6 mA/cm 2 .The decay constants λ used in the calculations are based on the half-life times t 1/2 : 6.65d for 177g Lu, 3.66h for 176m Lu, 3.31y for 174g Lu, and 142d for 174m Lu. Figure 6 plots the calculated depth profiles of 177 Lu in 80 MeV deuteron-irradiated 176 Yb at three different time points: 0 h, 3 h, and 24 h after the completion of irradiation.The irradiation time is set to 3 days.Three hours after the irradiation, the concentration changes of 177 Lu due to its decay are minimal.In 24 h after the irradiation, concentration decreases become apparent.However, the overall concentration changes are not significant.At the depth of peak concentration, 8.8 mm, the concentration of 177 Lu decreases from 1.24 × 10 19 atoms/cm 3 to 1.21 × 10 19 atoms/cm 3 after three hours and further decreases to 1.12 × 10 19 atoms/cm 3 after 24 h.The irradiation time is set to 3 days.Three hours after the irradiation, the concentration changes of Lu due to its decay are minimal.In 24 h after the irradiation, concentration decreases become apparent.However, the overall concentration changes are not significant.At the depth of peak concentration, 8.8 mm, the concentration of Lu decreases from 1.24 × 10 19 atoms/cm 3 to 1.21 × 10 19 atoms/cm 3 after three hours and further decreases to 1.12 × 10 19 atoms/cm 3 after 24 h.As a result of its much faster decay, the concentration change of 176m Lu differs significantly from that of 177 Lu. Figure 7 plots the 176m Lu concentration profiles at the same time points as shown in Figure 6.At the end of irradiation, the peak concentration of 176m Lu is 1.09 × 10 18 atoms/cm 3 .After 3 h, the concentration decreases to 4.22 × 10 17 atoms/cm 3 and further decreases to 1.16 × 10 16 atoms/cm 3 after 24 h.In contrast, both 174g Lu and 174m Lu exhibit negligible concentration changes, as shown in Figures 8 and 9.This lack of changes is due to their relatively long half-lives, which are 3.31 years for 174g Lu and 142 days for 174m Lu.It is worth noting that the peak concentrations of both isotopes, at 2.5-3.5 × 10 19 /cm³, are higher than the peak concentration of 177 Lu (about 1 × 10 19 /cm³).As a result of its much faster decay, the concentration change of 176m Lu differs significantly from that of 177 Lu. Figure 7 plots the 176m Lu concentration profiles at the same time points as shown in Figure 6.At the end of irradiation, the peak concentration of 176m Lu is 1.09 × 10 18 atoms/cm 3 .After 3 h, the concentration decreases to 4.22 × 10 17 atoms/cm 3 and further decreases to 1.16 × 10 16 atoms/cm 3 after 24 h.In contrast, both 174g Lu and 174m Lu exhibit negligible concentration changes, as shown in Figures 8 and 9.This lack of changes is due to their relatively long half-lives, which are 3.31 years for 174g Lu and 142 days for 174m Lu.It is worth noting that the peak concentrations of both isotopes, at 2.5-3.5 × 10 19 /cm 3 , are higher than the peak concentration of 177 Lu (about 1 × 10 19 /cm 3 ).1.0x10 19   1.5x10 19   2.0x10 19   2.5x10 19   3.0x10 19   3.5x10 19   Concentration (atoms/cm 3   1.0x10 19   1.5x10 19   2.0x10 19   2.5x10 19   3.0x10 19   3.5x10 19   Concentration (atoms/cm 3  Considering the differences in concentration distributions and decay rates, we propose two methods to increase the specific activity of 177 Lu.The first method involves reducing the deuteron beam energy to a value close to 21 MeV.This energy is high enough to activate the production of 177 Lu but not high enough to produce significant amounts of 174g Lu and 174m Lu. Figure 10 compares the isotope profiles for an incident energy of 80 MeV and an incident energy of 21 MeV.The calculations correspond to a post-irradiation processing time of 24 h, with the irradiation time set to 3 days.In the case of 21 MeV, 177 Lu reaches its peak concentration at a depth of 0.6 mm and drops to zero at approximately 1 mm depth.The unwanted isotope 174g Lu is present in small quantities near the surface and rapidly decreases to nearly zero at a depth of around 0.4 mm.The concentration of 174m Lu is located at even shallower depths and is negligible.Due to its rapid decay, the concentration of 176m Lu is reduced to a negligible level as well.Considering the differences in concentration distributions and decay rates, we propose two methods to increase the specific activity of 177 Lu.The first method involves reducing the deuteron beam energy to a value close to 21 MeV.This energy is high enough to activate the production of 177 Lu but not high enough to produce significant amounts of 174g Lu and 174m Lu. Figure 10 compares the isotope profiles for an incident energy of 80 MeV and an incident energy of 21 MeV.The calculations correspond to a post-irradiation processing time of 24 h, with the irradiation time set to 3 days.In the case of 21 MeV, 177 Lu reaches its peak concentration at a depth of 0.6 mm and drops to zero at approximately 1 mm depth.The unwanted isotope 174g Lu is present in small quantities near the surface and rapidly decreases to nearly zero at a depth of around 0.4 mm.The concentration of 174m Lu is located at even shallower depths and is negligible.Due to its rapid decay, the concentration of 176m Lu is reduced to a negligible level as well.1.0x10 19   1.5x10 19   2.0x10 19   2.5x10 19   3.0x10 19   3.5x10 19   Concentration (atoms/cm3 ) Depth (mm) The second method involves the use of a stacked foil target.The stacked-foil technique is commonly employed to measure excitation functions of nuclear reactions involving light ions as projectiles [31][32][33].In this technique, a target composed of multiple foils is used.In the present study, stacked foils are proposed to harvest isotopes at specific beam energies.Figure 11 illustrates the arrangement where 176 Yb targets with approximately 1 mm thickness are stacked and exposed to deuteron beams.The thickness of the The second method involves the use of a stacked foil target.The stacked-foil technique is commonly employed to measure excitation functions of nuclear reactions involving light ions as projectiles [31][32][33].In this technique, a target composed of multiple foils is used.In the present study, stacked foils are proposed to harvest isotopes at specific beam energies.Figure 11 illustrates the arrangement where 176 Yb targets with approximately 1 mm thickness are stacked and exposed to deuteron beams.The thickness of the target foils is slightly adjusted to ensure that the last foil corresponds to a depth ranging from 8.22 mm to 9.22 mm.The gray colored box indicates the last foil, where the specific activity of 177 Lu is maximized, and the unwanted isotopes are minimized.1.0x10 19   1.5x10 19   2.0x10 19   2.5x10 19   3.0x10 19   3.5x10 19   Concentration (atoms/cm 3  Tables 2 and 3 compare the daily isotope production from different depth regions: 8.22 mm to 9.22 mm (the last foil) and the entire depth range of 0 to 9.22 mm (all foils).The daily production is based on two rounds of irradiation, with each round lasting 12 h.For each round, the post-irradiation chemical separation time is 28 h.This condition arises after optimization to maximize specific activities.It does not represent the conditions to maximize radionuclidic purity nor the conditions optimized to balance both specific activity and radionuclidic purity.The conditions for different optimization needs will be discussed shortly.Table 2 presents the first optimization condition, prioritizing specific activity.The tables provide information on the activity, mass, specific activity, and radionuclidic purity of 174m Lu, 174g Lu, 176m Lu, and 177 Lu.Tables 2 and 3 compare the daily isotope production from different depth regions: 8.22 mm to 9.22 mm (the last foil) and the entire depth range of 0 to 9.22 mm (all foils).The daily production is based on two rounds of irradiation, with each round lasting 12 h.For each round, the post-irradiation chemical separation time is 28 h.This condition arises after optimization to maximize specific activities.It does not represent the conditions to maximize radionuclidic purity nor the conditions optimized to balance both specific activity and radionuclidic purity.The conditions for different optimization needs will be discussed shortly.Table 2 presents the first optimization condition, prioritizing specific activity.The tables provide information on the activity, mass, specific activity, and radionuclidic purity of 174m Lu, 174g Lu, 176m Lu, and 177 Lu.
In Table 2, which pertains to the last foil only, the activity of daily produced 177 Lu is 304 GBq, and its specific activity is 3084 GBq/mg.Although the activity is relatively low, the specific activity is remarkably high.Note that the majority of reactor-based neutron irradiation produces 177 Lu with a specific activity ranging from 740 to 1100 GBq/mg.In Table 3, which covers the entire depth region from 0 to 9.22 mm, the activity of 177 Lu is 1119 GBq, with an average specific activity of 1022 GBq/mg.Even though the specific activity is lower compared to the previous cases, it is still comparable to the quality of reactor-produced isotopes.  17Yb.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .The irradiation time is 12 h for each batch.The post-irradiation processing time is 28 h.This is the condition optimized to maximize specific activity.The conditions to maximize radionuclide activity and the conditions to balance both specific activity and radionuclide activity are different and will be separately discussed shortly.To maximize 177 Lu production, both in terms of total activity and specific activity, calculations were performed to determine the optimized conditions.The calculations changed both the irradiation time and the post-irradiation processing time incrementally.Figures 12 and 13 compare the isotope quality of the last foil and all foils.These plots emphasize the significance of selecting the appropriate processing time window.In the calculations, irradiation time changes using a step of 12 h, while post-irradiation processing time changes using a step of 4 h.All plots are normalized to one day of operation.If each batch requires a 12 h irradiation period, then one day of operation combines the yields from two batches.The post-irradiation processing start time is not limited to a duration shorter than one day.The calculation takes into account continuous operations, allowing the post-irradiation processing time to extend beyond one day if necessary.

Activity (GBq
Figure 12 provides a summary of the product quality of the last foil.All figures correspond to one day of operation (two batches per day).In Figure 12a, the total activity of 177 Lu reaches the maximum of approximately 337 GBq/day for an irradiation time of 12 h and a post-irradiation processing time of 4 h.Increasing either the irradiation time or the post-irradiation processing time leads to a decrease in activity.Figure 12b plots the specific activity and exhibits the existence of a peak region.At a given irradiation time, the specific activity initially increases and then decreases with increasing post-irradiation processing time.The peak value is approximately 3071 GBq/mg.For maximizing specific activity, the optimal post-irradiation processing time is around 20 h for short irradiation.The optimal post-irradiation processing time slightly reduces to about 12 h for long irradiation.Prolonged irradiation and post-irradiation processing times result in a drop in specific activity, with the lowest value reaching approximately 2590 GBq/mg, representing the worst scenario in the mapping.However, an overall high specific activity can still be ensured.In Figure 12c, the radionuclidic purity of the last foil is plotted.Unlike activity and specific activity, the radionuclidic purity approaches a saturated maximum of 99.6%.To achieve a high radionuclidic purity, an extended post-irradiation processing time is needed.By combining Figure 12a-c, an optimized time window can be identified.In summary, maximizing activity requires a short irradiation time and a short post-irradiation processing time, maximizing specific activity necessitates a post-irradiation processing time window of approximately 20 h, and maximizing radionuclidic purity calls for a prolonged postirradiation processing time.A balanced condition can be achieved, such as selecting a 12 h irradiation time and a 28 h post-irradiation processing time, resulting in an activity of 304 GBq/day, a specific activity of 3084 GBq/mg, and a radionuclidic purity of 95.4%.As mentioned earlier, this is not the condition to maximize radionuclidic purity.The condition for maximizing radionuclidic purity will be discussed shortly.
Figure 13a-c plots the activity, specific activity, and radionuclidic purity for all foils (corresponding to a depth region of 0 to 9.22 mm).As mentioned earlier, including these foils containing a high concentration of 174g Lu and 174m Lu degrade the overall isotope quality.However, these foils can still be used in certain medical applications where low specific activity is acceptable.In Figure 13a, it is evident that including all foils significantly increases the total activity.The highest activity of ~1260 GBq/day can be achieved by minimizing both the irradiation time (12 h) and the post-irradiation processing time (4 h).Regarding specific activity, as shown in Figure 13b, the highest value of about 1100 GBq/mg can be obtained by minimizing the irradiation and post-irradiation processing time.Even in the worst-case scenario with a prolonged post-irradiation processing time exceeding 60 h, the specific activity remains at approximately 740 GBq/mg or above, which is comparable to typical products obtained via reactor irradiation.For radionuclidic purity, a prolonged postirradiation processing time is favored, and the maximum value saturates at around 93%.
Different from Figure 12b, which shows a post-irradiation processing time window for achieving maximum specific activity, there is no such window observed from Figure 13b.This discrepancy arises from the high sensitivity of specific activity to the changes of 176m Lu quantity in the last foil, given that 176m Lu and 177 Lu are the predominant isotopes present, with 176m Lu having a rapid decay.In contrast, when all foils are considered, the mass changes contributed by 176m Lu are relatively insignificant due to the substantial contributions from 174g Lu and 174m Lu, which have almost negligible changes due to their relatively long half-lives.Consequently, the specific activity becomes less sensitive to changes in 176m Lu and more responsive to the activity changes of 177 Lu itself.
Back to the approach of harvesting 177 Lu from the last foil only, the obtained 177 Lu under optimized conditions, as shown in Figure 12b, exhibits a remarkably high specific activity of about 3084 GBq/mg.This makes the process very attractive for hospital applications.This specific activity clearly surpasses the current achieved results using reactors.Table 4 provides a summary of the typical specific activities of 177 Lu from different sources [13].It is worth noting that 3084 GBq/mg is about 75% of the highest specific activity achievable in carrier-free 177 Lu.The theoretically predicted maximum is 4104 GBq/mg [13].Having all foils made of 176 Yb is not a requirement in the stacked foil approach.Sacrificial materials of less expensive materials can be used in the other foils while reserving the last foil specifically for 176 Yb.Alternatively, for isotope production other than 177 Lu, different target materials can be used to replace the other foils.This flexibility is particularly valuable for isotopes that require a higher threshold energy for production.
The discussion above has assumed a 176 Yb target with a purity level of 100%, which represents an ideal scenario.In reality, targets of a purity level of >99.6% are commercially available (i.e., from ISOFLEX USA, San Francisco, CA, USA).In commercially enriched 176 Yb targets, impurity levels of other Yb isotopes decrease significantly as the mass numbers of Yb decrease [23].Consequently, 174 Yb is more abundant than other isotope impurities in 176 Yb-enriched targets.The three unwanted products originating from 174 Yb are 174g+m Lu and 173 Lu.These isotopes have relatively long lifetimes compared to others, resulting in their minimal contribution to the radionuclide impurities of 177 Lu.
To model the effect of purity, calculations were performed for the production and decay of 177 Lu, 174m Lu, 174g Lu, 176m Lu, and 173 Lu.The production calculations utilized cross-section data from Figures 4 and 5, while the decay calculations were based on the half-life times provided in Table 1.Table 5 compares the activity, specific activity, and radionuclidic purity of 177 Lu in 176 Yb targets at purity levels of 100%, 99.6%, 99%, and 98%, respectively.All values correspond to daily production, assuming two rounds of irradiation per day with a 12 h irradiation time for each batch and a 28 h post-irradiation processing time for each batch.The conditions include an 80 MeV beam energy, 1.6 mA beam current, and a 1cm 2 beam spot size.The comparison is made for collecting Lu from all foils (0 to 9.22 mm) and from the last foil (8.22 mm to 9.22 mm).  17Yb targets with purities of 100%, 99.6%, 99%, and 98%.Comparison was made for the depth region of 8.22 mm to 9.22 mm (the last foil) and the range of 0 mm to 9.22 mm (all foils) under 80 MeV deuteron irradiation.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .The irradiation time for each batch is 12 h, and the post-irradiation processing time is 28 h as the optimized conditions.The condition is not optimized to maximize radionuclidic purity.Table 5 shows that there is no significant difference when the purity is reduced from 100% to 99.6%.In the case of the last foil, the activity changes from 304 to 302 GBq and the specific activity changes from 3084 to 3052 GBq/mg.Even in the worst-case scenario of 98% purity, the activity is 335 GBq, and the specific activity is 2912 GBq/mg.These results suggest that a purity level of around 98% and above does not significantly degrade the quality of the final product.
Using 99.6% purity as the example, Table 6 lists the activity, mass, and specific activity of each Lu isotope, giving further details about the impurity effect.Judged by the radionuclidic purity, the largest impurity effect comes from 176m Lu, at a value of 4.3%.176m Lu has a specific activity of 137 GBq/mg.Although its mass is not the largest, its short half-life of 3.66 h makes its contribution large.On the other hand, 173 Lu, as a unique product from 174 Yb, has the smallest contribution in influencing 177 Lu radionuclidic purity.
As one highlight of the present study, irradiation, and processing conditions are identified to provide the quality range that is of particular interest to the isotope production community.The most demanded quality is specific activity > 2960 GBq/mg and radionuclidic purity > 99.5%.Figure 14a-d are for 176 Yb of 100% purity and for the last foil only (depth from 8.22 mm to 9.22 mm). Figure 14a maps the region where the activity exceeds 185 GBq/day, a condition that can be easily achieved based on the modeled conditions.The majority of regions surpass 259 GBq/day, except for a specific corner associated with significantly longer irradiation time and post-irradiation processing times.In Figure 14b, the plot showcases the region that surpasses 99.5% radionuclidic purity, which can be attained with post-irradiation processing times longer than 40 h.This region appears to be less sensitive to variations in irradiation times.Figure 14c presents the region of the specific activity exceeding 2960 GBq/mg.It shows a trade-off between irradiation time and post-irradiation processing times, whereby a longer irradiation time necessitates a shorter post-irradiation processing time.Figure 14d provides a summary of the region that satisfies the combined criteria of activity > 259 GBq/day, specific activity > 2960 GBq/mg, and radionuclidic purity > 99.5%.It represents the optimized conditions obtained by considering all restrictions.This region corresponds to irradiation times shorter than 60 h and post-irradiation processing times between 44 and 64 h.For a purity of 99.6%, Figure 15a-d plots the corresponding activity, specific activity, radionuclidic purity, and the optimized conditions for achieving activity > 259 GBq/day, specific activity > 2960 GBq/mg, and radionuclidic purity > 99.5%.These maps exhibit similarities to the case of 100% purity, with the expected difference that the regions are slightly smaller.The shrinking specific activity region and specific activity region impose For a purity of 99.6%, Figure 15a-d plots the corresponding activity, specific activity, radionuclidic purity, and the optimized conditions for achieving activity > 259 GBq/day, specific activity > 2960 GBq/mg, and radionuclidic purity > 99.5%.These maps exhibit similarities to the case of 100% purity, with the expected difference that the regions are slightly smaller.The shrinking specific activity region and specific activity region impose further constraints on the conditions.As shown in Figure 15d, although conditions are narrowed down, a region still exists for attaining the required quality.The necessary irradiation time ranges from 12 to 24 h, while the post-irradiation processing time is around 48 h.As pointed out in the introduction, the present study used 80 MeV as one example of high-energy LINAC facilities.However, the proposed multiple foil targets can be easily adjusted for other energies.The deuteron ions enter into the last foil at an energy of about 21 MeV.For other beam energies, as long as the foils prior to the last one can reduce beam energies down to 21 MeV, the product of the same quality can be obtained.
As shown in Figure 2, for deuterons reaching 21 MeV, deuterons penetrate about 4.7 mm for an initial beam energy of 60 MeV and about 1.9 mm for an initial beam energy of 40 MeV.As long as the foils ahead of the last one have a combined thickness matching these numbers, the same optimized conditions can be reached for the last foil.
Currently, isotope production is primarily dominated by reactor irradiation and cyclotrons.Most cyclotrons operate at relatively lower beam energies, typically around 40 MeV or lower.In contrast, LINACs are capable of delivering beam energies exceeding 40 MeV.LINACs can serve as versatile devices for isotope production, even for isotopes that favor lower beam energies, utilizing techniques like the one proposed in this study.It is important to note that typical beam currents for cyclotrons are around 100s µA, whereas LINACs can achieve beam currents of a few mA.For a high-energy LINAC, it is not ideal for Lu isotope production since much power is wasted if only the last foil is used.However, the design allows replacing these wasted foils with targets for producing other isotopes that require higher threshold (or optimized) energy.Table 6.The daily production of various Lu isotopes in the 176 Yb target with a purity of 99.6%.Collection is limited to the last foil of the depth region of 8.22 mm to 9.22 mm.The beam current is 1.6 mA, and the beam spot size is 1 cm 2 .The irradiation time for each batch is 12 h, and the post-irradiation processing time is 28 h as the optimized conditions.The parameters are optimized to maximize specific capacity.If radionuclidic purity needs to be maximized, a different condition is needed.

Conclusions
By employing a simulation approach that combines particle transport and isotope production/decay simulations, the process of producing 177 Lu via deuteron irradiation of 176 Yb has been optimized, with a particular focus on maximizing the specific activity of 177 Lu.Stacked foils have been proposed as the target for a linear accelerator operating at relatively high design energies.The selection of foils can be tailored to minimize the presence of 174m Lu and 174g Lu due to their distinct energy-dependent cross-sections.To minimize the production of 176m Lu, optimization of the post-irradiation processing time times has been investigated.Upon optimization, deuteron irradiation at 80 MeV and at a flux of 1 × 10 16 deuterons/cm 2 /s (equivalent to a beam current of 1.6 mA over a beam spot size of 1 cm 2 ) can result in daily production of 304 GBq of 177 Lu, with a high specific activity of 3084 GBq/mg and a high radionuclidic purity of 95.4%.If specific activity and radionuclidic purity need to be balanced, there is an optimized condition that can obtain activity greater than 259 GBq/day, specific activity greater than 2960 GBq/mg, and radionuclidic purity greater than 99.5%.The study suggested the feasibility of utilizing a high energy, high current linear accelerator for the production of 177 Lu at a specific activity level better than a typical reactor produced 177 Lu.

Figure 1 .
Figure 1.Projected ranges of deuteron as a function of deuteron incident energy in Yb.Figure 1. Projected ranges of deuteron as a function of deuteron incident energy in Yb.

Figure 1 .Figure 2 .
Figure 1.Projected ranges of deuteron as a function of deuteron incident energy in Yb.Figure 1. Projected ranges of deuteron as a function of deuteron incident energy in Yb.

Figure 2 .
Figure 2. Local deuteron energy as a function of depth in Yb for incident energies of 20, 40, 60, and 80 MeV.

Figure 3 .
Figure 3 should be replaced by the following.The second equation in the legend should be changed from Yb(d, n) Yb 177g+m 176 to Yb(d, p) Yb 177g+m 176 .The figure below has been corrected.

Molecules 2023 , 24 Figure 6
Figure 6 plots the calculated depth profiles ofLu in 80 MeV deuteron-irradiated176 Yb at three different time points: 0 h, 3 h, and 24 h after the completion of irradiation.The irradiation time is set to 3 days.Three hours after the irradiation, the concentration changes of Lu due to its decay are minimal.In 24 h after the irradiation, concentration decreases become apparent.However, the overall concentration changes are not significant.At the depth of peak concentration, 8.8 mm, the concentration of Lu decreases from 1.24 × 10 19 atoms/cm 3 to 1.21 × 10 19 atoms/cm 3 after three hours and further decreases to 1.12 × 10 19 atoms/cm 3 after 24 h.

2 Figure 6 .
Figure 6.Concentrations ofLu as a function of depth in 80 MeV deuteron-irradiated Yb .The irradiation time is 3 days.For comparison, the post-irradiation processing times considered are 0 h, 3 h, and 24 h.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .This corresponds to 1 × 10 16 deuterons/cm²/s.

Figure 6 .
Figure 6.Concentrations of177 Lu as a function of depth in 80 MeV deuteron-irradiated 176 Yb.The irradiation time is 3 days.For comparison, the post-irradiation processing times considered are 0 h, 3 h, and 24 h.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .This corresponds to 1 × 10 16 deuterons/cm 2 /s.

2 Figure 7 .
Figure 7. Concentrations ofLu as a function of depth in 80 MeV deuteron-irradiated Yb .The irradiation time is 3 days.The post-irradiation processing times are 0 h, 3 h, and 24 h.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .This corresponds to 1 × 10 16 deuterons/cm²/s.

2 Figure 8 .
Figure 8. Concentrations ofLu as a function of depth in 80 MeV deuteron-irradiated Yb .The irradiation time is 3 days.The post-irradiation processing times are 0 h, 3 h, and 24 h.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .This corresponds to 1 × 10 16 deuterons/cm²/s.

Figure 7 . 2 Figure 7 .
Figure 7. Concentrations of 176m Lu as a function of depth in 80 MeV deuteron-irradiated176 Yb.The irradiation time is 3 days.The post-irradiation processing times are 0 h, 3 h, and 24 h.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .This corresponds to 1 × 10 16 deuterons/cm 2 /s.

2 Figure 8 .
Figure 8. Concentrations of Lu as a function of depth in 80 MeV deuteron-irradiated Yb .The irradiation time is 3 days.The post-irradiation processing times are 0 h, 3 h, and 24 h.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .This corresponds to 1 × 10 16 deuterons/cm²/s.

Figure 8 .
Figure 8. Concentrations of 174g Lu as a function of depth in 80 MeV deuteron-irradiated176 Yb.The irradiation time is 3 days.The post-irradiation processing times are 0 h, 3 h, and 24 h.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .This corresponds to 1 × 10 16 deuterons/cm 2 /s.

Figure 9 .
Figure 9. Concentrations of Lu as a function of depth in 80 MeV deuteron-irradiated Yb .The irradiation time is 3 days.The post-irradiation processing times are 0 h, 3 h, and 24 h.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .

Figure 9 .
Figure 9. Concentrations of 174m Lu as a function of depth in 80 MeV deuteron-irradiated 176 Yb.The irradiation time is 3 days.The post-irradiation processing times are 0 h, 3 h, and 24 h.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .Molecules 2023, 28, x FOR PEER REVIEW 12 of 24

Figure 10 .
Figure 10.Concentration profiles of 177 Lu (red circle), 176m Lu (blue square), 174g Lu (black triangle), and 174m Lu (green triangle) for the incident energies of 80 MeV and 40 MeV.The irradiation time is 3 days.The calculations correspond to 24 h after the irradiation.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .

Figure 11 .
Figure 11.Concentration profiles of 177 Lu (red circle), 176m Lu (blue square), 174g Lu (black triangle), and 174m Lu (green triangle) for the incident energies of 80 MeV in a stacked foil target configuration.The irradiation time is 3 days.The calculations correspond to 24 h after the irradiation.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .

Figure 11 .
Figure 11.Concentration profiles of 177 Lu (red circle), 176m Lu (blue square), 174g Lu (black triangle), and 174m Lu (green triangle) for the incident energies of 80 MeV in a stacked foil target configuration.The irradiation time is 3 days.The calculations correspond to 24 h after the irradiation.The beam current is 1.6 mA.The beam spot size is 1 cm 2 .

Figure 12 .
Figure 12.(a) Activity, (b) specific activity, and (c) radionuclidic purity of 177 Lu collected from the last foil (corresponding to a depth from 8.22 mm to 9.22 mm) of 176 Yb irradiated using 80 MeV deuterons.The x-axis represents the irradiation time, and the y-axis represents the post-irradiation processing time.All yields are normalized to six days of operation.The flux is 1 × 10 16 deuterons/cm 2 /s, which is equivalent to a beam current of 1.6 mA over a beam spot size of 1 cm 2 .

Figure 12 . 24 Figure 12 .
Figure 12.(a) Activity, (b) specific activity, and (c) radionuclidic purity of 177 Lu collected from the last foil (corresponding to a depth from 8.22 mm to 9.22 mm) of 176 Yb irradiated using 80 MeV deuterons.The x-axis represents the irradiation time, and the y-axis represents the post-irradiation processing time.All yields are normalized to six days of operation.The flux is 1 × 10 16 deuterons/cm 2 /s, which is equivalent to a beam current of 1.6 mA over a beam spot size of 1 cm 2 .

Figure 13 .
Figure 13.(a) Activity, (b) specific activity, and (c) radionuclidic purity of 177Lu collected from all foils (corresponding to a depth from 0 mm to 9.22 mm) of 176Yb irradiated using 80 MeV deuterons.The x-axis represents the irradiation time, and the y-axis represents the post-irradiation processing time.All yields are normalized to one day of operation.The flux is 1 × 10 16 deuterons/cm 2 /s, which is equivalent to a beam current of 1.6 mA over a beam spot size of 1 cm 2 .

Figure 13 .
Figure 13.(a) Activity, (b) specific activity, and (c) radionuclidic purity of 177 Lu collected from all foils (corresponding to a depth from 0 mm to 9.22 mm) of 176 Yb irradiated using 80 MeV deuterons.The x-axis represents the irradiation time, and the y-axis represents the post-irradiation processing time.All yields are normalized to one day of operation.The flux is 1 × 10 16 deuterons/cm 2 /s, which is equivalent to a beam current of 1.6 mA over a beam spot size of 1 cm 2 .

24 Figure 14 .
Figure 14.(a) Activity, (b) specific activity, (c) radionuclidic purity of 177 Lu obtained from 80 MeV deuteron irradiation of 176 Yb with 100% purity, and (d) processing time window capable of achieving activity > 259 GBq/day, specific activity > 2960 GBq/mg, and radionuclidic purity > 99.5%.Only the last foil is processed.The beam current is 1.6 mA, and the beam spot size is 1 cm 2 .

Figure 14 .
Figure 14.(a) Activity, (b) specific activity, (c) radionuclidic purity of 177 Lu obtained from 80 MeV deuteron irradiation of 176 Yb with 100% purity, and (d) processing time window capable of achieving activity > 259 GBq/day, specific activity > 2960 GBq/mg, and radionuclidic purity > 99.5%.Only the last foil is processed.The beam current is 1.6 mA, and the beam spot size is 1 cm 2 .

Figure 15
Figure 15 should be replaced by the following one.The change is made in the legend of Fig. (d)."specificactivity > 2960 Ci/mg" should be changed to "specific activity > 2960 GBq/mg".

Figure 15 .
Figure 15.(a) Activity, (b) specific activity, (c) radionuclidic purity of 177 Lu obtained from 80 MeV deuteron irradiation of 176 Yb with 99.6% purity, and (d) processing time window capable of achieving activity > 259 GBq/day, specific activity > 2960 GBq/mg, and radionuclidic purity > 99.5%.Only the last foil is processed.The beam current is 1.6 mA, and the beam spot size is 1 cm 2 .
[30]l deuteron energy (dashed line) and cross-sections of producing 177 Lu (red circle), 176mLu (blue square), 174g Lu (green triangle), and 174m Lu (orange triangle), as a function of depth, for the case of 80 MeV deuteron irradiation of pure 176 Yb.The depth-dependent cross-sections are used to calculate the quantity of isotope products at different depths for specific bombardment time and processing time.The change of isotopes per unit volume () is determined by the following equation[30], where  is time,  is the end of irradiation time, R is the reaction rate per unit volume,  is the decay constant,  denotes the atomic density (which is 2.422 × 10 22 atoms/cm³ for Yb), and Φ the number of deuterons arriving on the surface per unit area per unit of time.For Φ, a value of 1 × 10 16 deuterons/cm 2 /s is used, which is typical for a high-performance plasma source.Note that 1 × 10 16 deuterons/cm²/s corresponds to 1.6 mA/cm 2 .The decay constants λ used in the calculations are based on the half-life times  / : 6.65d for Figure 5. Local deuteron energy (dashed line) and cross-sections of producing 177 Lu (red circle), 176m Lu (blue square), 174g Lu (green triangle), and 174m Lu (orange triangle), as a function of depth, for the case of 80 MeV deuteron irradiation of pure 176 Yb.

Table 2 .
The daily production of Lu isotopes in the depth region of 8.22 mm to 9.22 mm in 80 MeV deuteron-irradiated pure

Table 3 .
The daily production of Lu isotopes in the depth region of 0 mm to 9.22 mm.The irradiation condition is the same as in Table2.

Table 5 .
The daily production of 177 Lu in