Compact accelerator-based production of carrier-free ¹⁷⁷Lu from 18 MeV $D^{+}$ on [¹⁷⁶Yb]${\text{Yb}}_2{\text{O}}_3$

Abstract

Background

Recent EMA and FDA approvals of Lu-DOTATATE and Lu-PSMA-617 have led to increased demand for radiotherapeutic $_{}^{177}$Lu, due to its promising potential to treat castration-resistant neuroendocrine cancers. Conventional reactor production methods pose challenges related to cost, waste management, and local availability. In comparison, accelerators produce less waste, have lower maintenance costs, and can be directly integrated into hospital settings. In this study, we evaluate the production of radiotherapeutic $_{}^{177}$Lu using a 10 mA, 18 MeV $D^{+}$ compact linear accelerator design. The design consists of a single radio-frequency quadrupole (RFQ) and seven drift tube linacs (DTLs) that achieve a beam efficiency of 98.5% over a total length of $12\text{m}$. Deuteron activations on a 99% enriched [$_{}^{176}$Yb]${\text{Yb}}_2{\text{O}}_3$ target are estimated using experimental and simulated excitation functions.

Results

A circular target with a radius of 1 cm and 0.36 mm thickness is selected to optimize the yield of $_{}^{177}$Lu while minimizing the production of undesirable radioisotopes, including $_{}^{174g+m}$Lu and $_{}^{177m}$Lu. Model calculations indicate that the accelerator design can produce 11.3 μg of $_{}^{177}$Lu per hour. A 5-day irradiation is expected to yield approximately 1.07 mg of $_{}^{177}$Lu (4.4 TBq), while a 12-day irradiation can produce up to 1.9 mg (7.8 TBq). Following a 2-day processing period, the specific activity of the 5-day irradiated sample is projected to approach 0.6 TBq/mg, with a radiopurity of approximately 99.8%. The minimal burn-up of the ${\text{Yb}}_2{\text{O}}_3$ target suggests it may be recycled and reused over multiple irradiations.

Conclusions

The study confirms the feasibility of accelerator-based $_{}^{177}$Lu production as an alternative to existing reactor-based methods. The 10 mA, 18 MeV $D^{+}$ RFQ-DTL design achieves an exceptionally high $_{}^{177}$Lu radiopurity and a competitive overall yield, which can meet the dose requirements of thousands of patients.

Introduction

Several studies have reported on the potential of $_{}^{177}$Lu as an in vivo radioisotope useful for the treatment of metastatic lesions and neuroendocrine cancers (Dash et al. 2015; Nagai et al. 2022; Yang et al. 2023). $_{}^{177}$Lu is a desirable radioisotope due to its intermediate half-life ($t_{1/2}$ = 6.65 days) and moderate energy release. It beta decays to the stable ground state of $_{}^{177}$Hf (78.6% of the time), a 0.25 MeV excited state (9.2%), or a 0.32 MeV excited state (12.2%). Compared to other therapeutic radioisotopes (such as $_{}^{90}$Y, $_{}^{131}$I, and $_{}^{186}$Re), the localized beta particles produced by $_{}^{177}$Lu have a smaller mean penetration range in tissue of approximately $0.62\text{mm}$ (Patell et al. 2023). Since the excited states also produce low-energy gamma rays—113 keV (6.6%) and 208 keV (11%)—SPECT/CT image-guided, theranostic (therapy and diagnosis) treatments are possible (Praena 2020; Alliot et al. 2015; Vogel et al. 2021; Morgan et al. 2023). Furthermore, $_{}^{177}$Lu can be combined with other radionuclides, such as $_{}^{67}$Cu and $_{}^{90}$Y, for tandem use (Shao 2023).

For targeted radiotherapy, lutetium can be added to a variety of molecular carriers, antibodies, and peptides to preferentially accumulate in cell receptors overexpressed on tumor surfaces (Dash et al. 2015; Alliot et al. 2015; Ladrière et al. 2023). Examples include prostate-specific membrane antigen (PSMA) and peptide receptor radionuclide therapy (PRRT). An amino acid transporter protein, PSMA is expressed 100 to 1000 times more in prostate cancer than in normal tissue (Ribes et al. 2024; Patell et al. 2023; Sartor et al. 2021; Mendez et al. 2023; Ferdinandus et al. 2018). Successful treatments of patients with metastatic lesions and prostate cancer have led to recent approval by the EMA and FDA of $_{}^{177}$Lu-DOTATATE and $_{}^{177}$Lu-PSMA-617 for neuroendocrine cancers and PSMA-positive metastatic castration-resistant prostate cancer (mCRPC) (Shao 2023; Kong et al. 2024; Ladrière et al. 2023; Bhardwaj et al. 2017; Ribes et al. 2024; Sartor et al. 2021; Thaiss et al. 2023; Ahmadzadehfar et al. 2024; Bokhout et al. 2025). Early results indicate that $_{}^{177}$Lu-based drugs have limited side effects and a better toxicity profile compared to other radionuclides (Mendez et al. 2023; Thaiss et al. 2023; Ferdinandus et al. 2018). Consequently, the demand for $_{}^{177}$Lu has increased in recent years, with a particular focus on developing production facilities that are better equipped to meet treatment requirements.

In this study, we present the general design of an 18 MeV $D^{+}$ linear accelerator (linac) optimized for the production of high-purity $_{}^{177}$Lu. We develop a model based on experimental (Nagai et al. 2022; Hermanne et al. 2006; Manenti et al. 2011) and simulated (Koning et al. 2023) excitation functions to optimize the target width and yield of deuteron activations from a ${\text{Yb}}_2{\text{O}}_3$ target enriched to 99% $_{}^{176}$Yb. Based on our accelerator and target parameters, the expected radiopurity of carrier-free $_{}^{177}$Lu is estimated to exceed 99.8% after a 5-day irradiation. Longer irradiations offer similar radiopurity and produce 1 to 2 mg of $_{}^{177}$Lu. Compared with previous studies using reactor-based production, we show that accelerator-based production generates less target burn-up, reduced waste, higher radiopurity, and competitive overall yield. Since an accelerator facility is generally safer and easier to maintain than a high-flux reactor, the design is expected to better meet therapeutic production demand.

Methods

Accelerator design

Currently, $_{}^{177}$Lu is most commonly produced by neutron activation in a high-flux reactor (Dash et al. 2015; Knapp et al. 2005). This involves either irradiating an ordinary lutetium target or an enriched $_{}^{176}$Yb target (12.9% natural abundance), giving the reactions

$$\begin{array}{cc}\hfill _{}^{176}\text{Lu}+n⟶& _{}^{177}\text{Lu}+\gamma \text{(direct),}\hfill \end{array}$$ 1

$$\begin{array}{cc}\hfill _{}^{176}\text{Yb}+n⟶& _{}^{177}\text{Yb}+\gamma \text{(indirect)}.\hfill \end{array}$$ 2

In the indirect route, $_{}^{177}$Yb ($t_{1/2}$ = 1.91 h) is produced, which quickly beta-decays into $_{}^{177}$Lu. The drawbacks of reactor-based production include the high thermal neutron flux required (${10}^{14}$ ${\text{n/cm}}^2$/s) as well as the 2.6% natural abundance of $_{}^{176}$Lu ($t_{1/2}\sim 4\times {10}^{10}$ y). For both direct and indirect production routes, high neutron activation cross sections lead to significant target burn-up and radioactive waste, which also reduce the specific activity of $_{}^{177}$Lu (Bhardwaj et al. 2017; Zhernosekov et al. 2008). The waste products include $_{}^{174\text{g}}$Lu ($t_{1/2}=3.31$ y), $_{}^{174\text{m}}$Lu ($t_{1/2}=120.9$ d), $_{}^{176\text{m}}$Lu ($t_{1/2}=3.66$ d), and $_{}^{177\text{m}}$Lu ($t_{1/2}=160.4$ d) (Koning et al. 2019). Due to these contaminants, target waste and patient urine must be disposed of in a dedicated waste management facility (Praena 2020). Large amounts of stable $_{}^{175}$Lu in the target also reduce the specific activity of the desired $_{}^{177}$Lu product.

By comparison, accelerator-based production methods generate one-tenth as much nuclear waste, require lower maintenance costs (including decommissioning), and have a better safety profile (Wang et al. 2022). Proton beams are inadequate for lutetium production as a result of small Yb/Lu activation cross sections. However, deuteron beams, with moderate stopping power and high neutron-stripping cross sections, provide an ideal choice (Tárkányi et al. 2020).

Similar to before, $_{}^{177}$Lu is produced indirectly by deuterons through

$$\begin{array}{cc}\hfill _{}^{176}\text{Yb}+d⟶& _{}^{177}\text{Yb}+p(Q=3.34\text{MeV})\hfill \end{array}$$ 3

reactions, at a rate about nine times greater than for direct $_{}^{176}$Yb(d, n)$_{}^{177}$Lu reactions (Kambali 2018). The $_{}^{176}$Yb(d, p)$_{}^{177}$Yb cross section begins to increase around 5 MeV before reaching a peak of approximately 230 mb at 12.5 MeV, as shown in Fig. 1.

Fig. 1.

Experimental (Nagai et al. 2022; Hermanne et al. 2006; Manenti et al. 2011; Soppera et al. 2014) and simulated (Koning et al. 2019) $_{}^{176}$Yb(d, p)$_{}^{177}$Yb cross section data. Due to the large underestimation by TENDL-2023 for this reaction, we instead use an interpolation of the Hermanne (2006) and Manenti (2010) data for subsequent calculations

For higher deuteron energies, $_{}^{174g+m}$Lu production cross sections increase (Shao 2023). Hence, a higher purity of $_{}^{177}$Lu is obtained for deuteron beam energies below 20 MeV (Nagai et al. 2022). In this range, metastable $_{}^{176m}$Lu is produced but decays rapidly, while the production of longer-lived $_{}^{177m}$Lu is negligible due to its high spin value $J^{\pi }=23/2^{-}$ (Tárkányi et al. 2013).

To produce $_{}^{177}$Lu with high purity and high yield, we designed a 10 mA, 17.9 MeV $D^{+}$ linear accelerator (linac) (Xia et al. 2025). Our design consists of a 0.02 MeV injector, 3.8 m radio-frequency quadrupole (RFQ) accelerator, and seven drift tube linacs (DTLs). For the RFQ, a 2.1 MeV beam is generated in continuous wave (CW) mode with a simulated transmission efficiency of 98.63% (Wei et al. 2023). The RFQ requires four 1200 L/s vacuum pumps and one 440 L/s ion pump to maintain a vacuum pressure of ${10}^{-6}$ Pa. For the high-energy beam section, each DTL consists of a power coupler and six tuners (Wei et al. 2024). A crossbar H-mode (CH) cavity increases the ion energy across all seven DTLs from 2.11 MeV to 17.92 MeV over 8.17 m. The transverse focusing between cavities is achieved using quadrupole doublet and triplet magnets depicted in Fig. 2. The beam transmission in each CH-DTL is nearly 100%, while the entire line efficiency is 98.5%, due mostly to particles lost at low energy in the RFQ bunching section. The RFQ-DTL system operates in CW mode at a frequency of 162.5 MHz, for the parameters given in Tables 1 and 2.

Fig. 2.

Side-view schematic of the RFQ-DTL components, including water cooling ports, vacuum pumps, power couplers, and tuners. Labels correspond to: (1) microwave waveguide, (2) ECR (Electron Cyclotron Resonance) $D^{+}$ ion source, (3) solenoids, (4) emittance measuring device, (5) RFQ accelerator, (6) doublet magnets, (7) buncher, (8) DTLs, (9) RF power couplers, and (10) triplet magnets

Table 1.

General parameters of the CW mode RFQ-DTL accelerator design, optimized for $_{}^{177}$Lu production (Xia et al. 2025)

Accelerator parameters
Ion	$D^{+}$
Beam energy (MeV)	17.9
Current (mA)	10
Frequency (MHz)	162.5
Duty factor (%)	100
Transmission efficiency (%)	98.5

Table 2.

Structural parameters of the RFQ-DTL design (Xia et al. 2025)

Structure	Length (m)	Energy interval (MeV)
RFQ	3.8	0.02–2.11
DTL 1	0.52	2.11–3.28
DTL 2	0.81	3.28–4.92
DTL 3	1.01	4.92–7.03
DTL 4	1.26	7.03–9.37
DTL 5	1.42	9.37–12.01
DTL 6	1.51	12.01–14.86
DTL 7	1.64	14.86–17.92

The overall energy interval is 17.9 MeV and the total length of the accelerator is 11.97 m

The beam output was simulated using a TraceWin (CEA: TraceWin 2024) Monte Carlo simulation of 10,000 particles. Figure 3 plots a Gaussian kernel density estimation of particle energy and angular variations, which average 5.47 keV and $-1.{96}^{\circ }$, respectively. The covariance error ellipse is given 4.5 standard deviations from the mean value, corresponding to a ${\chi }^2$ value $>99.9$%. The x-z and y-z filtered flux values indicate a strongly mono-energetic beam profile.

Fig. 3.

Energy-phase diagram for the 17.9 MeV $D^{+}$ beam, which is nearly mono-energetic. The results are obtained from output simulated using TraceWin (CEA: TraceWin 2024)

Target optimization

For an ytterbium target, metallic $_{}^{176}$Yb (6.9 ${\text{g/cm}}^3$) is separated from silicate mineral gadolinite and synthesized into crystalline ${\text{Yb}}_2{\text{O}}_3$ (9.2 ${\text{g/cm}}^3$) (Haynes 2016). ${\text{Yb}}_2{\text{O}}_3$ is used as a target instead of pure Yb due to its better chemical and thermal stability, along with its higher melting point (2,355 $_{}^{\circ }\text{C}$ compared to 819 $_{}^{\circ }\text{C}$) (Praena 2020; Haynes 2016). Although natural ytterbium contains only 12.6% $_{}^{176}$Yb, it may be enriched to more than 97% (Dash et al. 2015; Knapp et al. 2005). A recent study by Yang et al. reported pilot-scale production of $_{}^{177}$Lu using a 99.33% [$_{}^{176}$Yb]${\text{Yb}}_2{\text{O}}_3$ enriched target acquired from Rosatom (Yang et al. 2023). Following irradiation, a ${\text{Yb}}_2{\text{O}}_3$ target can be dissolved in dilute mineral acid. Since Yb ions exist in a +2 oxidation state, forming an insoluble sulfate, micro amounts of +3 Lu may be separated from macro amounts of Yb, and synthesized into water-soluble ${\text{LuCl}}_3$ (Dash et al. 2015; Haynes 2016). Table 3 gives the material properties of natural Yb and ${\text{Yb}}_2{\text{O}}_3$ used in later calculations.

Table 3.

General properties of natural Yb and molecular ${\text{Yb}}_2{\text{O}}_3$ targets (Haynes 2016) 9

Target properties	Yb	${\text{Yb}}_2{\text{O}}_3$
Molecular weight (g/mol)	173.04	394.08
Density (${\text{g/cm}}^3$)	6.9	9.2
Melting point ($_{}^{\circ }\text{C}$)	819	2355
Specific heat capacity (J/g-K)	0.155	n.a
Thermal conductivity (W/m-K)	38.5	n.a
Mean excitation potential (eV)	684	512.4
Range of 17.9 MeV ${\text{D}}^{+}$ (mm)	0.75	0.49

The range of 17.9 MeV deuterons is calculated using equation 9

Unlike neutron activation, for which sharp resonances provide large cross section variations, charged particle activations are straightforward to calculate. The average energy lost per unit path-length, or electronic stopping power of a heavy ion in a dense medium is given by

$$\begin{array}{c}\hfill -\frac{\mathit{dE}}{\mathit{dx}}=\sum _i{N}_i\sum _n{E}_{\mathit{ni}}{\sigma }_{\mathit{ni}},\end{array}$$ 4

where $N_i$ is an atom or molecule of type i that is excited to an energy level $E_{\mathit{ni}}$ above its ground state, for a corresponding inelastic cross section ${\sigma }_{\mathit{ni}}$ (Fano 1963). Applying a first-order Born approximation, equation 4 transforms into the relativistic Bethe-Bloch equation

$$\begin{array}{c}\hfill -\frac{\mathit{dE}}{\mathit{dx}}=\frac{4\pi m_{\text{e}}{c}^2{r}_{\text{e}}^2{n}_{\text{e}}{z}^2}{{\beta }^2}\left\{ln,\left[\frac{2m_{\text{e}}{c}^2{\beta }^2}{⟨I⟩(1-{\beta }^2)}\right],-,{\beta }^2\right\}\end{array}$$ 5

where the electron density of the medium is $n_{\text{e}}$, the atomic number of the incident ion is z, and the mean excitation potential is $⟨I⟩$. Neglecting the shell and density corrections, which are small for intermediate deuteron energies, and using the fact that

$$\begin{array}{c}\hfill -ln\left(1,-,{\beta }^2\right)-{\beta }^2=\frac{{\beta }^4}{2}+\frac{{\beta }^6}{3}+\cdots <<1,\end{array}$$ 6

equation (5) becomes

$$\begin{array}{c}\hfill S=\frac{\omega z^2}{{\beta }^2}ln\left(\kappa ,{\beta }^2\right),\end{array}$$ 7

for $S=-dE/dx$, $\omega =4\pi n_{\text{e}}{m}_{\text{e}}{c}^2{r}_{\text{e}}^2$, and $\kappa =2m_{\text{e}}{c}^2/⟨I⟩$ (Morris et al. 2024).

Since the mean excitation potential for ${\text{Yb}}_2{\text{O}}_3$ molecules is not readily available, we estimate it by using Bragg’s formula,

$$\begin{array}{c}\hfill ln⟨I⟩\sim \frac{{\sum }_i{N}_i{Z}_{i}ln{I}_i}{{\sum }_i{N}_i{Z}_i}.\end{array}$$ 8

The mean excitation energy is 684 eV for ytterbium atoms and 95 eV for oxygen atoms (Kramida et al. 2022), giving $⟨I⟩\sim 512.4$ eV for ${\text{Yb}}_2{\text{O}}_3$. From equation 7, the average range of an ion can be estimated using the continuously slowing-down approximation

$$\begin{array}{c}\hfill R={\int }_0^E\frac{d{E}^{\prime }}{S(E^{\prime })}=\frac{m_0{c}^2}{2\omega z^2}{\int }_0^2\frac{{\beta }^{\prime 2}d{\beta }^{\prime 2}}{{(1-{\beta }^{\prime 2})}^{3/2}ln(\kappa {\beta }^{\prime 2})}.\end{array}$$ 9

Compared to ranges simulated by SRIM, equation 9 generally exhibits close agreement, with differences of less than 5 μm (Kambali 2018). Figure 4 plots equations 7 and 9 for deuterons in pure ytterbium and ${\text{Yb}}_2{\text{O}}_3$ targets, consistent with results obtained in references (Kambali 2018; Shao 2023; Praena 2020). Due to its higher molecular density and lower mean excitation energy, ${\text{Yb}}_2{\text{O}}_3$ offers greater stopping power to $D^{+}$ ions than pure Yb, resulting in a shorter range of travel. For estimating the yield of a reaction of type i with cross section $\sigma ={\sigma }^{\{i\}}$, it is convenient to introduce the range-averaged cross section

$$\begin{array}{c}\hfill 〈\sigma 〉=\frac{{\displaystyle {\int }_0^E\frac{\sigma (E^{\prime })}{S(E^{\prime })}d{E}^{\prime }}}{{\displaystyle {\int }_0^E\frac{d{E}^{\prime }}{S(E^{\prime })}}}\simeq \frac{{\displaystyle {\int }_0^E\sigma (E^{\prime })E^{\prime }d{E}^{\prime }}}{{\displaystyle {\int }_0^E{E}^{\prime }d{E}^{\prime }}}.\end{array}$$ 10

Since the log term in equation 7 varies slowly with energy $E\sim m{c}^2{\beta }^2/2$, it can be treated as a constant in equation 10, implying that the range-averaged cross section is nearly independent of the material stopping power. Thus, for thin targets, or those in which ions do not impart all of their energy on average, beam straggling may be neglected (Shao 2023).

Fig. 4.

a Stopping power plots for deuterons in Yb and ${\text{Yb}}_2{\text{O}}_3$ targets. b Range plots corresponding to ions that slow to rest, in the interval $E\to 0$ MeV (i.e. $R(E)<T$)

Figure 5 shows deuteron-induced cross sections extracted from Nagai et al. (2022) and TENDL-2023 (Koning et al. 2019). Since the simulated TENDL data underestimate the production cross section of $_{}^{177}$Lu (due to its larger mass number) (Müller et al. 2018; Rezaur Rahman and Amin 2022; López-Melero et al. 2024), the $_{}^{176}$Yb(d, p)$_{}^{177}$Lu excitation function is replaced by an interpolation of the experimental data (Fig. 1) (Hermanne et al. 2006; Manenti et al. 2011) in what we refer to as TENDL-2023$_{}^{†}$. With this modification, the range-averaged cross sections calculated using the precise version of equation 10 take on similar magnitudes. It is further observed that for $_{}^{177}$Lu, $〈\sigma 〉$ peaks around 17.9 MeV, which corresponds to the designed accelerator energy.

Fig. 5.

Short-lived radioisotope excitation functions given by a Nagai et al. (2022) (solid lines) and c TENDL-2023$_{}^{†}$ Koning et al. (2019) (dashed lines), in which we substituted the less accurate TENDL $_{}^{176}$Yb(d, p)$_{}^{177}$Yb cross section with data interpolated from Manenti et al. (2011); Hermanne et al. (2006). b,d Range-averaged cross sections are given for particles that slow completely to rest (i.e. $R(E)<T$), where E is the initial energy of a monoenergetic beam

As the stopping power increases for lower energies, the $_{}^{176}$Yb(d, p)$_{}^{177}$Yb cross section approaches zero. Therefore, shortening the target’s length to less than the range of the incoming deuterons reduces target heating while maintaining similar production efficiency. Since the deuterons now transmit through the target rather than stopping within it, the range-averaged cross section (10) becomes

$$\begin{array}{c}\hfill {〈\sigma 〉}_T=\frac{1}{T}{\int }_{E_T}^E\frac{\sigma (E^{\prime })}{S(E^{\prime })}d{E}^{\prime },\end{array}$$ 11

where $T=R(E)-R(E_T)$ is the target thickness and $E_T$ is the average energy of a deuteron after passing directly through the target (Morris et al. 2024). Figure 6 shows ${〈\sigma 〉}_T$ values for target widths corresponding to the intervals $E\to E_T=6,$ 8, and 10 MeV. When $E=E_T$, we see that ${〈\sigma 〉}_T=\sigma$, as expected. For higher values of $E_T$ (which correspond to a shorter target for a fixed beam energy), the maximum value of ${〈\sigma 〉}_T$ shifts between 17.9 and 12.5 MeV, where $\sigma$ is largest.

Fig. 6.

Range-averaged cross sections for ions in the intervals $E\to$ a 6 MeV, b 8 MeV, c 10 MeV (i.e. $T<R(E)$), where E is the initial energy of the beam. The calculations are made using excitation functions given by Nagai et al. (2022)

Since, for fixed beam energies, the yield of $_{}^{177}$Lu decreases with thinner targets, the beam energy and target thickness should be chosen to optimize production and cost. Table 4 considers three beams with fixed energies: 16, 18, and 20 MeV, which all deposit 10 MeV into a ${\text{Yb}}_2{\text{O}}_3$ target. Here, $\mathrm{\Delta }E/T$ is proportional to the heat absorbed by the target, $T{⟨\sigma ⟩}_T$ is proportional to the $_{}^{177}$Lu production rate, and $T{⟨\sigma ⟩}_T/E$ is proportional to the production rate per unit of applied beam energy. Although the 20 MeV beam has the highest production rate, the 18 MeV beam has greater production efficiency and saves the cost of an additional DTL. Compared to the 16 MeV beam, the 18 MeV beam has a higher yield and shifts the deuteron Bragg peak further outside the target, resulting in less energy deposited per unit distance.

Table 4.

$D^{+}$ energy and ${\text{Yb}}_2{\text{O}}_3$ target constants used to optimize the accelerator design for $_{}^{177}$Yb/$_{}^{177}$Lu production

$E\to E_T$ (MeV)	$16\to 6$	$18\to 8$	$20\to 10$
$\mathrm{\Delta }E$ (MeV)	10	10	10
T (mm)	0.32	0.36	0.40
$\mathrm{\Delta }E/T$ (MeV/mm)	31.3	27.8	25.0
${⟨\sigma ⟩}_T$ (mb)	167.4	175.4	167.9
$T{⟨\sigma ⟩}_T$ (mm-mb)	53.6	63.1	67.2
$T{⟨\sigma ⟩}_T/E$ (mm-mb/MeV)	3.35	3.51	3.36

Therefore, the 17.9 MeV $D^{+}$ design is well suited for optimal $_{}^{177}$Lu production. For a 0.36 mm ${\text{Yb}}_2{\text{O}}_3$ target, most ions are expected to deposit around 10 MeV of their initial kinetic energy. As a result, the target will be cooler than if the full 17.9 MeV was deposited, while the production losses will remain negligible. To further enhance target cooling, a water-cooled copper-backed plate—approximately 1 mm thick—can be incorporated into the assembly. A related study by Praena et al. examined water circulation speeds ranging from 5 to 15 m/s, which are also expected to be suitable for our device (Praena 2020).

Results

Production rates

The secondary ion flux for a reaction of type i, or the number of ions produced per unit radial distance squared per second, $\psi ={\psi }^{\{i\}}$, is given by

$$\begin{array}{c}\hfill \psi =\int \mathrm{\Phi }(E^{\ast })\int \frac{\mathrm{\Sigma }(E^{\prime })}{S(E^{\prime })}d{E}^{\prime }d{E}^{\ast }\end{array}$$ 12

where $\mathrm{\Phi }$ is the deuteron beam flux, $\mathrm{\Sigma }=N\sigma$ is the macroscopic cross section for the reaction, and N is the number density of Yb atoms in the target. Using the range-averaged cross section defined in equations 10 and 11, we can express the second integral in equation 12 as

$$\begin{array}{cc}\hfill \int \frac{\mathrm{\Sigma }(E^{\prime })}{S(E^{\prime })}d{E}^{\prime }=R(E^{\ast })〈\mathrm{\Sigma }〉(E^{\ast })& H(E_T-E^{\ast })\hfill \\ \hfill +T{〈\mathrm{\Sigma }〉}_T(E^{\ast })& H(E^{\ast }-E_T)\hfill \end{array}$$ 13

where the Heaviside step functions H(E) denote the boundary conditions for ions that stop in the target and those that pass through it. Since our design uses a thin target through which the beam fully traverses, the first part of equation 13 vanishes, resulting in a formula that does not explicitly depend on R.

For a Gaussian beam profile, the beam flux can be expressed as the product of the integrated flux $\varphi$ and a Gaussian shape function g:

$$\begin{array}{c}\hfill \mathrm{\Phi }(E^{\ast })=\varphi g(E^{\ast })\end{array}$$ 14

where $\varphi =ϵ\frac{J}{\mathit{qa}}$, $ϵ$ is the transmission efficiency of the beam, J is the current, q is the charge, and a is the area. In our case, we assume that a is equal to the frontal target area and that $ϵ=0.985$ when $J=10$ mA. Since the standard deviation of the beam energy is small relative to the overall beam energy (see Fig. 3), and because $\sigma$ changes little under these variations, we have $g(E^{\ast })\sim \delta (E^{\ast }-E)$, as for a purely mono-energetic beam. Hence, equation 12 becomes

$$\begin{array}{cc}\hfill \psi \simeq & \varphi T\int \delta (E^{\ast }-E){〈\mathrm{\Sigma }〉}_T(E^{\ast })d{E}^{\ast }\hfill \\ \hfill =& \varphi TN{〈\sigma 〉}_T(E).\hfill \end{array}$$ 15

The proportionality of the constants listed in Table 4 is now evident. Due to imperfect collimation, angular variations will cause some ions to have longer paths through the target, meaning that equation 15 will slightly underestimate the actual production rate. To account for this and for generality, we subsequently consider calculations over the interval $18\to 8$ MeV, which will differ only slightly from the designed 17.9 MeV accelerator.

For a circular ${\text{Yb}}_2{\text{O}}_3$ target with a radius of $r=1$ cm, enriched to 99% $_{}^{176}$Yb ($\eta =0.99$), Table 5 lists isotope production rates, calculated using $\mathrm{\Gamma }=\pi r^2\psi$, or

$$\begin{array}{c}\hfill \mathrm{\Gamma }=\eta ϵ\frac{J}{q}TN{〈\sigma 〉}_T(E).\end{array}$$ 16

Compared to a pure Yb target ($T=0.541$ mm), the ${\text{Yb}}_2{\text{O}}_3$ target ($T=0.359$ mm) produces fewer $_{}^{177}$Yb atoms—$1.065\times {10}^{13}$ compared to $1.367\times {10}^{13}$ atoms/s—when using the Nagai data. However, the range-averaged production rate of the ${\text{Yb}}_2{\text{O}}_3$ target exceeds that of pure Yb—$9.428\times {10}^{13}$ compared to $8.038\times {10}^{13}$ ${\text{atoms/cm}}^3$/s. The rates derived from the Nagai and ${\text{TENDL}}^{†}$ data are similar overall, particularly when using the interpolated experimental cross sections (Hermanne et al. 2006; Manenti et al. 2011) to calculate $_{}^{177}$Yb production. The direct production rate of $_{}^{177}$Lu differs by about a factor of 1.6 between the data sets. However, this difference has little consequence, since the $_{}^{177}$Yb production rate is 18 to 28 times greater.

Table 5.

Ion formation rates for 10 mA, 18 MeV $D^{+}$ on a 0.36 mm ${\text{Yb}}_2{\text{O}}_3$ target ($18\to 8$ MeV) calculated using data from Nagai et al. (2022) and ${\text{TENDL}}^{†}$ Koning et al. (2019), the latter of which includes $_{}^{176}$Yb(d, p)$_{}^{177}$Yb data interpolated from Manenti et al. (2011); Hermanne et al. (2006)

${\mathrm{\Gamma }}^{\{i\}}$ ($\times {10}^{13}$atom/s)	Nagai	TENDL-2023$_{}^{†}$
$_{}^{176}$Yb${(d,p)}^{177}$Yb	1.065	1.070
$_{}^{176}$Yb${(d,n\gamma )}^{177m}$Lu	n.a	$2.122\times {10}^{-2}$
$_{}^{176}$Yb${(d,n)}^{177g}$Lu	$3.853\times {10}^{-2}$	$6.051\times {10}^{-2}$
$_{}^{176}$Yb${(d,2n\gamma )}^{176m}$Lu	0.902	1.179
$_{}^{176}$Yb${(d,2n)}^{176g}$Lu	n.a	1.259
$_{}^{176}$Yb${(d,3n)}^{175}$Lu	n.a	2.885
$_{}^{176}$Yb${(d,4n\gamma )}^{174m}$Lu	$1.418\times {10}^{-3}$	$9.837\times {10}^{-6}$
$_{}^{176}$Yb${(d,4n)}^{174g}$Lu	$4.642\times {10}^{-2}$	$3.025\times {10}^{-5}$
$_{}^{176}$Yb$(d,\text{anything})$	n.a	7.105

Activations leading to stable Yb isotopes are excluded from the table

For stable isotopes not considered by Nagai et al., the simulated TENDL data allow us to estimate values that can be used for isotopic abundance and target burn-up calculations. The non-elastic cross section for deuterons can be expressed as

$$\begin{array}{cc}\hfill {\sigma }^{\text{non}}(d)=& \sum _{0\le {\nu }_n,{\nu }_p,\cdots }\sigma (d,\sum _{q=n,p,\cdots }{\nu }_{q}q)\hfill \\ \hfill =& \sigma (d,n)+\sigma (d,2n)+\cdots +\sigma (d,p)+\sigma (d,2p)\hfill \\ \hfill & +\cdots +\sigma (d,n+p)+\sigma (d,2n+p)+\cdots \hfill \end{array}$$ 17

where ${\nu }_q$ indicates the number of particles of type q produced in a single reaction. Since $_{}^{176}$Yb($d,d^{\prime }$) and $_{}^{176}$Yb($d,n+p$) reactions retain $_{}^{176}$Yb atoms in the target, the target burn-up cross section is given by

$$\begin{array}{cc}\hfill {\sigma }^{\ast }(d)=& {\sigma }^{\text{non}}(d)-\sigma (d,d^{\prime })-\sigma (d,n+p).\hfill \end{array}$$ 18

Figure 7 shows the non-elastic and burn-up cross sections for deuterons on Yb for $E_T=8$ MeV, with ordinary cross sections represented by dotted lines and range-averaged cross sections by solid lines. For $E=18$ MeV, ${〈\sigma 〉}_T^{\text{non}}$ and ${〈\sigma 〉}_T^{\ast }$ differ by less than 20%, resulting in a minimal effect on calculations. For a pure Yb target, the total reaction rate is $9.12\times {10}^{13}$ reactions/s, compared to $7.12\times {10}^{13}$ reactions/s for ${\text{Yb}}_2{\text{O}}_3$—seven times that of $_{}^{177}$Yb production. The burn-up rates are $7.77\times {10}^{13}$ reactions/s for Yb and $6.07\times {10}^{13}$ reactions/s for ${\text{Yb}}_2{\text{O}}_3$, respectively. Overall, it is projected to take more than 60 days of continuous irradiation to disintegrate more than 10% of $_{}^{176}$Yb in the target. This suggests that recycled targets can be reused multiple times (Yang et al. 2023).

Fig. 7.

a Non-elastic and target burn-up cross sections for $_{}^{176}$Yb. b Disintegration of $_{}^{176}$Yb in Yb and ${\text{Yb}}_2{\text{O}}_3$ targets over a 100-day period

Yield calculations

Since the produced radionuclides have short half-lives, isotope decay during and after irradiation must be considered as a function of time. The average density of a reaction rate in the target is given by dividing the reaction flux by the target thickness, $\psi /T=\varphi N⟨\sigma ⟩$. This quantity represents the number of reactions of type i per cubic centimeter. For indirect production of $_{}^{177}$Lu through $_{}^{176}$Yb(d, p)$_{}^{177}$Yb reactions, we have

$$\begin{array}{cc}\hfill \frac{dN_{_{}^{176}\text{Yb}}^{}}{\mathit{dt}}=& -\varphi ⟨\sigma ⟩_{_{}^{176}\text{Yb}}^{\ast }N_{_{}^{176}\text{Yb}}^{}\hfill \\ \hfill \frac{dN_{_{}^{177}\text{Yb}}^{}}{\mathit{dt}}=& \varphi ⟨\sigma ⟩_{_{}^{177}\text{Yb}}^{}N_{_{}^{176}\text{Yb}}^{}\hfill \\ \hfill & -\left(\lambda _{_{}^{177}\text{Yb}}^{},+,\varphi ,⟨\sigma ⟩_{_{}^{177}\text{Yb}}^{\ast }\right)N_{_{}^{177}\text{Yb}}^{}\hfill \\ \hfill \frac{dN_{_{}^{177}\text{Lu}}^{}}{\mathit{dt}}=& \lambda _{_{}^{177}\text{Yb}}^{}N_{_{}^{177}\text{Yb}}^{}\hfill \\ \hfill & -\left(\lambda _{_{}^{177}\text{Lu}}^{},+,\varphi ,⟨\sigma ⟩_{_{}^{177}\text{Lu}}^{\ast }\right)N_{_{}^{177}\text{Lu}}^{}.\hfill \end{array}$$

Here, $⟨\sigma ⟩_{_{}^{176}\text{Yb}}^{\ast }=⟨\sigma ⟩_{_{}^{176}\text{Yb},T}^{\ast }$ represents the average target burn-up cross section, while $⟨\sigma ⟩_{_{}^{177}\text{Yb}}^{}$ and $⟨\sigma ⟩_{_{}^{177}\text{Yb}}^{\ast }$ correspond to the production and burn-up of $_{}^{177}$Yb. The decay constant $\lambda _{_{}^{177}\text{Yb}}^{}$ leads to indirect production of $_{}^{177}$Lu, which further decays into stable $_{}^{177}$Hf. Generalizing the first-order differential equations for gain and loss terms, G and L, we can write them as

$$\begin{array}{cc}\hfill \dot{N_0}=& -L_0{N}_0\hfill \\ \hfill \dot{N_1}=& G_1{N}_0-L_1{N}_1\hfill \\ \hfill \dot{N_2}=& G_2{N}_1-L_2{N}_2.\hfill \end{array}$$

The equations are then solved by a modified version of Bateman’s formula (Cetnar 2006),

$$\begin{array}{c}\hfill N_n(t)=N_{0,T}\left(\prod _{j=1}^n,G_j\right)\sum _{k=0}^n{e}^{-L_{k}t}\prod _{l=0;l\ne k}^n{(L_l-L_k)}^{-1}\end{array}$$ 19

where $N_{0,T}=N_T(t=0)$ is the initial number density of the target and $N_n=N_n^{\{i\}}$ is the n-th decaying radionuclide produced by the reaction. As shown in Fig. 7, burn-up of the $_{}^{176}$Yb target ($n=0$) is given by

$$\begin{array}{c}\hfill N_{_{}^{176}\text{Yb}}^{}(t)=N_{0{,}^{176}\text{Yb}}e_{}^{-\varphi ⟨\sigma ⟩_{_{}^{176}\text{Yb}}^{\ast }t}\end{array}$$ 20

where t is the irradiation time. In contrast to neutron irradiations, where target burn-up is significant (Knapp et al. 2005), burn-up can be neglected in accelerator-based production calculations without making much difference. For indirect $_{}^{177}$Lu production without target burn-up, we have

$$\begin{array}{cc}\hfill \frac{dN_{_{}^{177}\text{Yb}}^{}}{\mathit{dt}}=& \varphi ⟨\sigma ⟩_{_{}^{177}\text{Yb}}^{}N_{_{}^{176}\text{Yb}}^{}-\lambda _{_{}^{177}\text{Yb}}^{}N_{_{}^{177}\text{Yb}}^{}\hfill \\ \hfill \frac{dN_{_{}^{177}\text{Lu}}^{}}{\mathit{dt}}=& \lambda _{_{}^{177}\text{Yb}}^{}N_{_{}^{177}\text{Yb}}^{}-\lambda _{_{}^{177}\text{Lu}}^{}N_{_{}^{177}\text{Lu}}^{},\hfill \end{array}$$

or,

$$\begin{array}{cc}\hfill \dot{N_1}=& \varphi {⟨\sigma ⟩}_1{N}_0-{\lambda }_1{N}_1\hfill \\ \hfill \dot{N_2}=& {\lambda }_1{N}_1-{\lambda }_2{N}_2,\hfill \end{array}$$

where the gain and loss terms now correspond only to the initial production rate and decay constants. Equation 19 now becomes

$$\begin{array}{c}\hfill N_n(t)=\frac{\varphi {⟨\sigma ⟩}_1{N}_0}{{\lambda }_n}\sum _{j=1}^n\left(1,-,e^{-{\lambda }_{j}t}\right)\prod _{k=1;k\ne j}^n{\lambda }_k{({\lambda }_k-{\lambda }_j)}^{-1}.\end{array}$$ 21

Hence, for $_{}^{176}$Yb(d, p)$_{}^{177}$Yb reactions, we have ($n=1$)

$$\begin{array}{c}\hfill N_{_{}^{177}\text{Yb}}^{}(t)=\frac{\varphi ⟨\sigma ⟩_{_{}^{177}\text{Yb}}^{}N_{_{}^{176}\text{Yb}}^{}}{\lambda _{_{}^{177}\text{Yb}}^{}}\left(1,-,e_{}^{-\lambda _{_{}^{177}\text{Yb}}^{}t}\right)\end{array}$$ 22

and ($n=2$)

$$\begin{array}{cc}\hfill N_{_{}^{177}\text{Lu}}^{}(t)=& \frac{\varphi ⟨\sigma ⟩_{_{}^{177}\text{Yb}}^{}N_{_{}^{176}\text{Yb}}^{}}{\lambda _{_{}^{177}\text{Lu}}^{}}\left(1,-,e_{}^{-\lambda _{_{}^{177}\text{Lu}}^{}t}\right)\hfill \\ \hfill & +\frac{\varphi ⟨\sigma ⟩_{_{}^{177}\text{Yb}}^{}N_{_{}^{176}\text{Yb}}^{}}{\lambda _{_{}^{177}\text{Lu}}^{}-\lambda _{_{}^{177}\text{Yb}}^{}}\left(e_{}^{-\lambda _{_{}^{177}\text{Lu}}^{}t},-,e_{}^{-\lambda _{_{}^{177}\text{Yb}}^{}t}\right).\hfill \end{array}$$ 23

Similarly, for $_{}^{176}$Yb(d, n)$_{}^{177}$Lu reactions, we have ($n=1$)

$$\begin{array}{c}\hfill N_{_{}^{177}\text{Lu}}^{}(t)=\frac{\varphi ⟨\sigma ⟩_{_{}^{177}\text{Lu}}^{}N_{_{}^{176}\text{Yb}}^{}}{\lambda _{_{}^{177}\text{Lu}}^{}}\left(1,-,e_{}^{-\lambda _{_{}^{177}\text{Lu}}^{}t}\right).\end{array}$$ 24

The overall yield is then found by summing over all of the contributing reactions: $N_{_{}^{177}\text{Lu}}^{}(t)=N_{_{}^{177}\text{Lu}}^{\{d,p\}}(t)+N_{_{}^{177}\text{Lu}}^{\{d,n\}}(t)$, or generally, for an isotope I,

$$\begin{array}{c}\hfill N_I(t)=\sum _i{\delta }_{\mathit{nI}}{N}_n^{\{i\}}.\end{array}$$ 25

Figure 8 shows the number of lutetium atoms in the target for long irradiations, with all possible reactions summed according to equation 25. Due to its short half-life ($t_{1/2}=3.66$ d), the production of $_{}^{176\text{m}}$Lu rapidly reaches saturation, while $_{}^{177}$Lu increases gradually for decaying $_{}^{177}$Yb. The bottom plot shows the specific activity of $_{}^{177}$Lu (mCi/mg of $_{}^{176}$Yb target) projected by our design, compared to that from neutron irradiation as reported in other studies (Dash et al. 2015).

Fig. 8.

a Radioisotope yields for long irradiations of 10 mA, 18 MeV $D^{+}$ ions on a 99% enriched [$_{}^{176}$Yb]${\text{Yb}}_2{\text{O}}_3$ target. b Comparison of the resulting Yb target specific activity with reactor-based production data extracted from reference (Dash et al. 2015). The x-markers indicate when target burn-up is included

Discussion

Although the main advantage of the accelerator-based production method is its higher radiopurity, its overall yield is also competitive with reactor-based methods. Here, the lower production cross section for the deuterons is offset by their higher flux—$1.99\times {10}^{16}$ d/${\text{cm}}^2$/s on the target compared to $2\times {10}^{15}$ n/${\text{cm}}^2$/s for the Oak Ridge High Flux Isotope Reactor (ORNL HFIR) and $1\times {10}^{14}$ n/${\text{cm}}^2$/s for the Missouri University Research Reactor (MURR). For our result, x-markers represent target burn-up given by equation 19, which results in only a marginal difference.

Since the activity of $_{}^{177}$Lu begins to saturate after a few days, shorter irradiation times are more effective. For an irradiation that ends at time $t=t^{\prime }$, we can express the remaining number of an m-th decay product as

$$\begin{array}{c}\hfill N_{I,m}(\tau )=\frac{1}{{\lambda }_m}\sum _{j=1}^m{N}_{I,j}^{\prime }\sum _{k=j}^m{\lambda }_k{e}^{-{\lambda }_k\tau }\prod _{l=j;l\ne k}^m{\lambda }_l{({\lambda }_l-{\lambda }_k)}^{-1}\end{array}$$ 26

where $\tau =t-t^{\prime }$ is the time elapsed after irradiation and $N_{I,j}^{\prime }$ is the concentration of the j-th product at $t^{\prime }$. For $_{}^{177}$Lu ($m=2$), we have

$$\begin{array}{cc}\hfill N_{_{}^{177}\text{Lu}}^{}(\tau )=& N_{_{}^{177}\text{Lu}}^{\prime }e_{}^{-\lambda _{_{}^{177}\text{Lu}}^{}\tau }\hfill \\ \hfill & +\frac{N_{_{}^{177}\text{Yb}}^{\prime }\lambda _{_{}^{177}\text{Yb}}^{}}{\lambda _{_{}^{177}\text{Lu}}^{}-\lambda _{_{}^{177}\text{Yb}}^{}}\left(e_{}^{-\lambda _{_{}^{177}\text{Yb}}^{}\tau },-,e_{}^{-\lambda _{_{}^{177}\text{Lu}}^{}\tau }\right).\hfill \end{array}$$ 27

Figure 9 now shows lutetium radioisotope yields after a 5-day irradiation. As before, the number of $_{}^{176m}$Lu atoms quickly saturate the target but now decay away rapidly after the irradiation is stopped.

Fig. 9.

a Lutetium isotope yields and b corresponding radiopurity after a 5-day irradiation

To determine the radiopurity of an isotope I, we divide its activity ${\alpha }_I(t)={\lambda }_I{N}_I(t)$ by the sum of all activities of the same nuclide. Although the radiopurity of $_{}^{176m}$Lu initially exceeds that of $_{}^{177}$Lu–$-$67.14% compared to 32.82%—it is quickly surpassed. After a 2-day processing time, the radiopurity of $_{}^{177}$Lu is 99.81%, while that of $_{}^{176m}$Lu is just 0.028%. For a 12-day irradiation and 2-day processing time, the radiopurity of each isotope is nearly the same. For longer processing times, the radiopurity of $_{}^{174g+m}$Lu and $_{}^{177m}$Lu increase since their half-lives are longer than that of $_{}^{177}$Lu. However, the activity of these longer-lived isotopes is generally negligible within the time frame during which the product can be used. After one half-life of $_{}^{177}$Lu, or 6.647 days following a 5-day irradiation, the radiopurity of $_{}^{177}$Lu remains above 99.73%.

Tables 6 and 7 list the yield and activity of each radioisotope. From our 1.04 g ${\text{Yb}}_2{\text{O}}_3$ target design, 1.07 mg of $_{}^{177}$Lu can be obtained after 5 days of irradiation. Producing 1.9 mg of $_{}^{177}$Lu—77% more than the initial amount—requires an additional 7 days of irradiation, a 140% increase in irradiation time. Optimal irradiation times are thus left to be determined by target processing costs. Due to saturation, the concentrations of $_{}^{177}$Yb and $_{}^{176m}$Lu are not affected by longer irradiations, while the production of $_{}^{174g+m}$Lu and $_{}^{177m}$Lu is insignificant.

Table 6.

Lutetium isotope yields after a 5-day irradiation and 48-hour processing time

$t=5$ d	$N_i$ ($\times {10}^{18}$atoms)	$M_i$ (mg)	$A_i$ (GBq)	$P_i$ (%)
$_{}^{177m}$Lu	0.0907	0.027	4.54	0.034
$_{}^{177g}$Lu	3.65	1.073	4406	32.82
$_{}^{176m}$Lu	0.172	0.05	9015	67.14
$_{}^{174m}$Lu	0.0061	0.002	0.342	0.003
$_{}^{174g}$Lu	0.02	0.058	1.328	0.01

$\tau =48$ hr	$N_i$ ($\times {10}^{18}$atoms)	$M_i$ (mg)	$A_i$ (GBq)	$P_i$ (%)
$_{}^{177m}$Lu	0.0899	0.026	4.50	0.12
$_{}^{177g}$Lu	3.05	0.897	3682	99.81
$_{}^{176m}$Lu	$2.0\times {10}^{-5}$	$6\times {10}^{-6}$	1.027	0.028
$_{}^{174m}$Lu	0.006	0.002	0.338	0.009
$_{}^{174g}$Lu	0.02	0.058	1.326	0.036

Table 7.

Lutetium isotope yields after a 12-day irradiation and 48-hour processing time

$t=12$ d	$N_i$ ($\times {10}^{18}$atoms)	$M_i$ (mg)	$A_i$ (GBq)	$P_i$ (%)
$_{}^{177m}$Lu	0.214	0.063	10.72	0.064
$_{}^{177g}$Lu	6.50	1.91	7840	46.47
$_{}^{176m}$Lu	0.172	0.05	9015	53.44
$_{}^{174m}$Lu	0.0142	0.004	0.807	0.005
$_{}^{174g}$Lu	0.48	0.14	3.181	0.019

$\tau =48$ hr	$N_i$ ($\times {10}^{18}$atoms)	$M_i$ (mg)	$A_i$ (GBq)	$P_i$ (%)
$_{}^{177m}$Lu	0.213	0.062	10.63	0.16
$_{}^{177g}$Lu	5.36	1.58	6469	99.76
$_{}^{176m}$Lu	$2.0\times {10}^{-5}$	$6\times {10}^{-6}$	1.027	0.016
$_{}^{174m}$Lu	0.014	0.004	0.8	0.012
$_{}^{174g}$Lu	0.48	0.138	3.177	0.049

For direct $_{}^{177}$Lu production by irradiating an 82% [$_{}^{176}$Lu]${\text{LuCl}}_3$ with thermal neutrons (${\varphi }_n=1.2\times {10}^{14}$ n/${\text{cm}}^2$/s), Sairanbayev et al. estimate activities ranging from 364 to 537 GBq/mg for irradiations lasting between 6.25 and 17 days (Sairanbayev et al. 2021). The corresponding ratio of $_{}^{177m}$Lu to $_{}^{177}$Lu activities was found to be less than 0.025. In our study, this ratio is $1.03\times {10}^{-3}$ for 5-day and $1.37\times {10}^{-3}$ for 12-day irradiations. After a 5-day irradiation and 2-day processing time, the specific activity of $_{}^{177}$Lu, averaged over the mass of all radionuclides, is 3.75 TBq/mg. Considering that long-lived $_{}^{176}$Lu and stable $_{}^{175}$Lu are also produced by (d, 2n) and (d, 3n) reactions, the specific activity averaged over the total lutetium mass is found to be 594 GBq/mg.

After irradiation, the ${\text{Yb}}_2{\text{O}}_3$ target can be dissolved in a 4 M solution of hydrochloric acid (Kuznetsov et al. 2019). Macro amounts of Yb are separated from the solution to isolate the $_{}^{177}$Lu product, which is ultimately precipitated into ${\text{LuCl}}_3$. Between 84–95% of Lu can be retained in this process (Yang et al. 2023) with Yb impurities less than ${10}^{-4}\%$ (Kuznetsov et al. 2019). As the overall processing only takes several hours, our design is expected to meet the requirement that radiochemical purity exceed 99%.

Conclusion

Currently, $_{}^{177}$Lu treatments cost around $14,500 per dose and require at least 4 doses in total (Vogel et al. 2021; Morgan et al. 2023). Given that these doses are administered every 6 to 8 weeks, it is necessary to localize production to ensure a reliable supply. Compared to reactor-based production methods, accelerators offer several advantages, such as easier supervision, enhanced safety, and lower maintenance costs (Wang et al. 2022). In addition, accelerators produce less nuclear waste and are capable of yielding a greater radiopurity of the desired isotope.

In this study, we demonstrated the feasibility of accelerator-based $_{}^{177}$Lu production and introduced new methods, based on experimental and simulated excitation functions, that can be used to optimize future accelerator designs. This includes the calculation of the target-averaged cross section ${⟨\sigma ⟩}_T$ and its corresponding relations, as provided in Table 4.

In conclusion, we presented the design of a 10 mA, 17.9 MeV $D^{+}$ linac intended to irradiate a 99% enriched [$_{}^{176}$Yb]${\text{Yb}}_2{\text{O}}_3$ target. We showed that our design is capable of producing 4.4 TBq of $_{}^{177}$Lu after 5 days and 6.4 TBq after 12 days, which meets the dose requirements for thousands of patients. The minimal burn-up of the target suggests that remaining ${\text{Yb}}_2{\text{O}}_3$ may be recycled and reused in multiple irradiations. Compared to traditional neutron-based production methods, our design achieves a competitive $_{}^{177}$Lu yield (1 mg in the first 5 days) and exceptionally high radiopurity (>99.8%). This design is expected to play an integral role in the future production of $_{}^{177}$Lu and other radioisotopes for the treatment of metastatic lesions and neuroendocrine cancers.

Author contributions

AAM conceptualized the study, conducted the investigation, developed the methodology, performed the formal analysis, and wrote the original draft. TW supervised the study and contributed to the investigation. ZW contributed to the conceptualization and supervision. YX and MH provided supervision. YL contributed to conceptualization, supervision, and manuscript review and editing. All authors read and approved the final manuscript.

Funding

Not applicable.

Availability of data and materials

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

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