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\begin{document}

\title{Electron Accelerator--Based Co--Production of Multiple Medical Isotopes Utilizing Molten Salt Targets\thanks{Work supported by the National Natural Science Foundation of China (No. 12435012, No. 12175300, No. 12475185) and Shanghai Natural Science Foundation (No. 24ZR1478500)}}

\author{J. Z. Lin\textsuperscript{1,2,3}, R. D. Yuan\textsuperscript{4}, X. X. Li\textsuperscript{1,2,3,}\thanks{lixiaoxiao@sinap.ac.cn}, D. Y. Cui\textsuperscript{1,2,3}, C. G. Yu\textsuperscript{1,2,3}, J. H. Wu\textsuperscript{1,2,3}, J. G. Chen\textsuperscript{1,2,3}\\
		\textsuperscript{1}Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China \\
		\textsuperscript{2}University of Chinese Academy of Sciences, Beijing 100049, China\\
	    \textsuperscript{3}State Key Laboratory of Thorium Energy, Shanghai Institute of Applied Physics, Chinese Academy\\ of Sciences, Shanghai 201800, China\\
	    \textsuperscript{4}College of Physics, Henan Normal University, Xinxiang 453007, China
	    }
	
\maketitle

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\begin{abstract}
 Medical radioisotopes serve as indispensable cornerstones for modern nuclear medicine diagnosis and therapeutic applications. Their stable supply and technological innovation are critical to advancing the healthcare industry. This study proposes a multi--isotope co--production method based on electron accelerator--induced irradiation of a molten salt uranium target. This method possesses online extraction capability and can simultaneously produce multiple critical medical isotopes, including \(^{99}\text{Mo}\), \(^{99m}\text{Tc}\), \(^{89}\text{Sr}\), and \(^{131}\text{I}\). To validate the feasibility of this method, FLUKA Monte Carlo simulations were employed to optimize the structural parameters of the molten salt target. Subsequently, the annual production capacity of the target isotopes was evaluated in combination with online extraction. Results indicate that this method enables high--yield and high--efficiency co--production, it can fully meet the annual domestic demand for \(^{99}\text{Mo}\), \(^{99m}\text{Tc}\), and \(^{89}\text{Sr}\), while satisfying up to 20\% of the annual demand for \(^{131}\text{I}\). This production performance is expected to alleviate China's long--term dependence on imported medical radioisotopes, thereby providing a new technical pathway and valuable reference for the independent production of medical radioisotopes.
 
\end{abstract}


\section{INTRODUCTION}
Medical radioisotopes refer to radioactive isotopes used in disease diagnosis, treatment, and medical research, playing an irreplaceable role in clinical practice. They are categorized into two main classes: diagnostic and therapeutic radioisotopes. In the field of diagnosis, they can be further divided into positron-emitting and single-photon diagnostic radionuclides, such as Molybdenum-99/Technetium--99m (\(^{99}\text{Mo}\)/\(^{99m}\text{Tc}\)), Iodine--123 (\(^{123}\text{I}\)), Gallium--67/68 (\(^{67,68}\text{Ga}\)), and Copper--64 (\(^{64}\text{Cu}\)). In the field of therapy, they are classified into $\alpha$--emitting, $\beta^-$--emitting, and Auger electron--emitting therapeutic radionuclides, such as Yttrium--90 (\(^{90}\text{Y}\)), Lutetium--177 (\(^{177}\text{Lu}\)), Strontium--89 (\(^{89}\text{Sr}\)), Iodine--131 (\(^{131}\text{I}\)) and Californium--225 (\(^{225}\text{Ac}\)) \cite{b1}.

Currently, the production of medical radioisotopes primarily relies on two methods: reactor irradiation and accelerator--based production. Among these, reactor irradiation remains the dominant one due to its advantages of high yield, relatively low cost, and simpler target preparation. However, this supply chain relies heavily dependent on reactors constructed in the 1950s\textasciitilde1960s. Both planned or unplanned reactor shutdowns occur frequently, stemming from safety and technical issues caused by long--term high--load operation \cite{b2}. It is projected that most reactors currently in operation will face decommissioning within the next decade or so \cite{b3}, which is expected to place greater pressure on the global medical radioisotope supply system.

With the vigorous development and performance improvement of accelerator technology, accelerator--based isotope production has gradually become one of the primary methods. This method offers significant advantages: more convenient regulatory supervision, higher safety, lower maintenance and decommissioning costs, reduced radioactive waste production, lower radiation levels and lower nuclear proliferation risk \cite{b4}. Currently, proton accelerators (i.e., cyclotrons) serve as the primary type of accelerator utilized for isotope production, whereas linear electron accelerators (LINACs) have not yet been widely adopted. In the case of cyclotrons, nuclear reactions are directly induced by protons. In contrast, electrons from LINACs do not directly initiate nuclear reactions. Instead, they bombard a conversion target made of high--atomic--number materials (e.g., tantalum or tungsten) to generate high--intensity bremsstrahlung radiation. These high--energy photons subsequently induce photonuclear processes, thereby producing the desired radioactive isotopes. Several studies have demonstrated the feasibility of using LINACs for radioactive isotope production \cite{b5}.

This study proposes a multi--isotope co--production method based on an electron accelerator. Notably, this method employs direct electron beam irradiation on a molten salt target, which eliminates the requirement for a conversion target, thereby enhancing the utilization efficiency of the electron beam. The unique flow characteristics of the liquid molten salt target provide exceptional thermal management capabilities, effectively overcoming the heat dissipation limitations inherent in solid targets while enabling the potential for continuous online extraction. Compared with solid target systems, the liquid target system significantly simplifies the target fabrication process. Furthermore, this approach allows for the simultaneous production of multiple medical isotopes by adjusting the molten salt composition, thereby improving production efficiency. To preliminarily assess the feasibility of this technical route, this study employed the FLUKA Monte Carlo simulation code to analyze the production capacity of different isotopes. The research findings are expected to provide critical data support and a theoretical basis for the engineering implementation of this production method.


\section{Structure and Materials​}
This study employed 72\%LiF--28\%UF$_4$ molten salt as the target material, which maintains a molten state at a working temperature of \SI{600}{\degreeCelsius}. Under electron irradiation, the incident electrons primarily generate secondary photons through bremsstrahlung. These secondary photons then produce secondary neutrons via photonuclear reactions \ce{($\gamma$, xn)}. Subsequently, the secondary neutrons subsequently induce fission with uranium to produce isotopes, or the secondary photons directly interact with uranium through \ce{($\gamma$, f)} reactions to produce isotopes. Consequently, the production of isotopes primarily originates from two pathways: neutron--induced fission and photofission of uranium. Among these pathways, neutron--induced fission is predominantly contributed by \(^{235}\text{U}\), whereas photofission is mainly attributed to \(^{238}\text{U}\). The content of \(^{235}\text{U}\) directly affects the relative contribution proportion of neutron-induced fission and photofission. Owing to the high average energy (\textasciitilde MeV) of secondary neutrons and their resultantly low fission cross--section, moderation of these neutrons is essential to enhance fission efficiency. To address this, a neutron reflector is implemented surrounding the molten salt target to moderate and reflect the secondary neutrons. Given that the cross--sections for photonuclear reactions and photofission are significantly higher within the photon energy range of 10--20 MeV \cite{b6}, and the intensity of bremsstrahlung photons is maximized when their energy is approximately half of the incident electron energy, this study selected an electron beam energy of \SI{40}{MeV} and a beam current of \SI{1}{mA}. The schematic diagram of the isotope production system and the FLUKA computational model is shown in Fig.~\ref{fig1}.

\begin{figure}[htbp]
	\includegraphics*[width=.8\columnwidth]{fig1.eps}
	\caption{(a) Isotope production system based on electron accelerator irradiation of molten salt; (b) FLUKA model of the molten salt target.}
	\vspace{-20pt} 
	\label{fig1}
\end{figure}

In the LiF--UF$_4$ molten salt system, various medical isotopes can be produced, such as \(^{99}\text{Mo}\), \(^{99m}\text{Tc}\), \(^{131}\text{I}\), \(^{89}\text{Sr}\), \(^{90}\text{Y}\), \(^{14}\text{C}\), \(^{225}\text{Ac}\) and \(^{238}\text{Ra}\). However, the yields of the latter four are relatively low. Therefore, this study focuses primarily on the production of the former four isotopes: \(^{99}\text{Mo}\), \(^{99m}\text{Tc}\), \(^{131}\text{I}\) and \(^{89}\text{Sr}\). To evaluate the isotope yield of this method, a preliminary analysis of several key parameters was conducted, including target dimension, reflector thickness, and \(^{235}\text{U}\) content, and then the annual production capacity was assessed.

\subsection{Molten Salt Target Dimensions and Reflector Thickness}
Target dimension is one of the key design parameters affecting isotope yield. An excessively small target leads to insufficient electron beam utilization, resulting in beam wastage and reduced yield; conversely, an excessively large target not only increases the required molten salt volume and material costs but also raises the complexity of system operation and maintenance. Additionally, the reflector’s material and thickness significantly affect the utilization efficiency of secondary neutrons, thereby exerting a direct impact on the yield of target isotopes. In this study, zirconium hydride (ZrH$_{1.6}$) was selected as the reflector material and the target body was designed with a cubic configuration. The target material adopted herein is LiF--UF$_4$ molten salt, which uses natural uranium (\(^{nat}\text{U}\)) with a \(^{235}\text{U}\) enrichment of 0.72\%. Subsequently, the influence of reflector thickness on neutron moderation and isotope yield was analyzed.

The energy spectrum of reflected neutrons and the isotope yield after 1 day of irradiation are shown in Fig.~\ref{fig2} and Fig.~\ref{fig3}, respectively. As the thickness of ZrH$_{1.6}$ increases, both the flux of reflected neutrons and the proportion of thermal neutrons gradually increase, leading to a corresponding rise in isotope yield. The yield gradually saturates after the thickness reaches \SI{8}{cm}. Compared with a thickness of \SI{1}{cm}, an \SI{8}{cm}--thick reflector increased the reflected neutron flux by 290.36\% and enhanced the isotope yields as follows: 108.66\% for \(^{99m}\text{Tc}\), 108.65\% for \(^{99}\text{Mo}\), 44.53\% for \(^{131}\text{I}\), and 118.18\% for \(^{89}\text{Sr}\), respectively. For thermal neutron-induced fission of \(^{235}\text{U}\), the cumulative fission yields of \(^{99m}\text{Tc}\), \(^{99}\text{Mo}\), \(^{131}\text{I}\) and \(^{89}\text{Sr}\) are 5.35\%, 6.07\%, 2.81\%, and 4.66\%, respectively \cite{b7}. Among these nuclides, \(^{131}\text{I}\) exhibits the lowest fission yield, which results in its lowest growth rate. Since \(^{99}\text{Mo}\) is the parent nuclide of \(^{99m}\text{Tc}\), the growth trends and rates of \(^{99m}\text{Tc}\) and \(^{99}\text{Mo}\) are nearly identical. Although the fission yield of \(^{89}\text{Sr}\) is lower than that of \(^{99m}\text{Tc}\) and \(^{99}\text{Mo}\), its longer half--life minimizes decay loss, consequently resulting in the highest growth rate among the studied nuclides.

\begin{figure}[htbp]
	\includegraphics*[width=.8\columnwidth]{fig2.eps}
	\caption{Flux of reflected neutrons as a function of ZrH$_{1.6}$ thicknesses.}
	\vspace{-5pt}
	\label{fig2}
\end{figure}

\begin{figure}[htbp]
	\includegraphics*[width=.8\columnwidth]{fig3.eps}
	\caption{Yield versus ZrH$_{1.6}$ reflector thickness.}
	\vspace{-15pt} 
	\label{fig3}
\end{figure}


With the reflector thickness fixed at \SI{8}{cm}, the impact of target dimension (i.e., the molten salt side length) on isotope yield was further evaluated (Fig.~\ref{fig4}). The results indicate that as the size increases, the isotope yield first shows an upward trend and then gradually tends to saturate. Once the side length reaches \SI{40}{cm}, the yields of various isotopes essentially stabilize, with values of \SI{7.36}{Ci} Ci for \(^{99m}\text{Tc}\), \SI{12.40}{Ci} for \(^{99}\text{Mo}\), \SI{1.43}{Ci} for \(^{131}\text{I}\), and \SI{0.46}{Ci} for \(^{89}\text{Sr}\). Further increasing the size provides diminishing returns in terms of yield enhancement. Therefore, considering both economic efficiency and yield benefits, a size of \SI{40}{cm} was selected as the design dimension for the molten salt target.

\begin{figure}[htbp]
	\includegraphics*[width=.8\columnwidth]{fig4.eps}
	\caption{Variation of yield with molten salt side length​​.}
	\vspace{-15pt}
	\label{fig4}
\end{figure}


\subsection{\(^{235}\text{U}\) content}
Neutron--induced fission is a significant source of isotopes. This fission is primarily induced by \(^{235}\text{U}\), due to its relatively large fission cross--section. Consequently, the content of \(^{235}\text{U}\) directly influences the isotope yield. Meanwhile, to mitigate nuclear proliferation risks, the \(^{235}\text{U}\) content should remain below the threshold for low--enriched uranium (LEU, \(^{235}\text{U}\) enrichment $<$ 20\%). The variation of isotope yield with different \(^{235}\text{U}\) contents was discussed (Fig.~\ref{fig5}). As \(^{235}\text{U}\) content increases, the yield significantly rises. Compared with \(^{nat}\text{U}\), the use of LEU resulted in yield increment of 654.43\% for \(^{99m}\text{Tc}\), 654.45\% for \(^{99}\text{Mo}\), 347.10\% for \(^{131}\text{I}\), and 724.50\% for \(^{89}\text{Sr}\). Similarly, this discrepancy is primarily attributed to the variation in cumulative fission yields among different isotopes under neutron-induced fissions. Specifically, higher \(^{235}\text{U}\) content leads to more neutron-induced fission events, thereby enhancing the isotope yield. It is noteworthy that the contribution of photofission to the total yield remains almost constant regardless of \(^{235}\text{U}\) content. This is due to the small difference in the photofission cross--sections between \(^{235}\text{U}\) and \(^{238}\text{U}\), with a peak cross--section difference of only 0.17 barns ($E_\gamma$$=$\SI{14}{MeV}) \cite{b6}. Therefore, as \(^{235}\text{U}\) content increases, the relative contribution of photofission gradually decreases (Fig.~\ref{fig6}). For \(^{131}\text{I}\) specifically, the contribution from photofission is significantly greater than that for other target isotopes. This is because the cumulative yield of \(^{131}\text{I}\) from the photofission of uranium is higher than that from neutron-induced fission. The contribution proportion of photofission to the production of \(^{99m}\text{Tc}\), \(^{99}\text{Mo}\), and \(^{89}\text{Sr}\) remains similar across different \(^{235}\text{U}\) contents, which is primarily attributed to the dominant role of the cumulative neutron--induced fission yield \cite{b8}. In summary, practical application requires a trade--off based on the target objectives: if prioritizing the reduction of nuclear proliferation risks, \(^{nat}\text{U}\) should be selected as the target material; if pursuing high isotope yields, LEU is the preferable choice.

\begin{figure}[h]
	\includegraphics*[width=.8\columnwidth]{fig5.eps}
	\caption{ ​​Variation of yield with \(^{235}\text{U}\) content​​.}
	\label{fig5}
\end{figure}

\begin{figure}[htbp]
	\includegraphics*[width=.8\columnwidth]{fig6.eps}
	\caption{Contribution proportion of photofission to the yield​​.}
	\label{fig6}
\end{figure}


\section{Production Capacity Analysis}
One core advantage of liquid molten salt as a target material lies in its inherent potential for online reprocessing, enabling continuous online extraction of isotopes. For instance, \(^{99}\text{Mo}\) can be directly separated and extracted online during operation via methods such as gas bubbling \cite{b9}, \(^{131}\text{I}\), meanwhile, can be stripped from the molten salt in the form of HI or gaseous Te (g) \cite{b10}. To quantify the extraction behavior, this study incorporates the online extraction process into its production capacity assessment system by introducing the parameter of extraction efficiency. For an extraction efficiency of 0.0001 s\(^{-1}\), the estimated annual production capacities of various isotopes using both \(^{nat}\text{U}\) and LEU are shown in Table~\ref{table1}. The use of LEU enables a higher annual isotopes production capacity. Compared with \(^{nat}\text{U}\), LEU increases the annual yield of \(^{99m}\text{Tc}\) by approximately 7.44 times, \(^{99}\text{Mo}\) by about 7.50 times, and \(^{89}\text{Sr}\) by about 7.98 times. The increase for \(^{131}\text{I}\) is relatively lower, at 4.56 times. Although \(^{99m}\text{Tc}\) has the highest yield, its half--life is only 6 hours, making it difficult to long--term storage and transportation. It must be used promptly after production to minimize decay losses. Without considering losses, a single production system using LEU target material can meet the national annual demand for \(^{99}\text{Mo}\), \(^{99m}\text{Tc}\) and \(^{89}\text{Sr}\), while also satisfying 20\% of the national demand for \(^{131}\text{I}\).

\begin{table}[htbp]
	\centering
	\renewcommand{\arraystretch}{1.3} 
	\caption{​​Annual Production Capacity of Isotopes}
	\label{table1}
	\begin{tabular}{l c c c c}
		\toprule[0.6 pt]
		\(^{235}\text{U}\) & \(^{99m}\text{Tc}\) & \(^{99}\text{Mo}\)  & 
		\(^{131}\text{I}\) & \(^{89}\text{Sr}\) \\
		 content & (Ci/year) & (Ci/year) & (Ci/year) & (Ci/year)\\
		\midrule[1pt]
		\(^{nat}\text{U}\) & 31830  &  4245 & 570 & 149 \\
		LEU & 236951  & 31832 & 2603  & 1188 \\
		\bottomrule[0.6 pt]
	\end{tabular}
\end{table}


\section{CONCLUSIONS}
To address the demand for medical or industrial isotopes, this study proposes a multi--isotope co--production method, which employs an electron accelerator for the irradiation of a molten salt uranium target. A notable advantage of this method is its inherent potential for online extraction---a feature that holds significant value for streamlining isotope recovery processes. To systematically validate the method’s feasibility and performance, key operational parameters were analyzed, and its annual production capacity was evaluated. The results indicate that the proposed production method achieves a high isotope yield, thereby confirming its effectiveness for practical isotope co--production applications. Specifically, it can satisfy the full annual national demand for \(^{99}\text{Mo}\), \(^{99m}\text{Tc}\) and \(^{89}\text{Sr}\), along with 20\% of the annual demand for \(^{131}\text{I}\).


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	\bibitem{b2}  R. V. Noorden, ``Radioisotopes: The medical testing crisis'', \textit{Nature}, vol. 504, p. 202--204, Dec. 2013. {doi: \url{10.1038/504202a}}
	\bibitem{b3}  H.H. Xiong \textit{et al.}, ``Neutronics analysis of a subcritical blanket system driven by a gas dynamic trap--based fusion neutron source for \(^{99}\text{Mo}\) production'', \textit{Nucl. Sci. Tech.}, vol. 34, No. 49, Feb. 2023. {doi: \url{10.1007/ s41365-023-01206-2}}
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	\bibitem{b6}  \url{https://www-nds.iaea.org/exfor/endf.htm}
	\bibitem{b7}  \url{https://wwwndc.jaea.go.jp/cgi-bin/FPYfig?typ=g3&yld=c}
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