## 1 Introduction  
Nanostructured metallic oxides can be prepared by various methods, such as a combination of the template-based method and sol-gel chemistry [1; 2; 3; 4], the facile wet chemical method [5], and the hydrothermal method [6; 7; 8; 9]. Hydrothermal synthesis has been an interesting technique for preparing materials with different nano-architectures, such as nanowires, nanorods, nanobelts, and nanoflowers [10; 11; 12], and its main advantage over other soft chemical routes is the ability to control the nanostructures by choosing the proper reaction temperature, time, solvent, and concentration without the need for any major structure-directing agents or templates. The effects of temperature, time, solvent, and concentration on the morphologies of powders prepared by the hydrothermal method have been extensively studied and reported [13; 14]; however, to our knowledge, there have been few studies on hydrothermal synthesis of rare earth metal oxides for use as radiotracers. Rare earth metallic oxide radiotracers can be used widely in science and engineering, particularly for industrial use, because they have high activation limits and rare metal elements, although they should be physically and chemically compatible with the material under investigation. A radiotracer for injection is labeled radioactively with a given material that allows it to be monitored as it moves through a system by external radiation detectors [15; 16]. Radiotracers must be produced relatively easily and cheaply by nuclear reactors and accelerators. Their chemical form is also important because they need to be in the same phase as the process medium, either aqueous or organic, and remain in that intended medium throughout the monitoring process. Radioisotope nanoparticles (NPs) have been synthesized with core-\({}^{198}\)Au shell-silica (\({}^{198}\)Au@SiO\({}_{2}\)) by neutron irradiation from the HANARO nuclear research reactor at the Korea Atomic Energy Research Institute (Daejeon, Korea) [17]. These core-shell radioisotope NPs have good physical and mechanical property because of SiO\({}_{2}\) shells in high energy gamma environments; however, the preparation process of \({}^{198}\)Au@SiO\({}_{2}\) radioisotope NPs is very complicated because of the capsulation of \({}^{197}\)Au NPs using SiO\({}_{2}\) in the presence of anchoring agents. Furthermore, only a very small amount of \({}^{198}\)Au@SiO\({}_{2}\) radioisotope NPs could be obtained because the Au NPs used as starting materials are commonly synthesized in amounts under \(10^{-3}\) M (mol/L). In addition, core-shell radioisotope NPs with multi gamma-emitting nuclides have been prepared by neutron irradiation at the HANARO research reactor [18]. The synthesis method of the core-shell radioisotope NPs with gamma-emitting nuclides have low yields. Therefore, synthesis methods with easy, simple, and good yields are needed to prepare radioisotope NPs for their use as radiotracers in various scientific, engineering, and industrial fields. In order to overcome the above problems, we also prepared four types of radioisotope NPs constructed with Au-ligand frameworks that were synthesized by a self-assembly process at room temperature for 3 h between 1,4-bis((1\(H\)-imidazol-1-yl)methyl)benzene (BIX), 2,6-bis((1\(H\)-imidazol-1-yl)nphthalene (BNX), di(1\(H\)-imidazol-1-yl)dimethylsilane (BIS), 4,4\({}^{\prime}\)-bis(pyridin-2-ylmethoxy) biphenyl (BPX), and radioisotope Au\({}^{3+}\) ions, which were prepared by the dissolution of Au-198 isotope in HNO\({}_{3}\)/HCl (mol-%, 1/3) mixture solution after neutron irradiation from the HANARO research reactor [19; 20]; however, the metal-ligand framework-constructed radioisotopes exhibited weak physical and chemical properties. In this study, nanostructured metallic oxides of MnO\({}_{2}\), Sm\({}_{2}\)O\({}_{3}\), and Dy\({}_{2}\)O\({}_{3}\) were synthesized by the hydrothermal process under various reaction conditions.