## 2 Experiments  
### Materials  
Manganese sulfate monohydrate (MnSO\({}_{4}\cdot\)H\({}_{2}\)O), samarium nitrate hydrate (Sm(NO\({}_{3}\))\({}_{3}\cdot\)H\({}_{2}\)O), dysprosium nitrate hydrate (Dy(NO\({}_{3}\))\({}_{3}\cdot\)H\({}_{2}\)O), triethylene glycol, pentanol, n-octane, ammonium persulfate ((NH\({}_{4}\))\({}_{2}\)S\({}_{2}\)O\({}_{8}\)), cetyltrimethylammonium bromide (CTAB), sodium hydroxide (NaOH), and methanol were obtained from Korea-Sigma-Aldrich, Seoul, Republic of Korea. and used in the treatments. Water was purified in a Milli-Q plus water purification system (Millipore Co. Ltd., Burlington, MA, USA) to a final resistance of 18.2 M\(\Omega\) cm\({}^{-1}\) and degassed prior to each measurement. Other chemicals were of reagent grade. Synthesis of Radioisotopes MnO\({}_{2}\), Sm\({}_{2}\)O\({}_{3}\), and Dy\({}_{2}\)O\({}_{3}\) NPs by Neutron Irradiation  
Manganese dioxide (MnO\({}_{2}\)) was synthesized by redox hydrothermal synthesis in aqueous solution at 120 \({}^{\circ}\)C for 8 h, as given by the following equation:  
\[\text{MnSO}_{4}+(\text{NH}_{4})_{2}\text{S}_{2}\text{O}_{8}+2\text{H}_{2}\text {O}\rightarrow\text{MnO}_{2}+(\text{NH}_{4})_{2}\text{SO}_{4}+2\text{H}_{2} \text{SO}_{4} \tag{1}\]  
In detail, 1.93 g (8.00 mmol) manganese sulfate monohydrate (MnSO\({}_{4}\cdot\)H\({}_{2}\)O) and 2.61 g (8.0 mmol) ammonium persulfate ((NH\({}_{4}\))\({}_{2}\)S\({}_{2}\)O\({}_{8}\)) were put into 50 mL distilled water at room temperature to form a homogeneous solution, which was then transferred into a 100-mL Teflon-lined stainless-steel autoclave. The sealed solution was kept at 120 \({}^{\circ}\)C for 8 h. After the autoclave was cooled down to room temperature naturally, the obtained products were filtered and washed with distilled water to remove any remaining ions. The as-prepared materials were dried overnight in a vacuum oven at 80 \({}^{\circ}\)C. In order to remove the organic elements, the as-prepared MnO\({}_{2}\) samples were calcined at 900 \({}^{\circ}\)C for 2 h under an air atmosphere. Finally, the nanostructured radioisotope MnO\({}_{2}\) was synthesized by neutron irradiation using the HANARO research reactor (Korea Atomic Energy Research Institute). Samarium oxide (Sm\({}_{2}\)O\({}_{3}\)) NPs can be synthesized by the W/O (water/oil) emulsion process and the calcination process as in the following equations:  
\[\mathrm{Sm(NO_{3})_{3}+3 NaOH\to SmOH+3 NaNO_{3}} \tag{2}\]  
\[\mathrm{2 SmOH+O_{2}\to Sm_{2}O_{3}+H_{2}O} \tag{3}\]  
In the first step, 2.0 mL of 1.5 mol/L Sm(NO\({}_{3}\))\({}_{3}\) aqueous solution was added to 1.0 g pentanol as a cosurfactant, 8.0 g n-octane as an organic solvent, and the appropriate amount of surfactant cetyltrimethylammonium bromide (CTAB), and then the mixture was agitated until it became a transparent microemulsion. The temperature was maintained by putting the whole setup into a thermostatic water bath. The microemulsion was slowly added to an NaOH aqueous solution under agitation, and this finally led to the formation of a suspension of surfactant-stabilized SmOH. After being stirred for 1 h, the suspension was allowed to stand for 24 h at a specified temperature to obtain as large an amount as possible of surfactant-stabilized SmOH NPs (in the form of a precipitate). The precipitate was then collected by centrifuging and washed several times with pure ethanol and distilled water. The collected products were dried in a vacuum oven at 75 \({}^{\circ}\)C for 5 h. In the second step, the dried precipitate (SmOH) was calcined at 500 \({}^{\circ}\)C for 6 h in the oxygen state to obtain the primrose yellow Sm\({}_{2}\)O\({}_{3}\) nanoparticles. Finally, nanostructured radioisotope Sm\({}_{2}\)O\({}_{3}\) was synthesized by neutron irradiation (neutron flux: 4.2 \(\times\) 10\({}^{13}\) n\(\cdot\)cm\({}^{-2}\cdot\)s\({}^{-1}\)) of the as-prepared Sm\({}_{2}\)O\({}_{3}\) powder by the HANARO research reactor (Korea Atomic Energy Research Institute).