## 2 Materials and Methods  
### Experimental Setup and Measurements  
A homogeneous water-gel phantom was prepared by mixing agar powder (C\({}_{14}\)H\({}_{24}\)O\({}_{9}\)) and water, with a ratio of 1/100 (in gm) (agar powder/water). The container used was high-density polyethylene (HDPE) with dimensions of 8 \(\times\) 10 \(\times\) 16 cm\({}^{3}\) and a wall thickness of 0.15 cm. The phantom geometry and PEMGRAPH are schematically shown in Figure 1. In addition, the material composition of the water-gel and HPDE container are listed in Table 1.  
The phantom was irradiated by a monoenergetic proton beam with 80 MeV energy for 60 s. The proton beam was pencil-like with a beam current of 10.20 nA and a diameter of \(\sim\)1 cm produced by an azimuthally varying field (AVF) cyclotron at the Cyclotron and Radioisotopes Centre (CYRIC) facility at Tohoku University, Japan. Considering the current that was used, about 3.8 \(\times\) 10\({}^{12}\) protons were used to irradiate the phantom. This value was higher than the typically used clinical beam, which was reported to be around 10\({}^{7}\) to 10\({}^{10}\) protons. We have employed higher number of protons than those used in clinical irradiations mainly to obtain more counts during the PEM scan. It is also well known that proton-induced activity only depends on the target fragmentation. The experimental setup for the irradiation of the water-gel phantom is shown in Figure 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Density (g/cm\({}^{3}\))** & \({}^{1}\)**H (\%)** & \({}^{12}\)C (\%)** & \({}^{16}\)**O (\%)** \\ \hline HDPE box & 0.950 & 14.29 & 85.71 & - \\ \hline Water-gel & 1.010 & 11.00 & 4.650 & 84.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Density and material composition (fraction by weight) of HDPE container and water-gel used in the proton irradiation experiment and PEM scan. Figure 1: Schematic diagram showing PEM heads and HPDE box containing water-gel being irradiated by a proton beam. The distance between the proton beam port and water-gel phantom was set to 25 cm (see Figure 2). The proton beam was adjusted to irradiate the center of the water-gel phantom. Upon proton irradiation, different positron emitting radioisotopes are produced by the inelastic nuclear interactions of protons with the target elements. The water-gel was mainly composed of oxygen and carbon (note: hydrogen (\({}^{1}\)H) was not considered, mainly because it does not produce stable positron emitting radioisotopes). The list of major nuclear reactions and the positron emitting radioisotopes produced as a result of proton irradiation is shown in Table 2.  
After proton irradiation, the irradiated water-gel phantom was placed in the PEMGRAPH system; this setup is shown in Figure 3. The irradiated water-gel phantom was scanned for 40 min with the PEMGRAPH system. The scanning of the irradiated water-gel phantom was started 15 min after the irradiation, mainly due to the time taken to carry the phantom from the irradiation room to the PEMGRAPH room after stopping the proton beam irradiation. \begin{table}
\begin{tabular}{c c c c} \hline
**Isotope** & **Half-Life (mins)** & **Reaction** & **Threshold (MeV)** \\ \hline \({}^{11}\)C & 20.33 & \({}^{12}\)C(p,pn)\({}^{11}\)C & 20.61 \\ \hline \({}^{15}\)O & 2.037 & \({}^{16}\)O(p,pn)\({}^{15}\)O & 16.79 \\ \hline \({}^{13}\)N & 9.965 & \({}^{16}\)O(p,2p2n)\({}^{13}\)N & 5.660 \\ \hline \end{tabular}
\end{table} 
Table 2: List of created isotopes, half-life, reaction and threshold reaction energy. Figure 3: Experimental setup of scanning the irradiated water-gel phantom using a dual-head PEMGRAPH system. Figure 2: Experimental setup of proton irradiation of water-gel phantom using a pencil-like proton beam with an energy of 80 MeV. A prototype PEMGRAPH (Mirai Imaging Inc., Fukushima, Japan) system was employed to scan the irradiated water-gel phantom.