# New Inorganic Scintillators' Application in the Electromagnetic Calorimetry in High-Energy Physics
## 2 Simulations in Geant4
### Validation of the Simulations for Pure GAGG and PWO Calorimeters  
Gamma spectra of \({}^{22}\)Na and \({}^{137}\)Cs radioactive sources were measured in GAGG crystals of different lengths. The measurements were conducted using a PMT-143 photomultiplier with a quantum efficiency of 17.6% [19]. The results of the measurements and approximations can be found in a previously published article [20]. The calculated weighted average value of the light yield was 420 \(\pm\) 16 phe/MeV. This value was further utilized in simulations to characterize the light yield of any length of GAGG crystal.  
The simulation of the response of a single crystal reproduces the experimental energy spectra of GAGG crystals obtained using radioactive sources (see Figure 3; crystal length 3 cm). The small deviation in the position of the second and third peaks can be explained by effects not included in the simulation; for instance, light absorption in the crystals.  
To validate the simulation model, the spatial and energy resolutions of the assembly consisting solely of PWO crystals were compared to the experimental data collected with the ALICE experiment's PHOS detector.  
To obtain the spatial resolution, a two-dimensional distribution of the distance from the photon's entrance point into the assembly to the cluster's center of gravity was calculated with a logarithmic weight [1] (Figure 4, left). The projection of such a distribution on the x-axis was then plotted (Figure 4, right), and the standard deviation, which represents the spatial resolution, was calculated.  
Figure 3: An example of the reproduction of experimental data in simulations. GAGG crystal length is 3 cm [20].  
The dependence of the spatial resolution of the assembly consisting of PWO crystals on the energy, with and without the noise being taken into account, is shown in Figure 5. The results of the PHOS detector of the ALICE experiment were used as a reference [1; 2].  
One can see that the spatial resolution obtained in the simulations reproduces the experimental data rather well, especially when the 5 MeV noise and the 10 MeV minimum cell energy cut are included.  
To calculate the energy resolution of the PWO-calorimeter, the obtained distributions of the deposited energy were approximated by the Gaussian function and its parameters \(\sigma\) and \(E_{mean}\) were determined.  
The obtained dependence of the energy resolution on the energy of the primary photons is shown in Figure 6. The experimental curve obtained in beam tests of the PHOS prototype is given as a reference [18]. One can see that the simulated resolution and experimental resolution are almost the same in the case of high noise, but the simulation generally offers a better resolution. This can be explained by the higher electronic noise level in the experiment. When the noise is reduced, the resolution improves across the entire energy range.  
Figure 4: (**Left**) An example of a two-dimensional distribution of the coordinates of the cluster center of gravity for \(10^{5}\) photons with an energy of 5 GeV; (**right**) a projection of the two-dimensional distribution on the x-axis [20].  
Figure 5: Energy dependence of the spatial resolution of PWO crystals in the simulation compared to experimental results [20].  
Thus, the simulation reproduces the spatial and energy resolution of the PWO crystals quite well. Therefore, it is possible to consider a model of a compound calorimeter of sequentially arranged GAGG and PWO crystals and predict the energy and spatial resolutions of the calorimeter based on our model with a sufficient degree of confidence.