In order to understand the performance of the PARIS (Photon Array for the studies with Radioactive Ion and Stable beams) detector, detailed characterization of two individual phoswich (LaBr$_3$(Ce)-NaI(Tl)) elements has been carried out. The detector response is investigated over a wide range of $E_{gamma}$ = 0.6 to 22.6 MeV using radioactive sources and employing $^{11}B(p,gamma)$ reaction at $E_p$ = 163 keV and $E_p$ = 7.2 MeV. The linearity of energy response of the LaBr$_3$(Ce) detector is tested upto 22.6 MeV using three different voltage dividers. The data acquisition system using CAEN digitizers is set up and optimized to get the best energy and time resolution. The energy resolution of $sim$ 2.1% at $E_gamma$ = 22.6~MeV is measured for the configuration giving best linearity upto high energy. Time resolution of the phoswich detector is measured with a $^{60}$Co source after implementing CFD algorithm for the digitized pulses and is found to be excellent (FWHM $sim$ 315~ps). In order to study the effect of count rate on detectors, the centroid position and width of the $E_{gamma}$ = 835~keV peak were measured upto 220 kHz count rate. The measured efficiency data with radioactive sources are in good agreement with GEANT4 based simulations. The total energy spectrum after the add-back of energy signals in phoswich components is also presented.
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