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Studies based on imaging the annihilation of the electron (e$^{-}$) and its antiparticle positron (e$^{+}$) open up several interesting applications in nuclear medicine and fundamental research. The annihilation process involves both the direct conversion of e$^{+}$e$^{-}$ into photons and the formation of their atomically bound state, the positronium atom (Ps), which can be used as a probe for fundamental studies. With the ability to produce large quantities of Ps, manipulate them in long-lived Ps states, and image their annihilations after a free fall or after passing through atomic interferometers, this purely leptonic antimatter system can be used to perform inertial sensing studies in view of a direct test of Einstein equivalence principle. It is envisioned that modular multistrip detectors can be exploited as potential detection units for this kind of studies. In this work, we report the results of the first feasibility study performed on a e$^{+}$ beamline using two detection modules to evaluate their reconstruction performance and spatial resolution for imaging e$^{+}$e$^{-}$ annihilations and thus their applicability for gravitational studies of Ps.

The J-PET detector, which consists of inexpensive plastic scintillators, has demonstrated its potential in the study of fundamental physics. In recent years, a prototype with 192 plastic scintillators arranged in 3 layers has been optimized for the study of positronium decays. This allows performing precision tests of discrete symmetries (C, P, T) in the decays of positronium atoms. Moreover, thanks to the possibility of measuring the polarization direction of the photon based on Compton scattering, the predicted entanglement between the linear polarization of annihilation photons in positronium decays can also be studied. Recently, a new J-PET prototype was commissioned, based on a modular design of detection units. Each module consists of 13 plastic scintillators and can be used as a stand-alone, compact and portable detection unit. In this paper, the main features of the J-PET detector, the modular prototype and their applications for possible studies with positron and positronium beams are discussed. Preliminary results of the first test experiment performed on two detection units in the continuous positron beam recently developed at the Antimatter Laboratory (AML) of Trento are also reported.