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In our search for a new pseudoscalar particle produced by positron-electron resonant annihilation, we propose a new method to enhance detection sensitivity. Previous studies have examined collisions between a positron stream into a fixed target. However, our research reveals that considering the momentum density of electrons within the target material significantly improves the detection sensitivity for these particles. This effect is particularly pronounced in high-Z materials like Uranium, where the target acts as a natural electron accelerator, substantially expanding the production region in the parameter space.