eng Science and Education Publishing International Journal of Physics 2333-4576 2025-09-23 13 4 91 104 10.12691/ijp-13-4-2 IJP20251342 article Mamadou COULIBALY mam.mcma@gmail.com 1 Ibrahima Gueye FAYE 1 Bassirou LO 1 Department of Physics, Cheikh Anta Diop University, Dakar, Senegal We present a comprehensive theoretical and numerical study of acceptor impurity states in polar semiconductors, combining a variational method with the Modified Generalized Exponential Cosine Screened Coulomb (MGECSC) potential. This potential accounts for long-range Coulomb screening, while central-cell corrections describe short-range lattice effects. Polaronic contributions are explicitly incorporated through the Huang¨CRhys factor, enabling the analysis of phonon-assisted photoionization spectra. Calculations are performed for GaAs and CdTe, with parameters calibrated against experimental binding energies. Our results show that plasma screening reduces binding energies, weakens vibronic coupling, and modifies spectral line shapes in agreement with experimental observations. The model demonstrates predictive capability for photoionization cross sections, bridging plasma physics and semiconductor physics, and provides valuable insights for the design of doped optoelectronic devices under controlled screening conditions. https://pubs.sciepub.com/ijp/13/4/2/ijp-13-4-2.pdf Impurity states Photoionization cross section Polaron effects MGECSC potential Central-cell correction plasma GaAs CdTe Electron¨Cphonon coupling Variational method Huang¨CRhys factor