Quantum mechanical effect of diffraction of a semi-classical plasma on the doubly excited singlet S states of positronium negative ion ( \(\hbox {Ps}^-\) ) are investigated. A pseudopotential containing two adjustable parameters is used to model the effective interaction potential in semi-classical plasmas. The screening parameter \(\kappa \) represents the collective screening effect, whereas the parameter \(\lambda \) pertaining to the de Broglie wavelength of the pair of interacting particles corresponds to the quantum mechanical effect of diffraction at short distances. Doubly excited states (DES) of \(\hbox {Ps}^-\) have been identified within the framework of the stabilization method by employing an extensive highly-correlated Hylleraas-type wavefunction containing 715 square integrable functions and a scaling parameter. The energies and the widths characterizing the DESs are then determined by fitting the density of the resonant states with the Lorentzian function. Convergence of the energy and width of each identified DES is examined by expanding the size of the employed wavefunction. For the plasma-free case, it has been possible to identify the existence of four DESs in \(\hbox {Ps}^-\) lying below the Ps(n=3) excitation threshold. The energies and widths of those states are found to be in excellent agreement with some reliable results in the literature. A comprehensive study is then carried out on the changes in the energies and widths of these states due to the variation of \(\kappa \) and \(\lambda \) . Our findings prove that the energies of the DESs increase with increasing \(\lambda \) at a given \(\kappa \) . However, variation of the width with respect to \(\lambda \) at a given \(\kappa \) is distinctive.
