S-wave resonances below the Ps( $$n=2$$ n = 2 ) threshold in positronic sodium interacting with screened Coulomb potentials

S-wave resonance states of the positronic sodium atom (\(e^+\hbox {Na}\)) interacting with screened Coulomb potentials (SCP) are studied. Two different SCPs are tested, namely static screened Coulomb potential (SSCP) and exponential cosine screened Coulomb potential (ECSCP). Resonance states are calculated by the stabilization method. Four S-wave resonance states are found to exist lying below the Ps(\(n=2\)) excitation threshold (\(E_\mathrm{ex}^{\mathrm{Ps}(2)}\)). For free atomic system, our reported results of resonance energy compare nicely with the reliable results available in the literature. To the best of our knowledge, our present results will be the first reported results of resonance of positronic–sodium atom under a screened environment.