Critical bound–continuum limit of the two-electron Z ee-system interacting with the generalised exponential cosine screened Coulomb potential

Abstract The effect of the generalised exponential cosine screened Coulomb potential (GECSCP) on the stability of a model two-electron atom ( Z e+e+e) interacting via this type of potential has been investigated. GECSCP is taken in the form: V ( ρ ; μ , θ ) = exp [ − ( μ cos ⁡ θ ) ρ ] cos ⁡ [ ( μ sin ⁡ θ ) ρ ] / ρ (in a.u.), where µ ( 0 ⩽ μ < ∞ ) and θ ( 0 ⩽ θ ⩽ π / 2 ) are two adjustable parameters. An extensive wavefunction, having 715 number of terms, is utilised to calculate the ground state energy of the model atom (for Z = 1 , 2 , 3 ) within the framework of the Ritz’s variational method. Convergence of the computed results with respect to the number of terms in the wavefunction is corroborated. An inclusive study is made on the variation of the ground state energy and other related quantities with respect to the parameters µ and θ . Special emphasis is given on the determination of the critical values of the parameters which correspond to the critical bound–continuum limits of the model atoms.