Complete critical bound region of the generalized exponential cosine screened Coulomb potential

Abstract The complete critical bound region of the generalized exponential cosine screened Coulomb potential (ECSCP) V ( r ) = − r − 1 e − ( β cos ⁡ θ ) r cos ⁡ ( β sin ⁡ θ ) r is investigated by employing the generalized pseudospectral method. Highly accurate critical screening parameters are determined over the entire parameter space, spanning from the exponential screened Coulomb potential ( θ = 0), via the oscillatory ECSCP ( θ = π / 4 ), to the strongest oscillatory cosine Coulomb potential (CCP) ( θ = π / 2 ). With an efficient extrapolation technique, the critical screening parameter for the CCP is estimated at about β c = 2.34 . By analyzing the variation of the ground state energy in the critical bound region, we separate the parameter space into two regions, i.e. the exponential region at small and moderate values of θ where the exponential screening term dominates the critical behavior of system, and the cosine region for θ close to π / 4 where the oscillatory cosine term dominates.