Critical screening parameters of one-electron systems with screened Coulomb potentials: circular Rydberg states

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The critical screening parameters (λ c ) of one-electron systems in circular states under short-range screened Coulomb potentials (SCPs) are investigated using the generalized pseudospectral method. High-precision values of λ c are obtained for bound states with the principal quantum number n up to a thousand. The polynomial fittings based on the numerical values indicate that the high-Rydberg limits of the n 2-scaled critical screening parameters, i.e. , are equal to , , and , respectively, for the Debye–Hückel, Hulthén, and exponential cosine SCPs. It is surprisingly found that these high-Rydberg limits can be well-reproduced from Bohr’s correspondence principle together with the semi-classical model of the hydrogen atom. We further show that both the present numerical calculations and the semi-classical analysis can be extended to other short-range potentials such as the generalized exponential, Lennard–Jones, modified Pöschl–Teller, shifted Morse, Woods–Saxon, and Manning–Rosen potentials that attract wide interest in atomic, molecular, and nuclear physics.