Critical Screening Parameters for the Generalized Screened Coulomb Potential

An approximate expression for the critical screening parameters associated with the attractive generalized screened Coulomb potential (GSCP) is obtained by utilizing the variational principle and the virial theorem. Subject to certain conditions, this expression is shown to represent a lower bound to the true critical screening parameters associated with the GSCP. Specific results are reported for the bound states $n$, $l=n-1\mathrm{}$ of the Debye-Hückel potential and for the ground state and first excited state of the exponential-cosine screened Coulomb potential.