Alternative approach to perturbation theory for screened Coulomb potentials

We study the problem of screened Coulomb potentials, using an alternative approach to perturbation theory. Assuming that the radial wave functions $R_{\mathrm{nl}}\mathrm{}\left(r\right)\mathrm{}$ can be written in exponential forms, we calculate the wave functions of the $K$-, $L$-, and $M$-shell electrons, through the fifth order in the perturbation parameter, by solving directly the set of resultant differential equations. The binding energies and wave functions obtained with this simple approach agree with previous work.