  Using the asymptotic iteration method, we obtain the S-wave solution for a
short-range three-parameter central potential with 1/r singularity and with a
non-orbital barrier. To the best of our knowledge, this is the first attempt at
calculating the energy spectrum for this potential, which was introduced by H.
Bahlouli and A. D. Alhaidari and for which they obtained the "potential
parameter spectrum". Our results are also independently verified using a direct
method of diagonalizing the Hamiltonian matrix in the J-matrix basis.
