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

Energy spectrum for a short-range 1/r singular potential with a non-orbital barrier using the asymptotic iteration method