Supersymmetry between deep and shallow nucleus-nucleus potentials

Supersymmetric quantum mechanis is applied to the determination of a shallow potential which is phase equivalent to a deep potential, and whose bound spectrum is identical except for the ground state which is suppressed. With this method, the nonphysical bound states encountered in the spectrum of microscopically founded potentials can be eliminated. The resulting shallow potentials present for small r values an ${\mathrm{r}}^{\mathrm{\ensuremath{-}}2}$ singularity in accord with a generalized Levinson theorem.

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