  We present a supersymmetric analysis of the wave problem with a
Demkov-Ostrovsky spherically symmetric class of focusing potentials at zero
energy. Following a suggestion of L\'evai, we work in the so-called R_0=0
sector in order to obtain the superpartner (fermionic) potentials within
Witten's supersymmetric procedure. General solutions of the superpotential for
the known physical cases are given explicitly.
