  The elementary quadratic plus inverse sextic interaction containing a
strongly singular repulsive core in the origin is made regular by a complex
shift of coordinate $x = s-{\rm i}\varepsilon$. The shift $\varepsilon>0$ is
fixed while the value of $s$ is kept real and potentially observable, $s \in
(-\infty,\infty)$. The low-lying energies of bound states are found in closed
form for the large couplings $g$. Within the asymptotically vanishing ${\cal
O}(g^{-1/4})$ error bars these energies are real so that the time-evolution of
the system may be expected unitary in an {\em ad hoc} physical Hilbert space.
