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The elementary quadratic plus inverse sextic interaction containing astrongly singular repulsive core in the origin is made regular by a complexshift of coordinate $x = s-{\rm i}\varepsilon$. The shift $\varepsilon>0$ isfixed 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 closedform for the large couplings $g$. Within the asymptotically vanishing ${\calO}(g^{-1/4})$ error bars these energies are real so that the time-evolution ofthe system may be expected unitary in an {\em ad hoc} physical Hilbert space.

The large-g observability of the low-lying energies in the strongly singular potentials $V(x)=x^2+g^2/x^6$ after their PT-symmetric regularization