  The spherically symmetric potential $a \,\delta (r-r_0)+b\,\delta ' (r-r_0)$
is generalised for the $d$-dimensional space as a characterisation of a unique
selfadjoint extension of the free Hamiltonian. For this extension of the Dirac
delta, the spectrum of negative, zero and positive energy states is studied in
$d\geq 2$, providing numerical results for the expectation value of the radius
as a function of the free parameters of the potential. Remarkably, only if
$d=2$ the $\delta$-$\delta'$ potential for arbitrary $a>0$ admits a bound state
with zero angular momentum.
