  It is well known that certain special classes of self-gravitating point-like
defects, such as global (non gauged) monopoles, give rise to non-asymptotically
flat space-times characterized by solid angle deficits, whose size depends on
the details of the underlying microscopic models. The scattering of
electrically neutral particles on such space-times is described by amplitudes
that exhibit resonant behaviour when the scattering and deficit angles
coincide. This, in turn, leads to ring-like structures where the cross sections
are formally divergent ("singular lensing"). In this work, we revisit this
particular phenomenon, with the twofold purpose of placing it in a contemporary
and more general context, in view of renewed interest in the theory and general
phenomenology of such defects, and, more importantly, of addressing certain
subtleties that appear in the particular computation that leads to the
aforementioned effect. In particular, by adopting a specific regularization
procedure for the formally infinite Legendre series encountered, we manage to
ensure the recovery of the Minkowski space-time, and thus the disappearance of
the lensing phenomenon, in the no-defect limit, and the validity of the optical
theorem for the elastic total cross section. In addition, the singular nature
of the phenomenon is confirmed by means of an alternative calculation, which,
unlike the original approach, makes no use of the generating function of the
Legendre polynomials, but rather exploits the asymptotic properties of the
Fresnel integrals.
