  Using techniques of supersymmetric quantum mechanics, scattering properties
of Hermitian Hamiltonians, which are related to non-Hermitian ones by
similarity transformations, are studied. We have found that the scattering
matrix of the Hermitian Hamiltonian coincides with the phase factor of the
non-unitary scattering matrix of the non-Hermitian Hamiltonian. The possible
presence of a spectral singularity in a non-Hermitian Hamiltonian translates
into a pronounced resonance in the scattering cross section of its Hermitian
counterpart. This opens a way for detecting spectral singularities in
scattering experiments; although a singular point is inaccessible for the
Hermitian Hamiltonian, the Hamiltonian "feels" the presence of the singularity
if it is "close enough". We also show that cross sections of the non-Hermitian
Hamiltonian do not exhibit any resonance behavior and explain the resonance
behavior of the Hermitian Hamiltonian cross section by the fact that
corresponding scattering matrix, up to a background scattering matrix, is a
square root of the Breit-Wigner scattering matrix.
