Particular spectral singularity in the continuum energies: a manifestation as resonances

We study the coalescence of two bound energy eigenstates embedded in the continuous spectrum of a real Hamiltonian H _W and the singular point produced by this coalescence. At the singular point, the two unnormalized Jost eigenfunctions are no longer linearly independent but coalesce to give rise to a bound state eigenfunction embedded in the continuum. We disturb the potential V _W by means of a truncation; this perturbation breaks the singular point in two resonances. The phase shift shows a jump of magnitude $2\pi$ and the shape of the cross section shows two inverted peaks; this behaviour is due to the interference between the two nearly degenerate resonances and the background component of the Jost function. (paper)