  We show that when an isolated doublet of unbound states of a physical system
becomes degenerate for some values of the control parameters of the system, the
energy hypersurfaces representing the complex resonance energy eigenvalues as
functions of the control parameters have an algebraic branch point of rank one
in parameter space. Associated with this singularity in parameter space, the
scattering matrix, S_l(E), and the Green's function, G_l^(+)(k; r,r'), have one
double pole in the unphysical sheet of the complex energy plane. We
characterize the universal unfolding or deformation of a typical degeneracy
point of two unbound states in parameter space by means of a universal
2-parameter family of functions which is contact equivalent to the pole
position function of the isolated doublet of resonances at the exceptional
point and includes all small perturbations of the degeneracy condition up to
contact equivalence.
