Resonances in few-body systems

It is shown how the resonance poles of the scattering amplitude correspond to eigenstates of the Hamiltonian that is analytically continued into the complex r-space via the dilatation group transformation, and how the corresponding eigenstates satisfy a modified form of the orthogonality condition. As an illustration of the results, examples of resonance in π-d, and α-d scattering as a three-body system, are given which demonstrated how the energy dependence in the cross section is not necessarily all due to resonances, but could partly be due to the square root threshold because two of the three particles in the system can form a resonance. 11 refs., 4 figs