The scattering of heavy ions gives clear evidence of resonances which may be grouped in families like the rotational bands. The classical Breit-Wigner theory makes use of fixed poles which describe locally the resonances, but the global character of the rotational sequences is completely lost. Furthermore, the phenomenology shows that the rotational sequences evolve into surface waves. Again the classical Breit-Wigner theory, in view of its local character, cannot describe this evolution. In this paper we describe the resonances by the use of poles of the scattering amplitude in the complex angular-momentum plane: moving poles. However, in order to interpolate a sequence of resonances belonging to the same family we must add to the poles a term which takes into account the repulsive forces due to the Pauli principle and to the hard core. This term describes the downward crossing, through π/2, of the phase shifts after each resonance. At higher energies the effect of the exchange forces tends to vanish and simultaneously the resonances evolve towards diffractive effects: we have the surface waves creeping around the target. This phenomenon is described in our theory by the moving poles as the imaginary part of the angular momentum increases for increasing energy. Besides a detailed study of this theory we present here an extensive analysis of the α-${}^{40}\mathrm{Ca}$ elastic scattering which gives clear phenomenological support to the model.

• Received 10 July 1996

DOI:https://doi.org/10.1103/PhysRevC.55.2593