Refractive scattering and the nuclear rainbow in the interaction of12, 13C with12C at 20MeV/N

The elastic and inelastic scattering and the neutron transfer have been measured for the systems¹²C +¹²C and¹³C +¹²C at 20MeV/N up to θ_cm= 60° with theQ3D -spectrometer. The angular distributions of the elastic scattering show an enhanced cross section at angles larger than 40°. It can be identified as refractive scattering with the clear signature of a nuclear rainbow.L-cut-off calculations show that these contributions come fromL-values which are significantly lower than the grazingL-value. The deflection function has a broad minimum in thisL-range which is typical for rainbow scattering. TheS-matrix is decomposed by a phenomenological parametrization into a refractive and a diffractive part. The interference of these amplitudes plays an important role in the rainbow enhancement. The spatial localization of the refractive scattering is deduced from the turning points of the corresponding trajectories; a localization between 2.5 fm and 4 fm is found. Semi-classical calculations with complex trajectories in the single-turning-point approximation show good agreement with the quantummechanical calculations. Refractive contributions are not observed in the inelastic scattering. This can be explained by reducing the strength of the conventional collective form factor in the internal region. In contrast to this the enhancement at large angles is seen in the one-neutron transfer channels where the refractive scattering is dominant. This is the first observation of such contributions to heavy-ion transfer reactions.