Sum Rule Approach To The Nuclear Response In The Isovector Spin Channel.

We study the global features of the response of infinite nuclear matter in the spin-isospin channel through the energy-weighted sum rules S1 and S−1. In particular we compare the outcome of the ring approximation with the exact RPA evaluation of the sum rules. We also investigate the influence of the collective character of the response, induced by the particle-hole force for longitudinal and transverse spin couplings. We show that S1 is insensitive to the collectivity of the response, as long as the Δ-degree of freedom is ignored. The inverse energy-weighted sum rule on the other hand, which is linked to the paramagnetic susceptibility, always reflects the hardening or softening of the nuclear response, due to the repulsive or attractive character of the p-h force. This quantity is well suited to the comparison with the experiments, which we perform for 12C and 56Fe.