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In this paper we calculate the nonlinear susceptibility and the resonantRaman cross section for the paramagnetic phase of the ferromagnetic QuantumIsing model in one dimension. In this region the spectrum of the Ising modelhas a gap $m$. The Raman cross section has a strong singularity when the energyof the outgoing photon is at the spectral gap $\omega_{f} \approx m$ and asquare root threshold when the frequency difference between the incident andoutgoing photons $\omega_{i} -\omega_{f} \approx 2m$. The latter featurereflects the fermionic nature of the Ising model excitations.

Probing Strong Correlations with Light Scattering: the Example of the Quantum Ising model