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