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We derive the 3D spatially homogeneous Boltzmann's equation with moderatelysoft potentials and singular angular interaction, from an interacting particlessystem. The collision kernel is of the form $B(z,\sigma)=|z|^{\gamma}b\left(\frac{z}{|z|}\cdot \sigma\right)$ and for $K>0$,$\sin(\theta)b\left(\cos(\theta)\right)\sim K\theta^{-1-\nu}$, with $\gamma\in(-2,-1)$ and $\nu\in(1,2)$ satisfying $\gamma+\nu>0$. We use at the particlelevel the regularizing effects of the grazing collisions, in order to controlthe singularity of the soft potential. This enables to use a classicalcompactness argument, and provide a qualitative convergence result from theinteracting particles system toward the solution of the limit macroscopicequation.

Derivation of the Boltzmann equation with moderately soft potentials from a perturbed Nanbu particles system