Distributions of relative velocity between the centre of mass of the binary and that of the single at the encounter location R_enc, for different disc velocity dispersions σ. The blue, orange, and red histograms correspond to σ = 10⁻¹, 10⁻², 10⁻³, and 10⁻⁴, respectively. The grey dotted line is a Maxwell-Boltzmann distribution, which is characteristic of isotropic clusters, and matches the velocity dispersion in σ-2. The grey dashed line indicates the typical velocity distribution for a NSC that does not host a central SMBH.