Illustration of the differential cross section for self-scattering of identical particles via a light mediator (referred to as Møller scattering in this work) for two values of the anisotropy parameter r defined in Eq. (3) (solid lines). Noting the logarithmic y-axis, the strong enhancement for θ → 0 and θ → π can be seen, and it becomes more pronounced the larger the r (i.e. the lighter the mediator mass). We note that the isotropic case (red dashed) is not flat due to the scaling of the cross section with sin(θ) (such that the lines represent the scattering rate within a given range (θ, θ + dθ) of the azimuthal angle, for any value of the polar angle). We also illustrate the division into small and large-angle scattering by a critical angle θ_c, for two representative values, exemplifying the hybrid approach studied in this work.