Dark sector interactions can be explored via the so-called type 3 model where dark matter and dark energy exchange momentum only, so as to minimize deviations from the $\mathrm{\Lambda }$ cold dark matter background expansion history. Using N-body simulations, we analyze the imprint of type 3 model parameters, the momentum exchange coupling constant $\beta$ and the slope of scalar field potential $\lambda$, on large-scale structure observables, particularly the matter pairwise velocity statistics. We find that the effects of $\beta$ ($<0$) and $\lambda$ on the mean matter peculiar pairwise velocity and velocity dispersion are degenerate. Our results highlight the potential of velocity statistics as a probe of dark sector interactions and underscore the importance of disentangling $\beta$ and $\lambda$ in cosmological analyses.

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• Cosmological parameters
• Cosmology
• Dark energy
• Dark matter
• Evolution of the Universe
• Lagrangian dynamics
• Large scale structure of the Universe