If dark matter has a finite size, the intrinsic interaction responsible for the structure formation is inevitable from the perspective of dark matter self-scattering. The sketch map of the calculation of the cross-section is shown, and a more realistic realization of the matter and charge distribution, the Chou-Yang model, is used in this paper. A new definition of velocity dependence and the implication on the small cosmological structures are studied. The numerical results show that the amplitude coefficient can affect the self-scattering cross-section to a large extent. In particular, we can restore the excluded parameter space in the presence of a non-vanishing amplitude coefficient. The correct relic density favors the super-heavy dark protons.
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