  Dark matter self-scattering is one of key ingredients for small-scale
structure of the Universe, while dark matter annihilation is important for the
indirect measurements. There is a strong correlation between the
velocity-dependent self-scattering cross section and the Sommerfeld enhancement
factor for the dark matter annihilation cross section. In this study, we
formulate a direct relation between them by the use of Watson's (initial
state/final state) theorem and Omn\`es solution, and our formulation reproduces
the Sommerfeld enhancement factor, which directly computed by solving the
Schr\"odinger equation, from the scattering phase shift.
