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Partial-wave scattering decomposes a scattering state into partial waves with definite orbital angular momentum. For a central potential, each channel has its own scattering phase shift and Partial-wave S-matrix.

For elastic scattering by a real central potential, the phase shift ${\delta }_l(k)$ measures the phase difference between the asymptotic radial wave in angular-momentum channel $l$ and the corresponding free wave. Its channel Partial-wave S-matrix is $S_l=e^{2i{\delta }_l}$.

The phase shift parametrizes elastic partial-wave scattering, rather than general scattering phenomena.