This has physical significance: h ℓ asymptotically (i.e. for large r) behaves as i e /(kr) and is thus an outgoing wave, whereas h ℓ asymptotically behaves as i e /(kr) and is thus an incoming wave. The incoming wave is unaffected by the scattering, while the outgoing wave is modified by a factor known as the partial-wave S-matrix element S ℓ :