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In conventional scattering theory, by large-distance asymptotics, at the costof losing the information of the distance between target and observer, oneimposes a large-distance asymptotics to achieve a scattering wave functionwhich can be represented explicitly by a scattering phase shift. In this paper,without large-distance asymptotics, we establish an arbitrary-dimensionalscattering theory. Arbitrary-dimensional scattering wave functions, scatteringboundary conditions, cross sections, and phase shifts are given withoutlarge-distance asymptotics. The importance of an arbitrary-dimensionalscattering theory is that the dimensional renormalization procedure in quantumfield theory needs an arbitrary-dimensional result. Moreover, we give adiscussion of one- and two-dimensional scatterings.

Scattering theory without large-distance asymptotics in arbitrary dimensions