Unitarity Relation in an Impact Parameter Representation

概要

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The unitarity relation for impact parameter amplitudes can be expressed in a transparent forth by using phase functions. There is no essential difference for the theoretical treatment of both partial wave and impact parameter amplitudes, whenever the reaction (or inelastic) channels have to he taken into account. The threshold behaviour of the impact parameter amplitude is shown by using the effective range theory. The imaginary part of the impact parameter phase function is not equal to zero ben below the lowest threshold of the reaction channels, while the non-zero value of the imaginary part of the partial wave phase shift corresponds to the existence of the reaction channels. At the higher energies or the large values of the impact parameter, the impact parameter amplitude becomes to be equal to the partial wave amplitude of the corresponding orbital angular momentum state.
理論物理学刊行会の論文