Klein-Gordon Type Equation Research Articles

In this paper we discuss the relativistic model of multiple scattering on the basis of similarity which may be established between the model and the nonrelativistic potential scattering. The problem of nonrelativistic high energy forward and backward scattering as obtained from the Klein-Gordon type equation as well as the many channel situation and the treatment of exchange forces are considered in detail in Section 2. It is found that all the usual high energy approximations require a smooth and nonsingular-atorigin behavior of the potential. Many of the results of Section 2 are found to be analogous to the results obtained by other means in the relativistic case. In particular, by assuming that the relativistic “effective potential” defined in the model of multiple scattering by means of single scattering is smooth and nonsingular at origin, the eikonal type approximations for forward and backward scattering are obtained. Restrictions due to unitarity on the high energy behavior of the derived scattering amplitude are discussed in terms of Martin's unitarity bound. A generalization of the procedure to an arbitrary inelastic process is given. Some interesting relations between forward and backward amplitudes at high energies are obtained. It is also shown that the model contains the absorption model as a special case, and corrections due to backward scattering and to the “Random phase assumption” are obtained. Unitarity places restrictions on the freedom of choice of the single scattering amplitude; in fact, the limit of the high energy behavior of the exchange interactions is found.

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