Elsevier

Nuclear Physics

Volume 11, May–June 1959, Pages 499-521
Nuclear Physics

The poles of the S-matrix of a rectangular potential well of barrier

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Abstract

To test the validity of current ideas on the poles of the S-matrix, a simple example is treated: non-relativistic scattering by a spherically symmetric rectangular potential well (on barrier). The poles of the S-matrix associated with this problem, in the case of zero angular momentum, are determined, and their behaviour as a function of the well depth (barrier height) is discussed. Some results for higher angular momenta are also given. The usual physical interpretation may be applied only to a very restricted class of poles. Difficulties appear in the case of “short-lived decaying states”. However, the present model leads to a connection between the limiting cases of strongly bound states in a deep well and of certain characteristic states attached to a “hard sphere” or to a perfect conductor (antenna). It is shown that some poles, previously described as “meaningless”, give rise to important physical effects.

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    Fellow of the National Research Council of Brazil; present address: Institute for theoretical Physics, University of Utrecht.

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