The main results of this paper are: 1) a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is real analyticity of the boundary of the obstacle, 2) a short proof that if 1 is an eigenvalue of the S-matrix, then k² is an eigenvalue of the Laplacian of the interior problem, and that in this case there exists a solution to the interior Dirichlet problem for the Laplacian, which admits an analytic continuation to the whole space R³ as an entire function.
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The ratio of the differential cross section of the charge exchange reaction of the deuteron to that of the nucleon, at small transferred momenta, has been discussed in order to estimate the spin-dependent part of the np → pn charge exchange amplitude.
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