Strong absorption and the distribution of zeros of the S-matrix |
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Authors: | K.W. McVoy P.A. Mello |
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Affiliation: | Physics Department, University of Wisconsin, Madison, Wisconsin 53706, USA;Instituto de Fisica, Departmento de Fisica Teorica, UNAM, AP 20-364, Mexico 20, DF, Mexico |
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Abstract: | The only distributions normally included in a discussion of the statistical theory of nuclear resonance reactions are the distributions of the widths (Γ) and spacings (D) of the levels of the compound nucleus. However, as the usual Hauser-Feshbach theory makes clear, and alone are not sufficient to determine the ratio . In an attempt to determine what further statistical information is sufficient to determine this ratio, in the special limit that it tends to zero for all cc′, c ≠ c′ (the “strong-absorption” limit), we study several “picket fence” S-matrix models, as well as a random-residue model exhibiting Ericson fluctuations. These models indicate that the strong-absorption limit is directly related to the distribution of the zeros of Scc′(E) in the upper half of the complex E-plane, and that strong absorption is reached only if these zeros are distributed with a high density in the region E → + i ∞. As a by-product, we obtain a generalization of the theorem of Moldauer and Simonius . Our generalization applies to individual optical S-matrix elements (and so to direct-reaction cross sections) rather than just to their determinant. |
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