Accession Number:

AD0276215

Title:

SYMMETRY PROPERTIES OF THE S-MATRIX WITH APPLICATION TO RESONANCE REACTIONS

Descriptive Note:

Corporate Author:

CARNEGIE INST OF TECH PITTSBURGH PA

Personal Author(s):

Report Date:

1962-12-01

Pagination or Media Count:

1.0

Abstract:

Symmetry relations of the S-wave, N-channel S-matrix are rederived and applied to a study of its structure in the vicinity of resonances, both away from and near thresholds. A resonance is defined as a pole of the S-matrix. For an isolated pole far from any threshold, the S-matrix can be expressed as the sum of a resonance factorable matrix and a nondiagonal, background matrix, a well-known result. The parametrization of this expression is discussed. Two types of threshold resonances are considered, corresponding to one and two poles of S respectively. For both cases, the S-matrix again has resonance and background contributions, but the off-diagonal elements involving the opening channel have no background The two-pole threshold resonance obeys the standard Breit-Wigner formula, while the one-pole case has a different behavior, which can only be obtained from the Breit-Wigner expression by making certain reduced widths infinite. Unitarity and symmetry relations impose some interesting restrictions on the distribution of poles and the shape of cross sections near threshold. Results are illustrated. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE


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