SYMMETRY PROPERTIES OF THE S-MATRIX WITH APPLICATION TO RESONANCE REACTIONS. (thesis). Technical Report No. 9

Technical Report · Mon Jan 01 04:00:00 EST 1962

OSTI ID:4805052

Davies, K T.R.; Baranger, M

Synametry 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. 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 offdiagonal 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. The results are illustrated with various two-channel examples. (auth)

• Research Organization: Carnegie Inst. of Tech., Pittsburgh
• NSA Number: NSA-16-024916
• OSTI ID: 4805052
• Report Number(s): NP-11738
• Country of Publication: United States
• Language: English

Related Subjects

BREIT-WIGNER FORMULA
CROSS SECTIONS
HOLES
INTERACTIONS
MATRICES
NEUTRONS
NUCLEAR REACTIONS
PHYSICS
QUANTUM MECHANICS
RESONANCE
S- MATRIX
S-WAVE
SCATTERING
SYMMETRY
THRESHOLD ENERGY