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Eigenphase shifts and eigentime delays near a resonance for a system of onediscrete state and two continua are shown to be functionals of the Beutler-Fano formulas using appropriate dimensionless energy units and line profileindices. Parameters responsible for the avoided crossing of eigenphase shiftsand eigentime delays are identified. Similarly, parameters responsible for theeigentime delays due to a frame change are identified. With the help of newparameters, an analogy with the spin model is pursued for the S matrix and timedelay matrix. The time delay matrix is shown to comprise three terms, one dueto resonance, one due to a avoided crossing interaction, and one due to a framechange. It is found that the squared sum of time delays due to the avoidedcrossing interaction and frame change is unity.Comment: 17 pages, 3 figures, RevTe

Identification of the Beutler-Fano formula in eigenphase shifts and eigentime delays near a resonance