Q-matrix eigenchannels and resonance eigenchannel space

The time-delay matrix Q(E) can be diagonalized by a unitary transformation 

The eigenvalues qY are real since Q(E) is Hermitian, as seen from Eq. (48). The set of original physical channels are linearly transformed into a new set of channels by the unitary matrix Uq. We refer to these new channels as Q-matrix eigenchannels, or Q-eigenchannels, for short. In the rest of Section 2, the eigenvalues qy and the corresponding Q-eigenchannels will turn out to be quite useful in resonance analysis. 

Substitution of the Breit-Wigner S matrix (34) into Eq. (48) for the Q matrix and the assumption of an energy-independent B, i.e., an energy-independent background Sb yield the expression 

We have seen that, if the background Sb is independent of energy, then 

we can extract Er and V from the trace or the only nonzero eigenvalue L(E) of Q, 

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