Physics – Quantum Physics
Scientific paper
2003-05-12
Physics
Quantum Physics
10 pages, 2 figures
Scientific paper
10.1103/PhysRevB.68.245305
The line shape of resonances in the overlapping regime is studied by using the eigenvalues and eigenfunctions of the effective Hamiltonian of an open quantum system. A generalized expression $\tilde q_k(E)$ for the Fano parameter of the resonance state $k$ is derived that contains the interaction of the state $k$ with neighboured states $l\ne k$ via the continuum. It is energy dependent since the coupling coefficients between the state $k$ and the continuum show a resonance-like behaviour at the energies of the neighboured states $l\ne k$. Under certain conditions, the energy dependent $\tilde q_k(E)$ are equivalent to the generalized complex energy independent Fano parameters that are introduced by Kobayashi et al. in analyzing experimental data. Long-lived states appear mostly isolated from one another in the cross section, also when they are overlapped by short-lived resonance states. The $\tilde q_k(E)$ of narrow resonances allow therefore to study the complicated interplay between different time scales in the regime of overlapping resonance states by controlling them as a function of an external parameter.
Magunov A. I.
Rotter Ingrid
Strakhova S. I.
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