Physical Review A
American Physical Society
We derive a simple semiclassical representation to describe the large-scale structure of the spectrum of regular systems weighted by some arbitrary function W. Examples of weighted spectra are the width-weighted spectrum, which represents the decay rate of an unstable system, and the oscillator-strength-weighted spectrum, which represents the photoabsorption rate. Semiclassical representations of such spectra involve stationary-phase contributions, which are periodic or closed orbits, and end-point contributions, which are loops on an extremal torus. The theory provides the link between semiquantal formulas and the closed-orbit theory of atomic photoabsorption. It also allows calculation of an average decay rate without knowledge of the widths of individual quantum states.
Beims, M. W.; Kondratovich, V.; and Delos, John B., Semiclassical Theory of Weighted Spectra for Regular Systems: Absorption Spectra and Decay Rates (2000). Physical Review A, 62(4).