Statistical fluctuations of decay rates

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Abstract
We introduce a general Hamiltonian describing two coupled subsystems, each having a finite zero-order decay probability. With use of simple statistical assumptions on the underlying states, we derive new probability distributions of individual decay rates. We analyze the cases of weak and intermediate to strong coupling, respectively. The resulting distributions often resemble a suitable χ2 distribution, but do not belong to that class of functions. An interpretation of decay rates in terms of a χ2 model thus may lead to wrong conclusions. As a concrete realization, we study a Hamiltonian describing the non-Born–Oppenheimer coupling of two electronic states via the nuclear motion. The model is applied to the calculation of absorption-type spectra of NO2 and C2H+4. We investigate statistical properties of energy levels, line intensities, and decay rates. For NO2, we find from all statistics a completely irregular behavior, consistent with random matrix predictions and demonstrating the strong mixing of zero-order states due to the nonadiabatic coupling. For C2H+4, all statistics exhibit characteristic deviations from the irregular limit that can be given a consistent interpretation.