Distribution of the widths of resonances for strong overlap and numerous decay channels: Influence on the average survival probability

Abstract

The distribution of the widths of N quasidegenerate metastable states decaying into a large number K of dissociation continua is studied in the framework of the random matrix theory. For strong overlap, the distribution of the imaginary parts of the eigenvalues of the effective Hamiltonian H−iΓ/2 is that of the eigenvalues of the width matrix Γ. The latter is found to belong to a model of random matrices proposed by Wigner and developed by Dyson. The analytical expression of the asymptotic density ρ(γ) for equal partial widths and N=K→∞ is a semicircular law centered at twice the mean width γ̄ times a function 1/γ. It predicts extensive fluctuations around the mean with a high density of small widths. As a result, the average survival probability of the metastable states lying within a narrow energy range decays more slowly than the exponential law which is assumed in the RRKM theory.