The coupling of unstable states within an isolated system is discussed with special emphasis on intramolecular transitions. Using timehyphen;independent perturbation theory and normalization in a closed box, the coupling of a discrete state with a onehyphen;dimensional freehyphen;particle continuum is considered. The structure of the exact levels depends on the relative positions of the discrete state and the continuum. When the discrete state is degenerate with a state in the continuum, it is broadened to approximately an asymmetric Lorentzian shape, slightly shifted towards higher energy and of width given approximately by the ldquo;golden rule.rdquo; A new state is also found below the continuum. When the discrete state lies below the continuum, it is quasishifted towards lower energies. In this case the broadening is far from being Lorentzian, but is rather a delta function at the exact discrete state and much smeared throughout the continuum. The coupling of two discrete states with a continuum and the coupling of two continua is then discussed. The first case is quite similar to the single statendash;continuum coupling. For the latter case the manifold of exact states is found to be approximately equal to the union of both interacting continua, except for a new discrete state that is found below the two continua. The broadening of any state of either continua has a strong singularity at its original energy valueE0of the form1thinsp;sol;thinsp;lpar;E0thinsp;minus;thinsp;Erpar;2. Hence the transition probability from one continuum to another is very small, and predissociation by optical excitation into one continuum is hardly possible.
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