  We study resonances generated by rank one perturbations of selfadjoint
operators with eigenvalues embedded in the continuous spectrum. Instability of
these eigenvalues is analyzed and almost exponential decay for the associated
resonant states is exhibited. We show how these results can be applied to
Sturm-Liouville operators. Main tools are the Aronszajn-Donoghue theory for
rank one perturbations, a reduction process of the resolvent based on
Feshbach-Livsic formula, the Fermi golden rule and a careful analysis of the
Fourier transform of quasi-Lorentzian functions. We relate these results to
sojourn time estimates and spectral concentration phenomena
