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Electromagnetic strength functions of halo nuclei exhibit universal features that can be described in terms of characteristic scale parameters. For a nucleus with nucleon + core structure the reduced transition probability, as determined, e.g., by Coulomb dissociation experiments, shows a typical shape that depends on the nucleon separation energy and the orbital angular momenta in the initial and final states. The sensitivity to the final-state interaction (FSI) between the nucleon and the core can be studied systematically by varying the strength of the interaction in the continuum. In the case of neutron + core nuclei analytical results for the reduced transition probabilities are obtained by introducing the effective-range expansion. The scaling with the relevant parameters is found explicitly. General trends are observed by studying several examples of neutron +core and proton +core nuclei in a single-particle model assuming Woods-Saxon potentials. Many important features of the neutron halo case can be obtained from a square-well model. Rather simple analytical formulas are found. The nucleon-core interaction in the continuum affects the determination of astrophysical S factors at zero energy in the method of asymptotic normalisation coefficients (ANC). It is also relevant for the extrapolation of radiative capture cross sections to low energies. (c) 2005 Elsevier B.V. All rights reserved.