th / 9 90 80 03 v 1 2 A ug 1 99 9 Microscopic Studies on Two - Phonon Giant Resonances

A new class of giant resonances in nuclei, namely double giant resonances, is discussed. They are giant resonances built on top of other giant resonances. Investigation on their properties, together with similar studies on low-lying two-phonon states, should give an answer on how far the harmonic picture of boson-type excitations holds in the finite fermion systems like atomic nuclei. The main attention in this review is paid to double giant dipole resonances (DGDR) which are observed in relativistic heavy ion collisions with very large cross sections. A great experimental and theoretical effort is underway to understand the reaction mechanism which leads to the excitation of these states in nuclei, as well as the better microscopic understanding of their properties. The Coulomb mechanism of the excitation of single and double giant resonances in heavy ion collision at different projectile energies is discussed in details. A contribution of the nuclear excitation to the total cross section of the reaction is also considered. The Coulomb excitation of double resonances is described within both, the second-order perturbation theory approach and in coupled-channels calculation. The properties of single and double resonances are considered within the phenomenologic harmonic vibrator model and microscopic quasiparticle-RPA approach. For the last we use the Quasiparticle-Phonon Model (QPM) the basic ideas and formalism of which are presented. The QPM predictions of the DGDR properties (energy centroids, widths, strength distributions, anharmonicities and excitation cross sections) are compared to predictions of harmonic vibrator model, results of other microscopic calculations and experimental data available.