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. : 24.30.Cz, 25.70.De, Pacs

In 16 O and 40 Ca an isoscalar, low-energy dipole transition (IS-LED) exhausting approximately 4% of the isoscalar dipole (ISD) energy-weighted sum rule is experimentally known, but conspicuously absent from recent theoretical investigations of ISD strength. The IS-LED mode coincides with the socalled isospin-forbidden E1 transition. We report that for N = Z nuclei up to 100 Sn the fully self-consistent Random-Phase-Approximation with finite-range forces, phenomenological and realistic, yields a collective IS-LED mode, typically overestimating its excitation energy, but correctly describing its IS strength and electroexcitation form factor. The presence of E1 strength is solely due to the Coulomb interaction between the protons and the resulting isospin-symmetry breaking. The smallness of its value is related to the form of the transition density, due to translational invariance. The calculated values of E1 and ISD strength carried by the IS-LED depend on the effective interaction used. Attention is drawn to the possibility that in N = Z nuclei this distinct mode of IS surface vibration can develop as such or mix strongly with skin modes and thus influence the pygmy dipole strength as well as the ISD strength function. In general, theoretical models currently in use may be unfit to predict its precise position and strength, if at all its existence. PACS. 24.30.Gd Other resonances -21.60.Jz Nuclear density functional theory and extensions -21.30.Fe Forces in hadronic systems and effective interactions -25.30.Dh Inelastic electron scattering to specific states

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A simple, yet accurate solution of the electron-phonon coupling problem in C 60 is presented. The basic idea behind it is to be found in the parametrization of the ground state electronic density of the system calculated making use of ab-initio methods, in term of sp 2+x hybridized orbitals. This parametrization allows for an economic determination of the deformation potential associated with the fullerene's normal modes. The resulting electron-phonon coupling constants are used to calculate Jahn-Teller effects in C − 60 , and multiple satellite peaks in the corresponding photoemission reaction. Theory provides an accurate account of the experimental findings.

The relativistic excitation of the double giant dipole resonance in ' Xe has been calculated, describing the resonance as a harmonic vibration of the mean field, damped through its coupling to doorway states. While the predictions associated with the one-phonon states provide an overall account of the experimental findings, the calculated cross section for the two-phonon states is much smaller than that extracted from the involved analysis of the data. The experimental elucidation of this discrepancy seems essential for assessing the validity of the standard picture of giant resonances.