Microscopic studies on two-phonon giant resonances

Abstract

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

The Two-Photon Decay of the 11-/2 Isomer of 137Ba and Mixed-Symmetry States of 92,94Zr and 94Mo

“…An introduction to the QPM -used to calculate the properties of the nuclei 92 Zr, 94 Zr and 94 Mo -is given in this section which follows closely the literature [Ber99,Wal10]. The QPM is a purely phenomenological but microscopic approach to nuclear structure.…”

“…5.19 is included in the diagonalization procedure being responsible for the mixing of two-quasiparticle states. The full QPM hamiltonian can be rewritten in the quasiparticle basis as [Ber99] with the multipole operators…”

“…However this is not feasible due to the high dimension of the resulting matrix. In the so called Quasiparticle Random-Phase Approximation (QRPA) approach one truncates the large basis utilizing the following ansatz for the phonon operator which projects the ground state on the excited states [Ber99]:…”

“…it is well known that the energies of the low-lying states are too high on the QRPA-level. The full QPM hamiltonian can be rewritten in terms of phonon operators as [Ber99] Figure 5.5: Comparison of the QRPA and QPM spectra of the lowest 2 + states of 92 Zr. Clearly, the Hamiltonian is not diagonal in the phonon basis because of the term H int which introduces a mixing of phonon states. In order to truncate the resulting matrix in the phonon basis to a feasible size the QPM includes only one, two -and three phonon states.…”

“…Today there are still many purely phenomenological nuclear structure models in use, as for example the Interacting Boson Model (IBM) [Ari75,Ari78] or the Quasi-Particle Phonon Model (QPM) [Ber99]. These models are still useful to design experiments and to obtain an understanding of a particular nuclear structure phenomenon.…”