, O. (1984). New magnetic dipole excitation mode studied in the heavy deformed nucleus 156Gd by inelastic electron scattering.

We study a model of a deformed nucleus in which protons and neutrons are described as interacting rigid rotors with axial symmetry. The nucleus as a whole is no longer axially symmetric. A magnetic-dipole collective state describing rotational oscillations of protons against neutrons is predicted.

An equation of motion method for solving the nuclear eigenvalue problem in a basis of microscopic multiphonon states is reformulated consistently in terms of Tamm-Dancoff phonons. The potential and limits of the method are illustrated through the calculation of the nuclear response to dipole and quadrupole external fields in 16O. The calculation is performed using either a Nilsson or a Hartree-Fock basis. The role of the multiphonon states is shown to depend strongly on the choice of the basis. The effect of the truncation of the three-phonon subspace is also discussed

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Recent high resolution (p, t) experiments have established the existence of a large number of low-lying excited 0 + levels in the deformed 158 Gd [1] and, later on, in some actinide nuclei [2] and 168 Er [3]. The number of 0 + states detected in 168 Er is particularly large, the levels below 4 MeV amounting to about 22 [4]. The distribution pattern of the two-nucleon transfer transition strengths shows that one single 0 + state is strongly populated in all nuclei, with the exception of 168 Er where the strength is fragmented into several small peaks.All theoretical studies performed so far have been confined to 158 Gd. The first was a phenomenological investigation [5], which shows that the extended (sdpf ) interacting boson model (IBM) can account for a large fraction of the detected 0 + states. The (sdpf ) IBM analysis points out the importance of the octupole degrees of freedom.In order to account for all detected states and to gain a detailed information on their properties, it is necessary to adopt microscopic approaches. The first calculation of this kind was performed in the framework of the projected shell model (PSM) [6] adopting a restricted space spanned by two and four quasiparticle states. Including the latter states was crucial for covering the whole spectrum. The calculation reproduces well all the energy levels and yields very small E2 decay strengths for the corresponding states.An extensive study of the 0 + states in 158 Gd was carried out recently [7], within the quasiparticle-phonon model (QPM) [8]. Energies, E2 and E0 transition strengths as well as two-nucleon transfer spectroscopic factors were computed and investigated. It came out that an appreciable fraction of the 0 + states in 158 Gd has large or dominant twophonon components, mostly built out of collective octupole phonons, in agreement with the IBM results [5]. The calculation has also confirmed the PSM prediction [6] of very weak quadrupole collectivity for all 0 + states. In fact, the 0 + one-phonon states came out to be linear combinations of several pairing correlated two-quasiparticle qq components. These, however, add coherently only in one state. Such a 0 + pairing collective state is strongly populated in (p, t) two-nucleon transfer reactions, in agreement with experiments.In [9] we extend the QPM study to 168 Er and some Th and U isotopes. All these nuclei were explored in the latest (p, t) experiments [2,3,4]. We intend to test if the QPM can account for the huge number of 0 + levels observed in 168 Er [4] and is able to offer a consistent picture of the properties of the 0 + states in deformed nuclei of different regions.Our study shows that it is necessary to go beyond the mean field approximation (RPA) in order to account for the large number of 0 + levels observed in 168 Er. RPA, in fact, generates only 15 0 + states be low 4 MeV. Moreover, according to our QPM calculation, several levels, specially above 3 MeV, correspond to states with appreciable, often dominant, two-phonon components. A few of these states carry to...

We adopt the quasiparticle-phonon model to investigate the microscopic structure of some low-lying states recently discovered in nuclei around shell closure. The study determines quantitatively the phonon content of these states and shows that their main properties are determined by a subtle competition between particleparticle and particle-hole quadrupole interactions and by the interplay between orbital and spin-flip motion. The results are in overall agreement with experiments and consistent with the interacting boson model and shell model calculations.

Abstract. The multipole response of neutron rich O and Sn isotopes is computed in Tamm-Dancoff and random-phase approximations using the canonical Hartree-Fock-Bogoliubov quasi-particle basis. The calculations are performed using an intrinsic Hamiltonian composed of a V lowk potential, deduced from the CD-Bonn nucleon-nucleon interaction, corrected with phenomenological density dependent and spin-orbit terms. The effect of these two pieces on energies and multipole responses is discussed. The problem of removing the spurious admixtures induced by the center of mass motion and by the violation of the number of particles is investigated. The differences between the two theoretical approaches are discussed quantitatively. Attention is then focused on the dipole strength distribution, including the low-lying transitions associated to the pygmy resonance. Monopole and quadrupole responses are also briefly investigated. A detailed comparison with the available experimental spectra contributes to clarify the extent of validity of the two self-consistent approaches. ‡ present address : Ecole Normale Superieur (ENS) de Cachan, 61 av. du Président Wilson, Cachan -France Self-consistent study of multipole response in neutron rich nuclei using a modified realistic potential2

An analysis of the construction of a q-deformed version of the 3-dimensional harmonic oscillator, which is based on the application of q-deformed algebras, is presented. The results together with their applicability to the shell model are compared with the predictions of the modified harmonic oscillator.