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

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

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The electromagnetic response in 16 O is studied within a recently developed approach that generates iteratively a microscopic multiphonon basis well suited for reformulating and solving exactly the nuclear eigenvalue problem within spaces of large dimensions spanned by complex configurations. These multiphonon configurations are seen to modify appreciably, dramatically in some cases, the mean field response. This is shown to be increasingly affected by the center-of-mass motion as the number of phonons increases. The method for removing such a spurious motion is briefly outlined and the effects discussed.

Background: The electric dipole strength detected around the particle threshold and commonly associated to the pygmy dipole resonance offers a unique information on neutron skin and symmetry energy, and is of astrophysical interest. The nature of such a resonance is still under debate.Purpose: We intend to describe the giant and pygmy resonances in 208 Pb by enhancing their fragmentation with respect to the random-phase approximation. Method:We adopt the equation of motion phonon method to perform a fully self-consistent calculation in a space spanned by one-phonon and two-phonon basis states using an optimized chiral two-body potential. A phenomenological density dependent term, derived from a contact three-body force, is added in order to get single-particle spectra more realistic than the ones obtained by using the chiral potential only. The calculation takes into full account the Pauli principle and is free of spurious center of mass admixtures. Results:We obtain a fair description of the giant resonance and obtain a dense low-lying spectrum in qualitative agreement with the experimental data. The transition densities as well as the phonon and particle-hole composition of the most strongly excited states support the pygmy nature of the low-lying resonance. Finally, we obtain realistic values for the dipole polarizability and the neutron skin radius. Conclusions:The results emphasize the role of the two-phonon states in enhancing the fragmentation of the strength in the giant resonance region and at low energy, consistently with experiments. For a more detailed agreement with the data, the calculation suggests the inclusion of the three-phonon states as well as a fine tuning of the single-particle spectrum to be obtained by a refinement of the nuclear potential.