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

No abstract

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.

Te and Xe isotopes above the N = 82 shell closure are investigated within a large-scale shell model approach based on an iterative matrix diagonalization algorithm. The spectra and transition strengths, computed using a realistic Hamiltonian, are in overall agreement with the available experimental data. The calculation predicts an increasing neutron weight in the lowest collective 2+ 1 state of the isotopes as they depart from the doubly magic 132Sn and move toward the neutron drip line. Such a neutron dominance is predicted to cause a breaking of the neutron-proton exchange symmetry and a dramatic drop of the strengths of the E2 and M1 transitions among the excited 2+ states. This drop establishes a strong asymmetry between Te and Xe isotopes above and below the N = 82 shell closure

The contribution of the two-phonon configurations to the ground state of 4 He and 16 O is evaluated nonperturbatively using a Hartree-Fock basis within an equation-of-motion phonon method using a nucleonnucleon optimized chiral potential. Convergence properties of energies and root-mean-square radii versus the harmonic oscillator frequency and space dimensions are investigated. The comparison with the second-order perturbation theory calculations shows that the higher-order terms have an appreciable repulsive effect and yield too-small binding energies and nuclear radii. It is argued that four-phonon configurations, through their strong coupling to two phonons, may provide most of the attractive contribution necessary for filling the gap between theoretical and experimental quantities. Possible strategies for accomplishing such a challenging task are discussed.

An importance-sampling iterative algorithm for diagonalizing shell model Hamiltonian matrices is reviewed and implemented in a spin uncoupled basis. Shell model spaces of dimensions up to N≲109 are considered. The analysis shows that about 10% of the basis states are enough to bring the eigenvalues to convergence. This fraction of states, however, is insufficient to lead to convergence of the transition strengths, thereby limiting the applicability of the method to not too large spaces. In its domain of validity, the method yields a large number of eigensolutions and can be usefully adopted for rather complete studies of low-energy spectroscopy. This is done here for 132,134Xe isotopes. The calculation yields spectra and electromagnetic responses in fairly good agreement with the available experimental data and unveils the properties of the low-energy states of these isotopes, including their proton-neutron symmetry