Microscopic multiphonon approach to spectroscopic properties of even and odd nuclei

The formalism of an equation of motion phonon method is outlined. In even-even nuclei, the method derives equations of motion which generate an orthonormal basis of correlated n-phonon states (n = 0, 1, 2, . . .), built of constituent Tamm-Dancoff phonons, and, then, solves the nuclear eigenvalue problem in such a multiphonon basis. In odd nuclei, analogous equations yield a basis of correlated orthonormal multiphonon particle-core states to be used for the solution of the full eigenvalue equations. The formalism does not rely on approximations, but lends itself naturally to simplifying assumptions. The method has been implemented numerically for studying the electric dipole response in the heavy neutron rich 208Pb and 132Sn, in the open shell 20O and in the odd 17O and 17F. Self-consistent calculations, using a chiral Hamiltonian, have confirmed the important role of the multiphonon states in enhancing the fragmentation of the strength in the giant and pygmy resonance regions consistently with the experimental data. Moreover, the spectroscopic properties at low energy of odd nuclei are also investigated through the calculation of moments, electromagnetic and β-decay transition strengths. The analysis of the particle-phonon composition of the eigenfunctions contributes to clarify the mechanism of excitation of levels and resonances and gives unique insights into their nature