A microscopic multiphonon approach to even and odd nuclei

The formalism of an equation of motion phonon method is briefly 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. As illustrated here, the method has been implemented numerically for studying the electric dipole response in the heavy neutron rich ²⁰⁸Pb and ¹³²Sn and in the odd ¹⁷O and ¹⁷F. Self-consistent calculations, using a chiral inspired 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. (paper)