MICROSCOPIC DESCRIPTION OF LOW-LYING ONE-PHONON AND 2-PHONON STATES AND APPLICATION TO ZR-96

A self-consistent approach to finite Fermi systems is expanded for the description of two-phonon states in non-magic nuclei with weak anharm onicity. It is based on a density-functional approach, the quasi-parti cle random-phase approximation (QRPA) and the Green's function method, the latter enabling one to calculate the diagrams of the phonon-phono n interaction in the coordinate representation. This approach is appli ed to the low-lying excitations in Zr-96. The transition density of th e two-phonon state [3(1)(-)circle times 3(1)(-)](6+) in Zr-96 is calcu lated. It is shown that interplay of one-phonon and two-phonon configu rations may lead to the origin of two 6(+) states with strongly differ ent excitation probabilities. Mixing coefficients and energy splitting of these states are estimated microscopically The transition probabil ities of the one-phonon states 3(1)(-) and 6(+) and the mixing coeffic ients of the one- and two-phonon 6(+) states resulting from the micros copic calculations are used as input for DWBA and coupled-channels cal culations for inelastic scattering of 22 MeV polarized deuterons. Calc ulated cross sections for the 6(+) states are compared with experiment al data.