Microscopic description of low-lying one- and two-phonon states and application to 96Zr

Abstract

A self-consistent approach to finite Fermi systems is expanded for the description of two-phonon states in non-magic nuclei with weak anharmonicity. It is based on a density-functional approach, the quasi-particle random-phase approximation (QRPA) and the Green's function method, the latter enabling one to calculate the diagrams of the phonon-phonon interaction in the coordinate representation. This approach is applied to the low-lying excitations in 96Zr. The transition density of the two-phonon state [3 1 −⊗3 1 −] 6+ in 96Zr is calculated. It is shown that interplay of one-phonon and two-phonon configurations may lead to the origin of two 6 + states with strongly different excitation probabilities. Mixing coefficients and energy splitting of these states are estimated microscopically. The transition probabilities of the one-phonon states 3 1 − and 6 + and the mixing coefficients of the one- and two-phonon 6 + states resulting from the microscopic calculations are used as input for DWBA and coupled-channels calculations for inelastic scattering of 22 MeV polarized deuterons. Calculated cross sections for the 6 + states are compared with experimental data.