The expansion coefficients of a fourth-order collective Hamiltonian for the low-lying quadrupole vibrations are derived from the microscopic fermion Hamilton operator by a modified Marumori boson-expansion method. Their dependence on the phonon structure, on the parameters of the two-body (surface $\delta$) interaction, and on the single-particle energies is numerically investigated. For the isotopes ${}_{}{}^{76}{}_{}{}^{}\mathrm{Se}$ and ${}_{}{}^{100}{}_{}{}^{}\mathrm{Ru}$, ${}_{}{}^{102}{}_{}{}^{}\mathrm{Ru}$ the results are compared with coefficients that are obtained from phenomenological fits to low-lying levels. Quadrupole moments and $B\left(E2\mathrm{}\right)\mathrm{}$ values are calculated in lowest order.

NUCLEAR STRUCTURE ${}_{}{}^{76,78}{}_{}{}^{}\mathrm{Se}$, ${}_{}{}^{100,102}{}_{}{}^{}\mathrm{Ru}$ collective states microscopically by boson expansion.

• Received 21 April 1975

DOI:https://doi.org/10.1103/PhysRevC.12.1035