Decoupling of collective isoscalar monopole and quadrupole oscillations in a soluble Hartree model with l-pole--l-pole interactions

The joint determination of the collective isoscalar monopole and quadrupole oscillations is studied in a self-consistent version of Suzuki's l-pole--l-pole interaction model with l restricted to the values 0 and 2. The resulting variational problem leads to Suzuki's self-consistent monopole-monopole and quadrupole-quadrupole strengths, although with opposite sign in the case of the former. It is shown that the monopole and quadrupole pair excitations are decoupled with random-phase-approximation excitation energies √6 h ω0 and √2 h ω0, respectively