QUADRUPOLE SPLITTING OF OCTUPOLE VIBRATIONAL-STATES

The octupole vibrational mode is studied in the deformed harmonic oscillator model. A residual octupole-octupole interaction for K = 0, 1, 2 and 3, and the corresponding coupling constants, are included by a self-consistent approach. Analytical solutions of the RPA equations are obtained for the excitation energies of all possible octupole vibrations at closed spherical (1:1), superdeformed (2:1) and hyperdeformed (3:1) shells. Simple approximate expressions are given for the deformation splitting of the (high-energy) giant octupole resonance.