Two-phonon quadrupole-octupole vibrations in spherical nuclei

Abstract

One-phonon quadrupole and octupole states in spherical nuclei are combined to give a quintet of close-lying states with spins 1 −, 2 −, 3 −, 4 −, 5 −. Quadrupole-octupole interactions, i.e. anharmonic potential terms coupling the two modes of excitation, are deduced from the requirement that the Hamiltonian be a scalar and Hermitian. Momentum-dependent terms are included. The level splittings are calculated in perturbation theory and by numerical diagonalization. The lowest-order interaction (cubic in the collective coordinates) gives the level order 4, 1, 5, 3, 2, with other locations also possible for the 3 −. The various fourth-order terms give the sequences 1, 5, 2, 3, 4; 1, 3 (degenerate), 5, 4, 2; 1, 2, 3, 4, 5 (rotational); 1, 4, 5, 2 3. Any of these fourth-order spectra may be inverted. The B(E3) values for the excitation of the 3 − member of the quintet are also calculated. The natural parity states are known in 114Cd, 148Sm and 150Sm, all having the order 1, 5, 3. To fit both the energies and the B(E3) values (known in 148, 150Sm) one needs both third and fourth orders in the interaction. More definite conclusions about the quadrupole-octupole interaction require more experimental data.