Volume 171, number 2,3 PHYSICS LETTERS B 24 April 1986 OCTUPOLE EXCITATIONS IN 0(6) NUCLEI J. ENGEL A. IV.. Wright Nuclear Structure Laboratory, Yale University, New Haven, CT06511, USA Received 20 January 1986 The coupling is discussed of an octupole boson to an 0(6) core in the interacting boson approximation, and the results are applied to several platinum isotopes. Many of the low-lying negative-parity states in the rare-earth region of the periodic table have been suc- cessfully interpreted as octupole (L 7r = 3-) shape vi- brations around a spherical or quadrupole deformed ground-state shape. These vibrations have been dis- cussed in different contexts; a quasiparticle RPA was applied [1] systematically throughout a large part of the rare-earth region and f bosons have been incorpo- rated into the interacting boson approximation (IBA) to describe negative-parity excitations phe- nomenologically. In the latter model, the coupling of an f boson to the usual s and d bosons in the U(5) and SU(3) analytic limits was discussed very early on [2] and successfully applied in a description of samarium isotopes [3]. However, an analysis of the coupling to an 0(6) [4] core - that is, a "r-unstable or triaxial nucleus - has never appeared. In what follows we discuss this case and apply the results to the low- spin negative-parity states in 190pt-196pt. The collective positive-parity states in many nuclei have been fit by an 0(6) IBA hamiltonian of the form H = -r Qsd. Qsd + r'L "L , (1) where QSd = d;s + std., (2) L u = ~ (2a, 2~ll~u)d?od¢ , d, = (-)"d_u , and the dot stands as usual for the scalar product of 148 two tensors. The spectrum associated with this hamiltonian is shown in ref. [4] ; a characteristic fea- ture is a low-lying 7 band. In the spirit of previous IBA studies of f coupling, we have added to the above hamiltonian an additional piece H' = enf + [3Qf " Qsd , (3) where Qu f = ~ (3a, 3/312#)f~ , (4) at3 and nf is the number of f bosons. Although we were not able to diagonalize this interaction analytically, we examined the results numerically for several dif- ferent sets of parameter values; the states organize themselves into a regular pattern, an example of which appears in fig. 1. This result is reminiscent of that obtained when coupling a particle of half-integer spin to an 0(6) core in the interacting boson-fermion approximation [5]. We now turn to the nuclei 190pt-196pt, where 0(6) is known [6] to provide a reasonable approxi- mation to the positive-parity energy levels and a good description of transition rates. These isotopes were studied some years ago [7] in terms of a "semi-de- coupled model" in which the negative-parity states could be expressed as linear combinations of two- quasiparticle states in a triaxial one-body field. The results of these calculations indicate that states with J ~< 4 are essentially of octupole phonon type (cohe- rent coupling of quasiparticles to L = 3) while those with J/> 5 have different structure. This conclusion 0370-2693/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)