Anharmonicities of Gamma Vibration in168Er

Abstract

Properties of the r·vibration in Er are examined both in a macroscopic and in a microscopic approach with special emphasis on the anharmonicities of two-phonon states. It is found that in order to account for recent ex­ perimental evidence it is necessary to assume large anharmonic components both in the collective potential energy surface and in the mass parameters. Points which are not clear in our present understanding of the gamma-motion are described. § l. Introduction The investigation of vibrational anharmonicities was a popular subject about 15''20 years ago. Systematic methods for the treatment of anharmonic effects have been developed by many people,1> mainly in connection with low­ frequency quadrupole vibrational excitations in nuclei. The an­ harmonicities manifest themselves through shifts and/or splittings of the multi­ phonon levels and through transition matrix-elements for the multipole operators that violate the selection rules implied by the harmonic picture. Roughly speaking, there are two cases in which the anharmonicities are large; either the collectivity of the vibration is so strong that the system is approaching to the instability of the corresponding degree of freedom, or the excitation mode has a single-particle character. The case of low-frequency quadrupole vibrations in nuclei belongs often to the former case. Consequently, it is often difficult to make a quantitative analysis of available data in terms of the basic coupling of the vibrational modes to other degrees of freedom, both collective and single-particle. A nice example of low-frequency octupole vib­ rations in spherical nuclei is the 3- state at 2.6 MeV in 208Pb. Although observed octupole vibrations in the neighbouring odd-A nuclei have been suc­ cessfully understood2> in terms of particle-vibration coupling8> which is a basic tool in the understanding of vibrational anharmonicities, none of the double octupole-phonon states have ever been detected experimentally in 208Pb. In the case of the octupole vibration in 147Gd (I;,.= 7 /2-) a member with the