ar X iv : n uc l - th / 9 80 70 83 v 1 3 1 Ju l 1 99 8 Anharmonic double - γ vibrations in nuclei and their description in the interacting boson model

Double-γ vibrations in deformed nuclei are studied in the context of the interacting boson model with special reference to their anharmonic character. It is shown that large anharmonicities can be obtained with interactions that are (at least) of three-body nature between the bosons. As an example the γ vibrations of the nucleus 166 68Er98 are studied in detail. Typeset using REVTEX 1 Nuclear quadrupole shape oscillations can be of two types: β or γ vibrations [1]. The β vibration preserves axial symmetry and a one-quantum excitation gives rise to a K = 0 band where K is the projection of the angular momentum on the axis of symmetry of the nucleus. A γ vibration breaks axial symmetry and leads to a K = 2 band. Although their existence has been conjectured a long time ago [2], the observation and interpretation of β-vibrational K = 0 bands is still fraught with questions and difficulties. In contrast, γ-vibrational K = 2 bands are systematically observed in deformed nuclei and their properties are correspondingly better understood. Since single-γ vibrations are so well established, it is natural to search for double-γ vibrations and to examine their harmonic nature (i.e., whether they occur at twice the energy of the single vibration.) Two intrinsic K = 2 quanta can be combined parallel or antiparallel and hence lead to two bands: one with K = 0 and another with K = 4. The experimental identification of double-γ vibrations in deformed nuclei is difficult since they are expected to lie above the pairing gap and to mix with two-quasiparticle excitations, resulting in fragmentation and a corresponding reduction in the collectivity of the states. During the last few years, however, a steady improvement of experimental techniques has allowed the measurement of low-spin states in the energy region of interest [3–5]. This possibility has reopened the old debate on the existence of two-phonon (β or γ) vibrational states and their properties. Experiments have been reported recently pointing out the existence of doubleγ vibrations in several deformed nuclei with a wide range of anharmonicities [6–11]. In particular, in Refs. [7,8] the first observation of the K = 0 and K = 4 double-γ states in one nucleus, Er, is reported. This information is of great interest since it provides a stringent test of nuclear models; for instance, the Quasiphonon Nuclear Model (QPNM) predicts no K = 0 two-phonon state below 2.5 MeV in Er [12]. Several calculations of two-phonon states, using either phenomenological or microscopic models, are available, particularly for Er and Er [12–17]. One of the models employed is the Interacting Boson Model (IBM) [18]. In the simplest version of this model, referred