Dynamical Symmetries in the sdg Interacting Boson Model

Abstract

The interacting boson model (IBM) proposed by Arima and lachello (1975, 1978a) in 1975 provides an algebraic description of the quadrupole collective properties of low-lying states in nuclei in terms of a system of interacting bosons. In this model the bosons are assumed to be made up of correlated pairs of valence nucleons (as Balantekin et al (1981) put it “the correlations are so large that the bosons effectively loose the memory of being fermion pairs — — — —”) and they carry angular momentum l = 0 (sboson representing pairing degree of freedom) or l = 2 (d-boson representing quadrupole degree of freedom). This model is remarkably successful in explaining experimental data (Iachello and Arima 1987; Casten and Warner 1988). In the words of Feshbach (Iachello 1981) “IBM has yielded new insights into the behaviour of low-lying levels and indeed has generated a renaissance of the field of nuclear spectroscopy” The extended sdg interacting boson model (sdgIBM or simply gIBM) where one includes in addition the hexadecupole (l = 4) g-bosons is ideally suited for analyzing E4 data. In the last ten years different types of E4 data (mainly in rare - earths) are obtained and they include: (i) s 4(hexadecupole deformation parameter) data for rare-earths and several actinide nuclei; (ii) isoscalar mass transition density B( \(IS4;0_{GS}^ + \to 4_r^ + \)) which gives information on Y 42 deformation; (iii) E4 transition matrix elements involving \(4_i^ + \) (i ≤ 6) states in some of the Cd, Pd, Er, Yb, Os and Pt isotopes; (iv) E4 strength distributions in 112 Cd, 150 Nd and 156 Gd; (v) hexadecupole transition densities for exciting some of the 4+ levels in Cd, Pd, Os and Pt isotopes; (vi) \({K^\pi } = 0_3^ + ,3_1^ + ,2_2^ + \) and 4+ bands which can be interpreted as bands built on hexadecupole vibrations.