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13 pages, 5 tables, 3 figures, accepted for publication in Physical Review CA systematic study of energy spectra throughout the rare-earth region (even-even nuclei from $_{58}$Ce to $_{74}$W) is carried out in the framework of the interacting boson model (IBM), leading to an accurate description of the spherical-to-deformed shape transition in the different isotopic chains. The resulting IBM Hamiltonians are then used for the calculation of nuclear charge radii (including isotope and isomer shifts) and electric monopole transitions with consistent operators for the two observables. The main conclusion of this study is that an IBM description of charge radii and electric monopole transitions is possible for most of the nuclei considered but that it breaks down in the tungsten isotopes. It is suggested that this failure is related to hexadecapole deformation

In the context of the interacting boson model with s, d and g bosons, the conditions for obtaining an intrinsic shape with octahedral symmetry are derived for a general Hamiltonian with up to two-body interactions.

Abstract. A geometric analysis of the sdg interacting boson model is performed. A coherent-state is used in terms of three types of deformation: axial quadrupole (β 2 ), axial hexadecapole (β 4 ) and triaxial (γ 2 ). The phase-transitional structure is established for a schematic sdg hamiltonian which is intermediate between four dynamical symmetries of U(15), namely the spherical U(5) ⊗ U(9), the (prolate and oblate) deformed SU ± (3) and the γ 2 -soft SO(15) limits. For realistic choices of the hamiltonian parameters the resulting phase diagram has properties close to what is obtained in the sd version of the model and, in particular, no transition towards a stable triaxial shape is found.

A systematic analysis of the spherical-to-deformed shape phase transition in even-even rare-earth nuclei from 58Ce to 74W is carried out in the framework of the interacting boson model. These results are then used to calculate nuclear radii and electric monopole (E0) transitions with the same effective operator. The influence of the hexadecapole degree of freedom (g boson) on the correlation between radii and E0 transitions thus established, is discussed.PACS numbers: 21.10. Ft, 21.10.Ky, 21.60.Ev, 21.60.Fw Electric monopole (E0) transitions between nuclear levels proceed mainly by internal conversion with no transfer of angular momentum to the ejected electron. For transition energies greater than 2m e c 2 , electronpositron pair creation is also possible; two-photon emission is possible at all energies but extremely improbable. The total probability for a transition between initial and final states |i and |f can be separated into an electronic and a nuclear factor, P = Ωρ 2 , where the nuclear factorwith R = r 0 A 1/3 (r 0 = 1.2 fm) and where the summation runs over the Z protons in the nucleus. The coefficient σ depends on the assumed nuclear charge distribution but in any reasonable case it is smaller than 0.1 and can be neglected if the leading term is not too small [1]. The charge radius of a state |s is given byIt is found experimentally that the addition of neutrons produces a change in the nuclear charge distribution, an effect which can be parametrized by means of neutron and proton effective charges e n and e p in the charge radius operatorT (r 2 ). This leads to the following generalization of Eq. (2):where the sum is over all nucleons and e k = e n (e p ) if k is a neutron (proton). An obvious connection between ρ and the nuclear charge radius is established in the approximation σ = 0 (which henceforth will be made). Again because of the polarization effect of the neutrons, one introduces an E0 operator of the form [2]The ρ defined in Eq.(1) with σ = 0 is then given by ρ = f|T (E0)|i /eR 2 . The basic hypothesis of this Letter is to assume that the effective nucleon charges in the charge radius and E0 transition operators are the same. If this is so, comparison of Eqs. (3) and (4) leads to the relationAt present, a quantitative test of the correlations between radii and E0 transitions implied by (5) cannot be obtained in the context of the nuclear shell model. The main reason is that E0 transitions between states in a single harmonic-oscillator shell vanish identically [3] and a non-zero E0 matrix element is obtained only if valence nucleons are allowed to occupy at least two oscillator shells. This renders the shell-model calculation computationally challenging (if not impossible), certainly in the heavier nuclei which are considered here. We have therefore chosen to test the implied correlations in the context of a simpler approach, namely the interacting boson model (IBM) of atomic nuclei [4]. In this model low-lying collective excitations of nuclei are described in terms of N b bosons distrib...