Nuclear shape coexistence : a study of the even-even Hg isotopes using the interacting boson model with configuration mixing

Background: The Po, Pb, Hg, and Pt region is known for the presence of coexisting structures that correspond to different particle-hole configurations in the shell model language or equivalently to nuclear shapes with different deformation. Purpose: We intend to study the configuration mixing phenomenon in the Hg isotopes and to understand how different observables are influenced by it. Method: We study in detail a long chain of mercury isotopes, Hg172-200, using the interacting boson model with configuration mixing. The parameters of the Hamiltonians are fixed through a least-squares fit to the known energies and absolute B(E2) transition rates of states up to 3 MeV. Results: We obtained the IBM-CM Hamiltonians and we calculate excitation energies, B(E2)'s, quadrupole shape invariants, wave functions, isotopic shifts, and mean-field energy surfaces. Conclusions: We obtain a fairly good agreement with the experimental data for all the studied observables and we conclude that the Hamiltonian and the states we obtain constitute a good approximation to the Hg isotopes

Mean sensitive, mean equicontinuous and almost periodic functions for dynamical systems

We show that an $R^d$-topological dynamical system equipped with an invariant ergodic measure has discrete spectrum if and only it is $\mu$-mean equicontinuous (proven for $Z^d$ before). In order to do this we introduce mean equicontinuity and mean sensitivity with respect to a function. We study this notion in the topological and measure theoretic setting. In the measure theoretic case we characterize almost periodic functions and in the topological case we show that weakly almost periodic functions are mean equicontinuous (the converse does not hold)

Quest of shape coexistence in Zr isotopes

Background: The mass region with A approximate to 100 and Z approximate to 40 is known to experience a sudden onset of deformation. The presence of the subshell closure Z = 40 makes it feasible to create particle-hole excitations at a moderate excitation energy and, therefore, likely intruder states could be present in the low-lying spectrum. In other words, shape coexistence is expected to be a key ingredient to understand this mass region. Purpose: The aim of this work is to describe excitation energies, transition rates, radii, and two-neutron separation energies for the even-even Zr94-110 nuclei and, moreover, to obtain information about wave functions and deformation. Method: The interacting boson model with configuration mixing will be the framework to study the even-even Zr nuclei, considering only two types of configurations: 0particle-0hole and 2particle-2hole excitations. On one hand, the parameters appearing in the Hamiltonian and in the E2 transition operator are fixed trough a least-squares fit to the whole available experimental information. On the other hand, once the parameters have been fixed, the calculations allow to obtain a complete set of observables for the whole even-even Zr chain of isotopes. Results: Spectra, transition rates, radii, rho(2)(E0), and two-neutron separation energies have been calculated and a good agreement with the experimental information has been obtained. Moreover, a detailed study of the wave function has been conducted and mean-field energy surfaces and deformation have been computed too. Conclusions: The importance of shape coexistence has been shown to correctly describe the A approximate to 100 mass area for even-even Zr nuclei. This work confirmed the rather spherical nature of the ground state of Zr94-98 and its deformed nature for Zr100-110 isotopes. The sudden onset of deformation in Zr-100 is owing to the rapid lowering of a deformed (intruder) configuration which is high-lying in lighter isotopes

Disentangling the nuclear shape coexistence in even-even Hg isotopes using the interacting boson model

We intend to provide a consistent description of the even-even Hg isotopes, 172-200Hg, using the interacting boson model including configuration mixing. We pay special attention to the description of the shape of the nuclei and to its connection with the shape coexistence phenomenon.Comment: To appear in CGS15 conference proceedings (EPJ Web of Conferences