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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, $^{172-200}$Hg, using the interacting boson model with configuration mixing. The parameters of the Hamiltonians are fixed through a least square 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., We are very grateful to K. Wrzosek-Lipska, E. Rapisarda, and L. Gaffney for generous sharing of theirmost recent results on Coulomb excitation (A = 182-188), beta-decay results for A = 182 and A = 184 and new lifetime data for A = 184 and A = 186. We thank M. Huyse and P. Van Duppen for continuous interest in this research topic and J. L. Wood for stimulating discussions in various stages of this work and his diligence to quote from his unpublished notes. Financial support from the "FWO-Vlaanderen" (K.H. and J.E.G.R.) and the InterUniversity Attraction Poles Programme, Belgian State, Federal Office for Scientific, Technical and Cultural Affairs (IAP Grant No. P7/12) is acknowledged. This work has also been partially supported by the Spanish Ministerio de Economia y Competitividad and the European regional development fund (FEDER) under Project No. FIS2011-28738-C02-02, by Junta de Andalucia under Project No. FQM318, and P07-FQM-02962, and by Spanish Consolider-Ingenio 2010 (CPANCSD2007-00042).

We show that, starting from density‐dependent nucleon‐nucleon interactions (extended Skyrme forces), one is able to construct an interaction that leads to correct saturation properties in the nucleus and also behaves as a good effective interaction in describing low‐lying excitations. This is illustrated in various mass regions. In those regions where many protons and neutrons determine the nuclear structure, one has to resort on collective model descriptions. We shortly point out the importance of symmetry considerations (the Interacting‐Boson model). More in particular, we concentrate on those modes of motion where the interplay of protons and neutrons is dominant: the M1 scissor mode, intruder 0+ excitations and shape coexistence. Results for the Cd region, the Pb region and the N=20 nuclei are presented.

The M1 strength distribution is studied in rare‐earth nuclei, starting from the Nilsson model and using the Quasi‐Particle Random Phase Approximation (QRPA), including monopole as well as quadrupole pairing, Coriolis mixing and residual quadrupole and spin‐isospin interactions. For the nucleus 164Dy the importance and effect of the different terms in the Hamiltonian are studied. Results are compared with experimental observations. Special attention is given to the higher‐lying spin strength in view of a recent (p,p’) experiment performed at TRIUMF on 154Sm.