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, $^{172-200}$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topic and J. L. Wood for stimulating discussions in various stages of this work and his diligence to quote from his unpublished notes.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)