CONFIGURATION MIXING AND OCTUPOLE STUDIES OF NUCLEI WITHIN THE INTERACTING BOSON MODEL.
AuthorBARFIELD, ARIEL FOOTE.
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PublisherThe University of Arizona.
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AbstractThe Interacting Boson Model (IBM) has been very successful in describing the collective properties of nuclei. This work concerns two systematic applications of the model, one involving configuration mixing, and the other involving octupole bands. The even isotopes of mercury are of special interest because of the coexistence of two sets of bands, of very different character, in the lighter nuclei. The neutron-proton IBM (IBM-2) with configuration mixing provides a good description, both of states built on the normal ground state and of those associated with a proton pair excitation across the Z = 82 closed-shell gap. Eleven isotopes are studied, ranging from the middle of the neutron shell to very near the doubly closed shell at ²⁰⁸Pb. The same Hamiltonian is used for all the nuclei studied, with parameters which are constant or smoothly varying. There have been extensive IBM studies of low-lying positive parity bands, which are based on the ground state and the quadrupole degree of freedom. The present work comprises the first systematic IBM study of the corresponding negative parity bands, which are based on the octupole degree of freedom. In this model, an f boson is coupled to a positive parity core, described by the usual s and d bosons. This is done within the original IBM framework, called IBM-1, which does not include separate neutron and proton degrees of freedom. The IBM octupole model is presented and the phenomenology is explored, both for the full model, and for the SU(3) limit of the model. Calculated energy spectra and B(E3) transition rates are presented for nine deformed rare-earth nuclei. There is good agreement with available experimental data for these nuclei. It is shown that nuclei for which the two lowest octupole bands are K = 2 and 0 cannot be described within the present model. In this case, it appears that separate neutron and proton octupole degrees of freedom are necessary. The exchange term in the Hamiltonian is shown to arise from a neutron-proton octupole-octupole interaction. A consistent octupole model is developed and successfully applied to the nucleus ¹⁶⁸Er.