Phonon mechanisms of mixing collective and quasiparticle excitations

Abstract

A phonon approach with subsequent mapping onto bosons is developed for describing transitional nuclei spectra including the first backbending energy region. Quasiparticle random-phase approximation and its modification with minimum ground state correlations are employed to find ${B}_{J}$ phonons (spin $J>~4)$ and most collective quadrupole D phonons, respectively. Phonon functions and matrix elements of $B\ensuremath{-}D$ interaction are calculated with factorized quasiparticle forces. Besides the interaction mechanisms known in the interacting boson fermion model (IBFM) a new one is introduced that leads to three into one boson transformation. After mapping onto s-, d-, and ${b}_{J}$-boson space a boson Hamiltonian comprises IBM1 Hamiltonian, whose parameters depend on the presence or absence of ${b}_{J}$ bosons and are determined phenomenologically, and ${b}_{J}\ensuremath{-}d$ interaction with constants calculated microscopically inside phonon space. This approach applied to energy spectra and $B(E2)$ values in ${}^{126,128}\mathrm{Ba}$ and ${}^{130}\mathrm{Ce}$ gives reasonable agreement with experiment.