Mapped interacting boson model for nuclear structure studies

The present status of the mapped interacting boson model studies on nuclear structure is reviewed. With the assumption that the nuclear surface deformation induced by the multi-nucleon dynamics is simulated by bosonic degrees of freedom, the interacting-boson Hamiltonian that provides energy spectra and wave functions is determined by mapping the potential energy surface that is obtained from self-consistent mean-field calculations based on the energy density functional onto the corresponding energy surface of the boson system. This procedure has been shown to be valid in general cases of the quadrupole collective states, and has allowed for systematic studies on spectroscopic properties of medium-heavy and heavy nuclei, including those that are far from the line of $\beta$ stability. The method has been extended to study nuclear structure phenomena that include shape phase transitions and coexistence, octupole deformation and collectivity, and the coupling of the single-particle to collective degrees of freedom, which is crucial to describe structures of odd nuclei, and $\beta$ and $\beta\beta$ decays.