Formulating the interacting boson model by mean-field methods

Abstract

The interacting boson model (IBM) Hamiltonian is determined microscopically for general cases of low-lying quadrupole collectivity. Under the assumption that the multinucleon-induced surface deformations, which reflect nuclear forces and the Pauli principle, can be simulated by bosons, the interaction strengths of the IBM Hamiltonian are derived by mapping the potential energy surface of the mean-field model with Skyrme force onto the corresponding one of the IBM. These interaction strengths turn out to change gradually as functions of valence nucleon numbers. The energy eigenvalues and the wave functions are calculated with the exact treatment of the particle number and the angular momentum. We demonstrate how well the method works by taking Sm isotopes as an example, where a typical spherical-deformed shape-phase transition is reproduced successfully. We show that the physically relevant IBM interaction strengths can be determined unambiguously by the use of wavelet analysis. In addition, by the diagonalization of the boson Hamiltonian, quantum-mechanical correlation effects can be included in the eigenenergies, by which the basic properties of these nuclei are properly reproduced. The present method is applied to several other isotopic chains, Ba, Xe, Ru, Pd, W, and Os, in comparison to the experimental data. We point out the relevance of our results to the recently proposed critical-point symmetries. The predicted spectra and the $B(\mathrm{E}2)$ ratios are presented for heavy neutron-rich exotic nuclei in experimentally unexplored regions such as the right-lower corner of $^{208}\mathrm{Pb}$ on the nuclear chart.