Collective Hamiltonian for Multi-O(4) Model

The collective Hamiltonian up to the fourth order for multi-O(4) model is derived based on the self-consistent collective-coordinate (SCC) method,which is formulated in the framework of the time-dependent Hartree-Bogoliubov (TDHB) theory.The validity of the collective Hamiltonian is checked in the two special cases of the multi-O(4) modelthe case where the number of the shells is equal to one (a single j-shell case),and the case where the Hartree-Bogoliubov equilibrium point is spherical (the spherical case).The collective Hamiltonian constitutes a good starting point to study nuclear shape coexistence.