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The collective Hamiltonian up to the fourth order for a multi-O(4) model is derived for the first time based on the self-consistent collective-coordinate(SCC) method,which is formulated in the framework of the time-dependent Hartree-Bogoliubov(TDHB) theory.This collective Hamiltonian is valid for the spherical case where the HB equilibrium point of the multi-O(4) model is spherical as well as for the deformed case where the HB equilibrium points are deformed.Its validity is tested numerically in both the spherical and deformed cases.Numerical simulations indicate that the low-lying states of the collective Hamiltonian and the transition amplitudes among them mimic fairly well those obtained by exactly diagonalizing the Hamiltonian of the multi-O(4) model.The numerical results for the deformed case imply that the “optimized RPA boundary condition” is also valid for the well-known η*,η expansion around the unstable HB point of the multi-O(4) model.All these illuminate the power of the SCC method.
The collective Hamiltonian up to the fourth order for a multi-O (4) model is derived for the first time based on the self-consistent collective-coordinate (SCC) method, which is formulated in the framework of the time-dependent Hartree- Bogoliubov (TDHB) theory. This collective Hamiltonian is valid for the spherical case where the HB equilibrium point of the multi-O (4) model is spherical as well as for the deformed case where the HB equilibrium points are deformed. numerically in both the spherical and deformed cases. Numerical simulations indicate that the low-lying states of the collective Hamiltonian and the transition amplitudes among them mimic fairly well and those won by exactly diagonalizing the Hamiltonian of the multi-O (4) model. results for the deformed case imply that the “optimized RPA boundary condition” is also valid for the well-known η *, η expansion around the unstable HB point of the multi-O (4) model. All these illuminate the power of th e SCC method.