Application of the SCC method to the multi-O(4) model: The collective Hamiltonian

Abstract

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.self-consistent collective-coordinate method, multi-O(4) model, time-dependent Hartree-Bogoliubov theory, collective Hamiltonian Atomic nuclei exhibit rich collective motions: rotational, vibrational, wobbling, fission, fusion and shape coexistence motions. They are the collective excitations of nucleons. A powerful tool for understanding both low-lying collective states and giant resonances is the random phase approximation(RPA), the approximation, which should be good for collective vibrations as long as their amplitudes are small. One has to go beyond the RPA in order to describe kinds of large amplitude collective motions (LACM)such as fission and shape coexistence. Microscopic understanding of the LACM is a long-standing fundamental subject of nuclear structure physics.A useful microscopic tool for describing the LACM is the generator coordinate method (GCM) [1−4] . The GCM wave function is usually taken as a combination of many intrinsic states, calculated self-consistently within constrained Hartree-Fock-Bogoliubov (HFB) theory. The constraining operators define collective degrees of freedom. The GCM wave function is rich enough to accommodate correlation absent in the mean field and is not limited to the adiabatic

Recent progress in theoretical nuclear physics related to large-scale scientific facilities

“…A new collective Hamiltonian up to the fourth order for a multi-O(4) model is derived for the first time [85] based on the self-consistent collective-coordinate (SCC) method [86,87], which is formulated in the framework of the timedependent 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.…”