Nuclear collective tunneling transitions between Hartree states deformed in quadrupole symmetry

In a nucleus which has two Hartree states deformed in quadrupole symmetry, i.e., prolate state and oblate state, the nuclear residual interaction derived in the present theory beyond the Hartree approximation acts as the restoring force for the spherical symmetry of the nuclear system to be recovered so that the deformed nucleus makes collective tunneling transitions between prolate states and oblate states. We derive the Hamiltonian that is effective not only for the Hartree states but also for the collective tunneling transitions between the Hartree states. Solving the secular equation for the effective Hamiltonian on the basis states expressed in terms of SU(5) algebra, we analyze the nuclear collective tunneling transitions between a prolate state and an oblate state in the real-time description. The collective tunneling transitions are discussed to proceed through tri-axially asymmetric deformed states.