Nuclear collective tunneling between Hartree states

We formulate the nuclear collective tunneling transition from one Hartree state to another, consistently with the Hartree states. A Hamiltonian effective for the collective tunneling as well as for Hartree states is obtained with the parameters determined by the Hartree calculations. A real-time description for the tunneling is proposed. It is shown that a nuclear system governed by the Hamiltonian symmetric between two Hartree states collectively tunnels back and forth between the two states owing to the residual interaction, so that the system makes harmonic tunneling oscillations. While a crowd of quantum fluctuations coherently shifts back and forth in phase with the tunneling oscillations of the center of mass of two wave packets, the symmetric nuclear system retains the energy for the harmonic tunneling oscillations. The collective tunneling transitions are analyzed in an adiabatic approximation.