## Abstract

We propose an adiabatic mean-field model for dynamical collective state transitions of a nuclear system. The transition process is described in terms of the nuclear mean-field wave functions which are adiabatically determined in the course of the transition. A principal steering meson field approximation simplifies the model. In the simplified model, the Hamiltonian is expressed by a tridiagonal matrix on the basis of the adiabatic mean-field states, because the mean-field states are coupled by the residual interaction. The model has two degenerate lowest mean-field states. These states are separated by a potential barrier made of intermediate mean-field states and are coupled to each other by the interaction through the intermediate states. We solve the eigenvalue equation for the Hamiltonian both in an exact diagonalization and in a perturbation method. The perturbation expression for the splitting of the energies of the two almost degenerate ground states exhibits analytically a coherent structure in favor of the dynamical transition between the two isolated lowest mean-field states. The net current for the collective tunneling from an initial lowest mean-field state to the degenerate counterpart through the potential barrier is much smaller than the quantum mechanically fluctuating local currents. The energy eigenvalue equation for a tridiagonal Hamiltonian matrix leads to a Schrödinger difference equation on a finite range of integral discrete coordinates. Higher energy states on a repulsive parabolic potential on the finite range of discrete coordinate are shown to have some features resembling the energy states of a harmonic oscillator: equispacing energy levels and Gaussian distribution of the wave functions.

Original language | English |
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Article number | 034315 |

Pages (from-to) | 343151-3431516 |

Number of pages | 3088366 |

Journal | Physical Review C - Nuclear Physics |

Volume | 61 |

Issue number | 3 |

Publication status | Published - 2000 Mar |

## ASJC Scopus subject areas

- Nuclear and High Energy Physics