Relativistic Hartree States and Collective Tunneling Transition of a Nucleus

Abstract

The study of relativistic Hartree theory for finite nuclei by the Nuclear Theory Group at the University of Tsukuba is reviewed. It is argued that negative energy nucleons should be taken into account in nuclear physics. When negative energy nucleons are taken into account in the relativistic mean-field approximation, the Dirac sea contributes to suppress the single-particle potential and to increase the nuclear radius. The fundamental mechanism of these effects of the Dirac sea is analyzed in the positive energy nucleon state sector picture of a nucleus by showing that N vacuum polarizations correct the meson exchange interactions between positive energy nucleons, suppressing the coupling constant and increasing the range of the σ-meson exchange interaction. The renormalized N vacuum polarization functions depend on the nuclear medium nucleon density. Therefore the vacuum polarizations create repulsive effective three-body interactions in the nucleus. The values of the three-body interaction energy obtained from the N vacuum polarizations are on the order of the three-body interaction energy extracted from the experimental nuclear energy data. As an extension of the nuclear mean-field theory, we formulate a collective tunneling transition from one nuclear mean-field state to another. We determine a Hamiltonian to describe this nuclear transition, in view of the quantum fluctuations of the meson fields needed to steer the transition. The structure of the meson mean fields in two nuclear mean-field states uniquely determines the Hamiltonian in terms of the meson fields needed to steer the nuclear transition from one mean-field state to another. The Hamiltonian, which recovers the symmetries of the nuclear system, yields nuclear eigenstates in terms of a linear combination of the two nuclear mean-field states with definite angular momentum.