Relativistic Hartree-Fock model of nuclear single-particle resonances based on real stabilization method

Abstract

The research areas in atomic nuclei have been further expanded with the development of radioactive ion beam devices along with associated nuclear experimental detection technologies, illustrating many new aspects of nuclear excitation as well as the physics of exotic nuclei far from the $\beta$-stability line. For weakly bound nuclei, the Fermi surface may lie near the continuum, which facilitates the easy scattering of valence nucleons into the continuum to occupy the resonance state. These continuum effects are of crucial importance in explaining the unusual structure of unstable nuclei. In this work, with the real stabilization method in coordinate space, nuclear structure model for single-particle resonances is developed within the framework of the relativistic Hartree-Fock (RHF) theory. The evolution of single-particle states in the continuum with the altered Box size is worked in order to extract potential single-particle resonance structures. To avoid the instability of nuclear binding energy, the pairing correlations were not taken into account during the calculation. As an important motive, the role of Fock terms in the energies, widths and spin-orbit splitting is discussed for low-lying neutron resonance states of $^{120}$Sn. Compared to the relativistic mean field (RMF) model, it is found that the inclusion of exchange terms in the RHF model changes the in-medium balance of nuclear interactions and the equilibrium of nuclear dynamics, which in turn affects the description of the single-particle effective potential. For several neutron resonance states in $^{120}$Sn with finite resonant width, RHF models predict relatively lower resonant energies and smaller widths than RMFs. For the single-particle states around the continuum threshold, the featured signals of resonance could depend sensitively on the choice of effective interactions. In addition, for the spin-partner states $\nu i_{13/2}$ and $\nu i_{11/2}$ in resonance states, the effect of Fock terms on their spin-orbit splitting is analyzed. In comparison with the bound states, the wave functions of resonant spin-partner states could differ remarkably from each other, alternating the effective potential and single-particle energies correspondingly. Thus, additional components in the single-particle effective potential may also contribute to the spin-orbit splitting of resonance states, aside from the spin-orbit interaction. In order to elucidate the mechanism of Fock terms in single-particle resonance physics, it is anticipated that subsequent works will incorporate more numerical techniques that have been recently developed into the RHF methodology.