Tensor-force effects on shell-structure evolution in $N = 82$ isotones and $Z = 50$ isotopes in the relativistic Hartree-Fock theory

Abstract

The evolution of the energy difference between the neutron states 1i 13/2 and 1h 9/2 in the N = 82 isotones and that between the proton states 1h 11/2 and 1g 7/2 in the Z = 50 isotopes are investigated within the framework of the relativistic Hartree-Fock theory, using the density-dependent effective interactions PKA1 and PKOi (i = 1, 2, 3). By identifying the contributions of the tensor force, which is naturally induced via the Fock terms, we find that the tensor force plays crucial roles in the evolution of the shell structure. The strength of the tensor force is also explored. It is found that moderately increasing the coupling strength of pion-nucleon coupling, i.e., fπ, will significantly improve the description of the shell-structure evolution. In particular, reducing the density dependence of fπ is shown to be more preferable, in comparison to enlarging fπ with a factor. This is in consistence with the idea of "tensor renormalization persistency" and provides valuable guidance for the development of nuclear energy density functional in the relativistic framework.

Exploring effects of tensor force and its strength via neutron drops

“…( 3). In our previous work [101], we have shown that weakening the density dependence of the π-PV coupling, i.e., reducing a π , can improve the description of the shell-structure evolution along the N = 82 isotones and the Z = 50 isotopes more efficiently, compared with enlarging f π (0) with a factor. Inevitably, the beyond-meanfiled correlations in the experimental single-particle energies make the comparison with the results on the meanfiled level ambiguous.…”

“…Here, Γ φ (x, y) and D φ (x, y) are the interaction vertices and the propagators of a given meson-nucleon coupling φ, respectively; their explicit expressions can be referred to Refs. [77,82,83,[98][99][100][101][102]. Obviously, the photon field is not considered in the case of neutron drop.…”

“…In the RHF theory, ĥ (r, r ) contains the kinetic energy ĥK , the direct local potential ĥD , and the exchange nonlocal potential ĥE ; see Refs. [78,82,101,103] for the detailed expressions. Notice that the tensor force contributes only to the nonlocal potentials.…”

Exploring effects of tensor force and its strength via neutron drops *

“…Here, and are the interaction vertex and the propagator of a given meson-nucleon coupling , respectively; their explicit expressions can be found in Refs. [78,83,84,[99][100][101][102][103]. Evidently, the photon field is not considered in the case of neutron drops.…”