Relativistic interpretation on the nature of nuclear tensor force

The spin-dependent nature of the nuclear tensor force is studied in details within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in $\sigma$-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with/without nodes, to further understand the tensor force nature within relativistic model. It is shown that the interference between two components of nucleon spinors brings distinct violations on the tensor sum rules in realistic nuclei , which is mainly due to the opposite sign on $\kappa$ quantities of the upper and lower components as well as the nodal difference. Even though, the sum rules can be precisely reproduced if taking the same radial wave functions for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of tensor force.

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