The tensor force is a hot topic in nuclear physics, which affects the shell evolution. Moreover, the short-range correlation, which is dominated by the strong tensor force between unlike nucleons, is also an intriguing issue in current nuclear physics. 

The zero-range tensor potential was firstly present in the original Skyrme interaction in 1956. And so far it has been widely used in nuclear physics.  

However, in a recent paper published in Physical Review C, researchers from the Institute of Modern Physics (IMP) of the Chinese Academy of Sciences demonstrated that the tensor force plays no role in Skyrme density functionals. 

The zero-range momentum-dependent Skyrme effective interaction is obtained through the simplification of the Fourier transform for the interaction in coordinate space via low-momentum expansion. 

Based on the derived tensor force in momentum space via partial-wave expansion, researchers demonstrated such a tensor force invalid, and hence the widely employed tensor force of the Skyrme interactions invalid.  

The individual reasons for the drop of each tensor channel in Skyrme-type interaction can be grouped as four types: ³S₁ channel is exactly zero; zero due to the orthogonality between spherical harmonics for off-diagonal matrix element, such as ³SD₁ channel; beyond the order of k², such as ³D₂ channel; can be reabsorbed into existing Skyrme t₂-x₂ component, such as ³P₀channel. 

To replace the tensor force so as to improve the description of single-particle levels, researchers then proposed a new scheme by introducing the central σ₁ · σ₂ term and accordingly built two new Skyrme interactions—IMP1 and IMP2. The shell evolution in Sn isotopes and N = 82 isotones can be well reproduced by IMP2.  

According to the study, the introduction of the central σ₁· σ₂ interaction is just a phenomenological treatment. Therefore, the parameter sets applicable to shell evolutions could not be anticipated being valid for excited states such as Gamow-Teller and spin-dipole states. 

Fig.1 The improvement of the shell evolution in Sn isotopes and N=82 isotones resulting from the σ₁· σ₂ term. (Image by Dong Jianmin)