Research Progress

Researchers Prove Tensor Force Invalid in Skyrme Density Functionals

Date：05-02-2020 | 【Print】 【close】

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: ^{3}S_{1}_{ }channel is exactly zero; zero due to the orthogonality between spherical harmonics for off-diagonal matrix element, such as ^{3}SD_{1}_{ }channel; beyond the order of *k*^{2}, such as^{ }^{3}D_{2 }channel; can be reabsorbed into existing Skyrme *t*_{2}-*x*_{2}_{ }component, such as ^{3}P_{0}channel.

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 *σ*_{1} · *σ*_{2} 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 *σ*_{1}· *σ*_{2}* *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.

Link to the paper: __https://journals.aps.org/prc/abstract/10.1103/PhysRevC.101.014305__

Fig.1 The improvement of the shell evolution in Sn isotopes and N=82 isotones resulting from the *σ*_{1}· *σ*_{2}* *term. (Image by Dong Jianmin)

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