A systematic study of the tensor-force impact in neutron-proton drops has been reported using the relativistic Hartree-Fock (RHF) theory with the $\ensuremath{\pi}\text{\ensuremath{-}}N$ coupling strength optimized to the relativistic Brueckner-Hartree-Fock (RBHF) results for neutron drops. The evolutions of the neutron spin-orbit splittings as a function of the neutron number for neutron-proton drops with one proton behave similarly to the pure neutron drops, which show the tensor-force effect. By adding one more proton or neutron in the neutron drop with $N=20$, it is found that the tensor-force effect is more prominent between neutrons and protons than between neutrons. This can be attributed to the isospin factor in the tensor term of the $\ensuremath{\pi}\text{\ensuremath{-}}N$ interaction in the RHF density functional theory, which reflects the fact that the neutron-proton tensor force is stronger than the neutron-neutron one. Similar behavior for the spin-orbit splitting evolutions has also been found for the neutron-proton drops with 20 protons, where the tensor-force strength $\ensuremath{\lambda}$ is redetermined according to the RBHF results due to the large central densities of the systems.

中文翻译：

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张量力对中子-质子滴中自旋轨道分裂的影响

使用相对论 Hartree-Fock (RHF) 理论和 $\ensuremath{\pi}\text{\ensuremath{-}}N$ 耦合强度优化了中子-质子滴中张量力影响的系统研究中子落下的相对论 Brueckner-Hartree-Fock (RBHF) 结果。对于具有一个质子的中子-质子滴，作为中子数函数的中子自旋轨道分裂的演变与纯中子滴的行为相似，显示出张量力效应。通过在$N=20$的中子滴中再添加一个质子或中子，发现中子和质子之间的张量力效应比中子之间更显着。这可以归因于 RHF 密度泛函理论中 $\ensuremath{\pi}\text{\ensuremath{-}}N$ 相互作用的张量项中的同位旋因子，这反映了中子-质子张量力比中子-中子张量强这一事实。对于具有 20 个质子的中子 - 质子滴也发现了类似的自旋轨道分裂演化行为，其中张力强度 $\ensuremath{\lambda}$ 由于中心密度大而根据 RBHF 结果重新确定的系统。