Yan-Zhao Wang1,2,3,4, Yang Li1,2, Chong Qi3, Jian-Zhong Gu4**
1Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043 2Institute of Applied Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043 3Department of Physics, Royal Institute of Technology (KTH), Stockholm SE-10691, Sweden 4China Institute of Atomic Energy, Beijing 102413
Abstract：In the framework of the Skyrme–Hartree–Fock–Bogoliubov approach with the SkT interaction, the pairing effects on the proton bubble structures of $^{46}$Ar and $^{206}$Hg are discussed. In calculations, three kinds of pairing forces (volume, surface and mixed pairing interactions) are used. For $^{46}$Ar, it is shown that the bubble structure with the volume pairing is almost the same as that with the mixed pairing. The bubble with the surface pairing is less pronounced than those with the volume and mixed pairings. Analyzing the density distributions and occupation probabilities of the proton $s$ states and the quasi-degeneracy between the proton 2$s_{1/2}$ and 1$d_{3/2}$ orbitals, we explain the difference between the bubble structure with the surface pairing and those with the volume and mixed pairings. For $^{206}$Hg, it is seen that the proton density distribution with the surface pairing is different from those with the volume and mixed pairings in the whole region of the radial distance. In addition, it is found that the bubbles with the three pairing forces are different from each other and the least pronounced bubble is obtained with the surface pairing. Thus the selection of the pairing force is important for the study of the nuclear bubble structure.
2019, Vol. 36 
