In this article, we study the possible relationship between degrees of freedom of collectivity in protons and neutrons' last orbitals and different patterns of quadrupole transition possibilities in the shape coexistence candidates. Because of the dependence of shape coexistence on the arrangement of nucleons in the nuclear structure, we classified the candidates of shape coexistence based on neutrons and protons' last orbitals using the shell-model configuration. In the orbitals corresponding to the neutron numbers in the N=40, 60, and 90 regions, there is a limitation in the degree of freedom for neutrons, and proton-induced shape coexistence occurs. Also, for the orbitals corresponding to the atomic numbers of the Z=40, 52, and 82 regions, the degree of freedom is limited for protons, and neutron-induced coexistence occurs. In this article, we study both the nuclei that belong to the neutron and proton-induced shape coexistence categories and the nuclei that are candidates for shape coexistence but do not belong to the mentioned two categories. The study of different patterns indicates that the $\frac{|\mathrm{B}\left(\mathrm{E}2;2_2^{+}\to 0_1^{+}\right)-\mathrm{B}\left(\mathrm{E}2;2_1^{+}\to 0_1^{+}\right)|}{\mathrm{B}\left(\mathrm{E}2;2_1^{+}\to 0_1^{+}\right)}$, $\frac{|\mathrm{B}\left(\mathrm{E}2;2_2^{+}\to 0_1^{+}\right)-\mathrm{B}\left(\mathrm{E}2;4_1^{+}\to 2_1^{+}\right)|}{\mathrm{B}\left(\mathrm{E}2;4_1^{+}\to 2_1^{+}\right)}$, $\frac{|\mathrm{B}\left(\mathrm{E}2;2_2^{+}\to 0_1^{+}\right)-\mathrm{B}\left(\mathrm{E}2;6_1^{+}\to 4_1^{+}\right)|}{\mathrm{B}\left(\mathrm{E}2;6_1^{+}\to 4_1^{+}\right)}$, $\frac{|\mathrm{B}\left(\mathrm{E}2;2_3^{+}\to 0_1^{+}\right)-\mathrm{B}\left(\mathrm{E}2;2_1^{+}\to 0_1^{+}\right)|}{\mathrm{B}\left(\mathrm{E}2;2_1^{+}\to 0_1^{+}\right)}$, $\frac{|\mathrm{B}\left(\mathrm{E}2;2_3^{+}\to 0_1^{+}\right)-\mathrm{B}\left(\mathrm{E}2;4_1^{+}\to 2_1^{+}\right)|}{\mathrm{B}\left(\mathrm{E}2;4_1^{+}\to 2_1^{+}\right)}$, and $\frac{|\mathrm{B}\left(\mathrm{E}2;2_3^{+}\to 0_1^{+}\right)-\mathrm{B}\left(\mathrm{E}2;6_1^{+}\to 4_1^{+}\right)|}{\mathrm{B}\left(\mathrm{E}2;6_1^{+}\to 4_1^{+}\right)}$ follow a similar repetition range)in most cases(for ratios related to the neutrons and protons' last orbitals classification. Also, in addition to the mentioned transition possibilities, in transitions related to the neutrons' last orbitals classification, the $\frac{|\mathrm{B}\left(\mathrm{E}2;2_3^{+}\to 2_1^{+}\right)-\mathrm{B}\left(\mathrm{E}2;4_1^{+}\to 2_1^{+}\right)|}{\mathrm{B}\left(\mathrm{E}2;4_1^{+}\to 2_1^{+}\right)}$ and $\frac{|\mathrm{B}\left(\mathrm{E}2;2_3^{+}\to 2_1^{+}\right)-\mathrm{B}\left(\mathrm{E}2;6_1^{+}\to 4_1^{+}\right)|}{\mathrm{B}\left(\mathrm{E}2;6_1^{+}\to 4_1^{+}\right)}$ have a repetition pattern. In the orbitals where neutrons and protons have fewer degrees of freedom (proton and neutron-induced shape coexistence occurs), the results show that the data related to repetition patterns are less correlated than in other orbitals. The study includes information on specific Nilsson orbitals, which are crucial in investigations related to shape coexistence. Correlating observations to these orbitals allows for a more accurate representation of the underlying microscopic picture, enhancing the quality of analysis and strengthening the connection between observations and the SC phenomenon.

在本文中，我们研究了质子和中子集体自由度之间的可能关系。形状共存候选者中的最后轨道和四极杆的不同模式跃迁可能性。由于形状共存依赖于核结构中核子的排列，因此我们根据中子和质子对形状共存的候选者进行了分类。使用壳模型配置的最后一个轨道。在N=40、60和90区域中子数对应的轨道中，中子的自由度受到限制，并且发生质子诱导的形状共存。此外，对于对应于Z=40、52和82区域的原子序数的轨道，质子的自由度受到限制，并且发生中子诱导共存。在本文中，我们研究了属于中子和质子诱导的形状共存类别的原子核，以及作为形状共存候选但不属于上述两个类别的原子核。对不同模式的研究表明 $\frac{|\mathrm{乙}（\mathrm{乙}2;2_2^{+}\to 0_1^{+}）-\mathrm{乙}（\mathrm{乙}2;2_1^{+}\to 0_1^{+}）|}{\mathrm{乙}（\mathrm{乙}2;2_1^{+}\to 0_1^{+}）}$,$\frac{|\mathrm{乙}（\mathrm{乙}2;2_2^{+}\to 0_1^{+}）-\mathrm{乙}（\mathrm{乙}2;4_1^{+}\to 2_1^{+}）|}{\mathrm{乙}（\mathrm{乙}2;4_1^{+}\to 2_1^{+}）}$,$\frac{|\mathrm{乙}（\mathrm{乙}2;2_2^{+}\to 0_1^{+}）-\mathrm{乙}（\mathrm{乙}2;6_1^{+}\to 4_1^{+}）|}{\mathrm{乙}（\mathrm{乙}2;6_1^{+}\to 4_1^{+}）}$,$\frac{|\mathrm{乙}（\mathrm{乙}2;2_3^{+}\to 0_1^{+}）-\mathrm{乙}（\mathrm{乙}2;2_1^{+}\to 0_1^{+}）|}{\mathrm{乙}（\mathrm{乙}2;2_1^{+}\to 0_1^{+}）}$,$\frac{|\mathrm{乙}（\mathrm{乙}2;2_3^{+}\to 0_1^{+}）-\mathrm{乙}（\mathrm{乙}2;4_1^{+}\to 2_1^{+}）|}{\mathrm{乙}（\mathrm{乙}2;4_1^{+}\to 2_1^{+}）}$， 和$\frac{|\mathrm{乙}（\mathrm{乙}2;2_3^{+}\to 0_1^{+}）-\mathrm{乙}（\mathrm{乙}2;6_1^{+}\to 4_1^{+}）|}{\mathrm{乙}（\mathrm{乙}2;6_1^{+}\to 4_1^{+}）}$遵循类似的重复范围）在大多数情况下（对于与中子和质子的最后轨道分类相关的比率。此外，除了提到的跃迁可能性之外，在与中子的最后轨道分类相关的跃迁中，$\frac{|\mathrm{乙}（\mathrm{乙}2;2_3^{+}\to 2_1^{+}）-\mathrm{乙}（\mathrm{乙}2;4_1^{+}\to 2_1^{+}）|}{\mathrm{乙}（\mathrm{乙}2;4_1^{+}\to 2_1^{+}）}$和$\frac{|\mathrm{乙}（\mathrm{乙}2;2_3^{+}\to 2_1^{+}）-\mathrm{乙}（\mathrm{乙}2;6_1^{+}\to 4_1^{+}）|}{\mathrm{乙}（\mathrm{乙}2;6_1^{+}\to 4_1^{+}）}$有重复模式。在中子和质子自由度较小的轨道中（发生质子和中子诱导的形状共存），结果表明与重复模式相关的数据与其他轨道相比相关性较低。该研究包括有关特定尼尔森轨道的信息，这对于形状共存相关的研究至关重要。将观测结果与这些轨道相关联可以更准确地表示底层的微观图像，从而提高分析质量并加强观测结果与 SC 现象之间的联系。