Abstract

The inverse square potential is used to provide the ‘pictures’ of the transitions symmetry from U(5) to O(6) via the variational procedure of the E(5) solutions. The variation of the single-parameter \(\beta _{0}\) of the inverse square potential shifts the E(5) solutions: the energy eigenvalues increase when \(\beta _{0}\) increases. In the theoretical prediction of \(R_{L/2}\), \(\beta _{0}=0\) yields solutions that correspond to the U(5) symmetry of the Bohr Hamiltonian with \(R_{4/2}=2.00\). As \(\beta _{0}\) increases, the solutions of E(5) materialize with \(R_{4/2}=2.189\) at \(\beta _{0,max}=3.986\). The solutions leave E(5) and approach O(6) with \(R_{4/2}=2.466\) at \(\beta _{0}=25\). The solutions of \(^{132}Xe\) and \(^{134}Xe\) of the E(5) symmetry candidates are fitted and compared with the available experimental values. With the same variational method, the ratios of B(E2) transition rates within the ground state leave O(6) and approach E(5) solution as \(\beta _{0}\) increases.

Graphic abstract

中文翻译：

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通过E（5）反平方势解的U（5）和O（6）形状相变

摘要

平方反比电势用于通过E（5）解的变分过程提供从U（5）到O（6）对称过渡的“图像” 。平方反比的单参数\（\ beta _ {0} \）的变化使E（5）解移位：当\（\ beta _ {0} \）增加时，能量特征值增加。在的理论预测\（R_ {L / 2} \） ，\（\测试_ {0} = 0 \）的产率的解决方案，对应于û玻尔哈密顿量的（5）对称地\（R_ {4 / 2} = 2.00 \）。随着\（\ beta _ {0} \）的增加，E的解（5）在\（\ beta _ {0，max} = 3.986 \）处以\（R_ {4/2} = 2.189 \）实现。解离开E（5）并以\（R_ {4/2} = 2.466 \）在\（\ beta _ {0} = 25 \）处接近O（6 ）。拟合E（5）个对称候选的\（^ {132} Xe \）和\（^ {134} Xe \）的解，并将其与可用的实验值进行比较。使用相同的变分方法，随着\（\ beta _ {0} \）的增加，基态中B（E 2）跃迁速率的比率离开O（6）并接近E（5）解。

图形摘要