Low-lying collective quadrupole states in even–even nuclei are studied for the particular case of a γ-unstable potential within the Bohr Hamiltonian. In particular, the quasi-exactly solvable β-sextic potential is extended to cover the most relevant part of the low-lying spectra in nuclei. In previous papers (2004 Phys. Rev. C 69 014304, 2010 Phys Rev. C 81 044304), the same situation was solved for β-wavefunctions with up to one node (M = 0, 1), which are relevant for the first few low-lying states. Here, the model space is enlarged by including β-wavefunctions also with two nodes (M = 2), which generate many more states, in order to make it useful for actual fittings and more detailed checking of shape phase transitions between spherical and γ-unstable β-deformed shapes in nuclei. In addition to the energy eigenvalues and wavefunctions, closed analytical formulas are obtained for electric quadrupole and monopole transition probabilities too. The model is applied to the chains of even Ru and Pd isotopes to illustrate the transition between the spherical and deformed γ-unstable phases. These applications indicate that the optional extension of the model with a phenomenologic rotational term L ⋅ L is consistent with the experimental data.

针对玻尔哈密顿量内的γ不稳定势的特殊情况，研究了偶数核中的低位集体四极子态。特别是，准精确可解的β-性势被扩展到覆盖原子核中低位光谱的最相关部分。在之前的论文 (2004 Phys. Rev. C 69 014304, 2010 Phys Rev. C 81 044304) 中，针对具有最多一个节点 ( M = 0, 1) 的β波函数解决了相同的情况，这与第一个相关地势低洼的国家很少。这里，模型空间由包括放大β -wavefunctions还具有两个节点（中号= 2)，这会产生更多的状态，以使其可用于实际拟合和更详细地检查球形和核中γ不稳定β变形形状之间的形状相变。除了能量特征值和波函数外，还获得了电四极子和单极子跃迁概率的闭合解析公式。该模型应用于偶数 Ru 和 Pd 同位素链，以说明球形和变形γ不稳定相之间的转变。这些应用表明，具有现象学旋转项L ⋅ L的模型的可选扩展与实验数据一致。