In the present paper, we study the collective states of even–even nuclei in γ-rigid mode within the sextic potential and the minimal length (ML) formalism in Bohr–Mottelson model. The eigenvalues problem for the latter is solved by combined means of quasi-exact solvability and a quantum perturbation method. Numerical calculations are performed for 35 nuclei: ⁹⁸⁻¹⁰⁸Ru, ^100−102Mo, ^116−130Xe, ^180−196Pt, ¹⁷²Os, ^146−150Nd, ^132−134Ce, ¹⁵⁴Gd, ¹⁵⁶Dy and ^150−152Sm. Through this study, it appears that our elaborated model leads to an improved agreement of the theoretical results with the corresponding experimental data by reducing the rms with a rate going up to 63% for some nuclei. This comes from the fact that we have combined the sextic potential, which is a very useful phenomenological potential, with the formalism of the ML, which is based on the generalized uncertainty principle and which is in turn a quantum concept widely used in quantum physics. In addition, we investigate the effect of ML on energy ratios, transition rates, moments of inertia and a shape phase transition for the most numerous isotopic chains, namely Ru, Xe, Nd and Pt.

在本文中，我们研究了γ-刚性模式下的 stic 势和 Bohr-Mottelson 模型中的最小长度 (ML) 形式主义中偶偶核的集体状态。后者的特征值问题是通过准精确可解性和量子微扰法相结合的方法解决的。：数值计算为35级的核进行^98-108的Ru，^100-102沫，^116-130的Xe，^180-196的Pt，¹⁷²的OS，^146-150钕，^132-134的Ce，¹⁵⁴的Gd，¹⁵⁶ Dy和^150-152米。通过这项研究，我们精心设计的模型似乎通过降低 rms 来提高理论结果与相应实验数据的一致性，某些原子核的比率高达 63%。这是因为我们将性势（一种非常有用的现象学势）与基于广义不确定性原理的 ML 的形式主义相结合，而后者又是量子物理学中广泛使用的量子概念。此外，我们研究了 ML 对大多数同位素链（即 Ru、Xe、Nd 和 Pt）的能量比、跃迁率、惯性矩和形状相变的影响。