六次势下最小长度γ-刚性四极哈密顿量中偶偶核的集体态
Collective states of even-even nuclei in gamma-rigid quadrupole Hamiltonian with Minimal Length under the sextic potential
摘要：
本文在玻尔-莫特森模型的六次势和最小长度（ML）形式下，研究了偶偶核在伽玛刚性模式下的集体态。后者的本征值问题是通过联合解决的准精确可解性（QES）和量子微扰法（QPM）。对（98 108）Ru，（100 102）Mo，（116 130）Ru，（180 196）Pt，（172）Os，（146 150）Nd，（132 134）Ce，（154）Gd，（156）Dy和（150 152）Sm等35个核进行了数值计算.通过这项研究，看来，我们的精心设计的模型导致了一个改进的协议的理论结果与相应的实验数据，通过降低均方根率高达63%的一些核。这是因为我们将六次势（一种非常有用的唯象势）与基于广义不确定原理的ML的形式主义结合起来，而ML又是量子物理学中广泛使用的量子概念。此外，我们还研究了ML对最多的同位素链，即Ru，Nd，Pt，的能量比，跃迁速率，转动惯量和相变形状的影响。
英文摘要：
In the present paper, we study the collective states of even even nuclei in gamma rigid mode within the sextic potential and the Minimal Length (ML) formalism in Bohr Mottelson model. The eigenvalues problem for this latter is solved by means conjointly of Quasi-Exact Solvability (QES) and a Quantum Perturbation Method (QPM). Numerical calculations are performed for 35 nuclei:(98 108)Ru, (100 102)Mo, (116 130)Xe, (180 196)Pt, (172)Os, (146 150)Nd, (132 134)Ce, (154)Gd, (156)Dy and (150 152)Sm. 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 out 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. Besides, 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.
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