论文标题
来自非定位集群模型的$α+α$系统中的谐振和散射状态
Resonant and Scattering States in the $α+α$ System from the Non-Localized Cluster Model
论文作者
论文摘要
非定位集群模型提供了有关核聚类效应的新观点，并已成功地应用于各种结合状态和准结合状态（即长期存在的共鸣状态）的群集结构。在这项工作中，我们将非定位集群模型的应用范围进一步扩展到谐振和散射状态。遵循$ r $ -MATRIX理论，将构型空间通过大通道半径分为内部和外部区域，从而使核力量和反对称效应在外部区域的簇之间可以忽略不计。在内部区域中，通过采用边缘 - tohsaki-horiuchi-schuck-röpke（Brink-Thsr）波的底波作为构建内部波浪功能的碱基，从数学上实现了非定位聚类的图像。 Bloch-Schrödinger方程用于将内波函数与谐振态的渐近边界条件连续匹配，在通道半径处的散射状态，这最终导致了问题的解决方案。作为对形式主义的首次测试，研究了$ {}^{8} $的低洼共振状态，并研究了$α+α$弹性散射的相移。数值结果与实验数据非常吻合，该数据显示了理论框架的有效性。
The non-localized cluster model provides a new perspective on nuclear cluster effects and has been applied successfully to study cluster structures in various bound states and quasi-bound states (i.e., long-lived resonant states). In this work, we extend the application scope of the non-localized cluster model further to resonant and scattering states. Following the $R$-matrix theory, the configuration space is divided into the interior and exterior regions by a large channel radius such that the nuclear forces and the antisymmetrization effects become negligible between clusters in the exterior region. In the interior region, the picture of non-localized clustering is realized mathematically by adopting the Brink-Tohsaki-Horiuchi-Schuck-Röpke (Brink-THSR) wave functions as the bases to construct the interior wave functions. The Bloch-Schrödinger equation is used to match the interior wave functions continuously with the asymptotic boundary conditions of the resonant and scattering states at the channel radius, which leads eventually to solutions of the problem. As a first test of the formalism, the low-lying resonant states of ${}^{8}$Be and the phase shifts of the $α+α$ elastic scattering are studied. The numerical results agree well with the experimental data, which shows the validity of the theoretical framework.
