$α+α$体系非定域团簇模型的共振态和散射态
Resonant and Scattering States in the $α+α$ System from the Non-Localized Cluster Model
摘要：
非定域团簇模型为研究核团簇效应提供了一个新的视角，并已成功地应用于研究各种束缚态和准束缚态（即，长寿命共振态）。在这项工作中，我们扩展的非定域集群模型的应用范围进一步共振和散射状态。根据$R$ -矩阵理论，通过大的通道半径将组态空间分为内部和外部区域，使得外部区域中团簇之间的核力和反对称化效应变得可以忽略。在内部区域，以Brink-Tohsaki-Horiuchi-Schuck-Röpke（Brink-THSR）波函数为基础构造内部波函数，在数学上实现了非定域聚类图像。利用Bloch-薛定谔方程将内波函数与通道半径处的共振态和散射态的渐近边界条件进行连续匹配，最终得到问题的解.作为形式主义的第一个测试，低的低洼共振态的${}^{8}$ Be和$α+α$弹性散射的相移进行了研究。数值计算结果与实验数据吻合较好，表明了理论框架的有效性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
