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发展一种准确的正式主义以预测双中子halo核的性质：22C案例研究

Development of an accurate formalism to predict properties of two-neutron halo nuclei: case study of $^{22}$C

Facility for Rare Isotope Beams, Michigan State University（稀有同位素束流设施，密歇根州立大学）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎萨克雷大学，法国国家科学研究中心/法国国家核子与粒子物理研究所，IJCLab）；Department of Physics and Astronomy, Michigan State University（密歇根州立大学物理与天文学系）

Patrick McGlynn, Chloë Hebborn

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AI总结：

本研究发展了一种准确的三体形式主义，通过投影方法更准确地施加泡利原理，用于预测双中子halo核22C的性质，并展示了高效计算方法。

摘要：

当远离稳定性或在松散结合系统中，出现少体聚类结构，如双中子halo核。这些结构源于多体和少体自由度之间的相互作用，以及结合态与连续态之间的强耦合。这促使开发能够准确描述少体动力学并施加壳效应的模型。本工作有两个目标：理解如何在少体模型中准确施加泡利原理，以及展示新的技术发展，使三体计算更加稳健和经济。我们专注于双中子halo核22C的性质，但认为结论适用于其他少体系统。我们使用三体、超球面谐波形式结合R矩阵法。我们比较了从现象学相互作用出发预测22C性质的预测，使用两种方法去除泡利禁止状态，即投影和超对称方法。我们还展示了算法和推导。此外，我们探讨了允许减少计算时间的模型空间截断。我们展示了对于K_max~40的结合态和散射态计算的收敛性。两种施加泡利排斥原理的方法导致了22C性质的不同预测；投影方法更准确。我们发现一种高效的通道截断，将计算成本减少了20%。我们的研究阐明了投影方法比超对称方法更准确地施加泡利排斥原理。技术性和算法性发展使双中子halo性质的准确和高效计算成为可能。这一发展为三体预测的稳健不确定性量化铺平了道路，并为处理更复杂系统和可观测量提供了有用的起点。

英文摘要：

When moving away from stability or in loosely-bound systems, few-body clusterized structures like two-neutron halo nuclei appear. These emerge from the interplay between the many- and few-body degrees of freedom, and/or strong coupling between bound and continuum states. This motivates the development of models that can accurately describe few-body dynamics while enforcing shell effects. This work has two goals: understanding how to accurately enforce the Pauli principle in few-body models, as well as presenting new technical developments that allow for more robust and cheaper three-body calculations. We focus on properties of the two-neutron halo 22C, but expect the conclusions to apply to other few-body systems. We use a three-body, hyperspherical harmonics formalism combined with the R-matrix method. We compare predictions for properties of 22C starting from phenomenological interactions and using two methods to remove Pauli-forbidden states, the projection and supersymmetric methods. We also present the algorithms and derivations used. Additionally, we explore model space truncations that allow for reduced computational time. We show convergence of the calculation of both bound and scattering states for $K_{max}\sim 40$. The two methods to enforce the Pauli-exclusion principle lead to different predictions of 22C properties; the projection method is more accurate. We find one efficient channel truncation that reduces the computational cost of our calculations by 20%. Our study clarifies that the projection method is more accurate than the supersymmetric one to enforce the Pauli-exclusion principle. Technical and algorithmic developments enable accurate and efficient computation of two-neutron halo properties. This development paves the way to robust uncertainty quantification in three-body predictions, and is a useful starting point to tackle more complex systems and observables.

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