AI 中文总结
该研究扩展自洽格林函数方法至双开壳核，开发变形方案并在\texttt{FoxTrot}中实现，以$^{28}$Si为例验证方法精度，为重核的准确从头描述奠定基础。
AI 中文摘要
从第一性原理描述原子核是核理论的核心目标之一。多项式标度展开方法已将亚百分之一精度的从头计算扩展到中等质量核及少数闭壳重核，但变形双开壳重核与超重核仍超出研究范围。本文将自洽格林函数（SCGF）形式扩展至双开壳核，允许单体传播子自发破缺SU(2)旋转对称性。所得到的变形自洽格林函数（dSCGF）方案基于截断至一阶、二阶和三阶的代数图构造，在新开发的多体套件\texttt{FoxTrot}中实现。本文详细讨论了处理相关无对称性约束的M方案工作基所需的数值策略。通过基于1.8/2.0（EM）哈密顿量对$^{28}$Si的研究示例说明该方法：检验了三核子相互作用及其秩约化近似对变形哈特利-福克总能量曲线的影响，结果表明，约束dSCGF计算得到的关联曲线与平均场曲线存在显著差异；关联曲线最小值对应的物理解可通过从变形哈特利-福克曲线上任意点开始的无约束计算得到，证明了该方法的自洽性。外推至无穷基组大小极限的三阶$^{28}$Si基态结合能与实验值的偏差在2.1%以内，而激发的长椭球解与观测到的$0^+_3$形状同核异能态一致。本文的进展为近期准确从头描述所有（极）重核开辟了道路。
英文摘要
The description of atomic nuclei from first principles constitutes one of the central goals of nuclear theory. Polynomial-scaling expansion methods have extended \textit{ab initio} calculations at sub-percent accuracy to medium-mass nuclei and a few closed-shell heavy nuclei, but deformed doubly open-shell heavy and superheavy nuclei remain out of reach. The self-consistent Green's function (SCGF) formalism is here extended to doubly open-shell nuclei by allowing the one-body propagator to spontaneously break SU(2) rotational symmetry. The resulting deformed SCGF (dSCGF) scheme, based on the algebraic diagrammatic construction truncated at first, second, and third order, is implemented in a newly developed many-body suite, \texttt{FoxTrot}. Numerical strategies required to handle the associated, symmetry-unrestricted $M$-scheme working basis are discussed in detail. The method is illustrated through a study of $^{28}$Si based on the 1.8/2.0 (EM) Hamiltonian. The impact of the three-nucleon interaction and of its rank-reduction approximation on the deformed Hartree-Fock total energy curve is examined, and the correlated curve obtained from constrained dSCGF calculations is shown to differ appreciably from the mean-field one. Physical solutions appearing as minima of the correlated curve are shown to be reachable via unconstrained calculations starting from any point along the deformed Hartree-Fock curve, demonstrating the self-consistent character of the method. The $^{28}$Si ground-state binding energy at third order, extrapolated to the infinite basis-size limit, reproduces experiment within $2.1\%$, while the excited prolate solution is consistent with the observed $0^+_3$ shape isomer. The present developments open the way to an accurate ab initio description of all (very) heavy nuclei in the near future.
Comments14 pages, 7 figures
