标题： 可调保真度波函数用于描述散射和反应的\textit{从头开始} 显示英文标题

标题： Tunable-fidelity wave functions for the \textit{ab initio} description of scattering and reactions

摘要： 核无关壳模型（NCSM）是一种\textit{从头开始}方法，通过将多粒子波函数展开到（通常是）谐振子基底中，并最小化能量以获得展开系数来解决原子核的多体问题。 NCSM 的扩展，例如将其与微观聚集体基态耦合，进一步允许对天体物理学和核技术应用中感兴趣的轻离子核反应进行\textit{从头开始}处理。 该方法的一个缺点是基底大小随着核子数量和激发量子数的增加呈指数增长，这限制了它在质量为$A\lesssim 16$的原子核中的适用性，除非通过某种截断方案进一步减少基底。 我们考虑了一种适用于 NCSM 的基底选择方法，该方法捕获了原子核波函数的基本自由度，从而实现了计算复杂度的有利缩放，并能够在$sd$壳层核中实现\textit{从头开始}反应计算。 NCSM 基底内的粒子构型根据它们对由投影到多体基底产生的哈密顿矩阵的第一矩的贡献进行排序。 然后截断方案包括仅保留最低的第一矩构型，这些构型通常只包含少数多体基态（Slater 表面式）。 我们使用从手征有效场论推导并用相似重整群方法软化的核-核相互作用，计算了$^7$锂和$n+^{12}$碳散射。 所得能级始终表现出随基底大小呈指数收敛，我们在散射计算中发现了改进的收敛性。 为了展示这种方法所带来可能性，我们还展示了从$^{24}$Mg 散射中子的第一个计算结果。 显示英文摘要

摘要： The no-core shell model (NCSM) is an \textit{ab initio} method that solves the nuclear many-body problem by expanding the many-particle wave function into a (typically) harmonic oscillator basis and minimizing the energy to obtain the expansion coefficients. Extensions of the NCSM, such as its coupling with microscopic-cluster basis states, further allow for an \textit{ab initio} treatment of light-ion nuclear reactions of interest for both astrophysics and nuclear technology applications. A downside of the method is the exponential scaling of the basis size with increasing number of nucleons and excitation quanta, which limits its applicability to mass $A\lesssim 16$ nuclei, except for variants where the basis is further down-selected via some truncation scheme. We consider a basis selection method for the NCSM that captures the essential degrees of freedom of the nuclear wave function leading to a favorable complexity scaling for calculations and enabling \textit{ab initio} reaction calculations in $sd$-shell nuclei. The particle configurations within the NCSM basis are ordered based on their contribution to the first moment of the Hamiltonian matrix that results from the projection onto the many-body basis. The truncation scheme then consists in retaining only the lowest-first-moment configurations, which typically contain only few many-body basis states (Slater determinants). We present calculations for $^7$Li and $n+^{12}$C scattering using nucleon-nucleon interactions derived from chiral effective field theory and softened using the similarity renormalization group method. The obtained energy levels invariably demonstrate exponential convergence with the size of the basis, and we find improved convergence in scattering calculations. To demonstrate the possibilities enabled by the approach, we also present a first calculation for the scattering of neutrons from $^{24}$Mg.