标题： 轻中质量核单极共振的从头描述：I. 从头PGCM计算的技术方面与不确定性 显示英文标题

标题： Ab initio description of monopole resonances in light- and medium-mass nuclei: I. Technical aspects and uncertainties of ab initio PGCM calculations

摘要： 集体运动在原子核等介观系统中表现为巨大的共振（GRs）。直到最近，理论研究主要依赖于基于经验能量密度泛函（EDFs）的（准粒子）随机相位近似（（Q）RPA）及其扩展形式。作为当前努力的一部分，旨在用从头算理论框架描述GRs，本文推广了投影生成坐标法（PGCM）的应用。该方法能够处理非简谐效应，同时满足核哈密顿量的对称性，在系统的规模上表现出有利的（即平均场类）缩放特性。目前，聚焦于轻至中等质量核的同位旋标量巨大单极共振（GMR），展示了PGCM在包含配对、变形和形状共存效应的闭壳层和开壳层核中提供广泛从头算GRs研究的潜力。与一致的QRPA计算的比较突出了PGCM的独特属性，并揭示了核集体激发之间复杂的相互作用。本文是四篇系列论文中的第一篇，重点介绍了使用双开壳层 $^{46}$Ti 作为示例的从头算PGCM GMR计算的技术细节和不确定性量化。第二篇论文展示了物理相关核的一组结果，并进一步与一致的（变形）从头算QRPA计算进行比较。第三篇论文分析了单极强度函数的有用矩及其在PGCM计算中的不同获取方式，而第四篇论文则关注对称性恢复对单极强度函数的影响。 显示英文摘要

摘要： Giant resonances (GRs) are a striking manifestation of collective motions in mesoscopic systems such as atomic nuclei. Until recently, theoretical investigations have essentially relied on the (quasiparticle) random phase approximation ((Q)RPA), and extensions of it, based on phenomenological energy density functionals (EDFs). As part of a current effort to describe GRs within an ab initio theoretical scheme, the present work promotes the use of the projected generator coordinate method (PGCM). This method, which can handle anharmonic effects while satisfying symmetries of the nuclear Hamiltonian, displays a favorable (i.e. mean-field-like) scaling with system's size. Presently focusing on the isoscalar giant monopole resonance (GMR) of light- and medium-mass nuclei, PGCM's potential to deliver wide-range ab initio studies of GRs in closed- and open-shell nuclei encompassing pairing, deformation, and shape coexistence effects is demonstrated. The comparison with consistent QRPA calculations highlights PGCM's unique attributes and sheds light on the intricate interplay of nuclear collective excitations. The present paper is the first in a series of four and focuses on technical aspects and uncertainty quantification of ab initio PGCM calculations of GMR using the doubly open-shell $^{46}$Ti as an illustrative example. The second paper displays results for a set of nuclei of physical interest and proceeds to the comparison with consistent (deformed) ab initio QRPA calculations. While the third paper analyzes useful moments of the monopolar strength function and different ways to access them within PGCM calculations, the fourth paper focuses on the effect of the symmetry restoration on the monopole strength function.