标题： 轻核和中等质量核单极共振的从头描述：IV. 角动量投影与转动-振动耦合 显示英文标题

标题： Ab initio description of monopole resonances in light- and medium-mass nuclei: IV. Angular momentum projection and rotation-vibration coupling

摘要： 巨共振是有限核集体性质最明显的表达方式，与核转动一起，构成了这一领域的重要研究对象。然而，这两种激发类别传统上是在不同的理论框架内描述的，使得振动和转动自由度被分开处理，并且通常忽略了它们之间的耦合效应。 本研究提出了一种方法，旨在对振动和转动进行一致性的处理。具体而言，本文是关于通过从头算投影生成坐标法（PGCM）研究双开壳核巨单极共振的四篇系列文章中的最后一篇。当前的重点是探讨此类计算中角动量恢复的处理及其影响。 由于PGCM基于变形平均场态，因此在求解特征方程以提取振动激发时执行角动量恢复。在此背景下，研究表明，仅在求解特征方程之后才进行角动量恢复会污染单极响应，使其与旋转运动产生非物理耦合，这一点同样也在最近基于变形参考态的（准粒子）随机相位近似计算中得到了验证。 最终，基于PGCM的本研究确认，在同时处理两种集体运动时，事先进行角动量恢复是必要的。这进一步支持了未来应实现完整的投影（准粒子）随机相位近似的观点。 显示英文摘要

摘要： Giant Resonances are, with nuclear rotations, the most evident expression of collectivity in finite nuclei. These two categories of excitations, however, are traditionally described within different formal schemes, such that vibrational and rotational degrees of freedom are separately treated and coupling effects between those are often neglected. The present work puts forward an approach aiming at a consitent treatment of vibrations and rotations. Specifically, this paper is the last in a series of four dedicated to the investigation of the giant monopole resonance in doubly open-shell nuclei via the ab initio Projected Generator Coordinate Method (PGCM). The present focus is on the treatment and impact of angular momentum restoration within such calculations. The PGCM being based on the use of deformed mean-field states, the angular-momentum restoration is performed when solving the secular equation to extract vibrational excitations. In this context, it is shown that performing the angular momentum restoration only after solving the secular equation contaminates the monopole response with an unphysical coupling to the rotational motion, as was also shown recently for (quasi-particle) random phase approximation calculations based on a deformed reference state. Eventually, the present work based on the PGCM confirms that an a priori angular momentum restoration is necessary to handle consistently both collective motions at the same time. This further pleads in favor of implementing the full-fledged projected (quasi-particle) random phase approximation in the future.