Microscopic theory of nuclear collective states

一个中心目标是完成一本关于核模型基础的两卷本书，作者是实验学家J.L.木材.这本书的主要目的是建立核结构模型和理论的实验和数学基础，以便以后的发展可以建立在它们的基础上。这个长期项目，现在接近完成，也确保我们的研究计划的总体目标仍然是重点。它还有助于确定数据和理论中可以填补的关键空白。因此，约翰·伍德是一个实验研究团队的领导者，在Triumf实验室使用ISAC，我是该实验室的顾问成员。在理论方面，我的计划的一个主要部分是给宏观集体模型一个相互作用核子的微观表达。因此，集体模型和壳模型被视为互补的，从一个模型中获得的直觉被用来指导另一个模型的应用。 例如，集体模型在多极矩而不是历史形状坐标方面的教学发展，将集体模型的状态从液滴模型提高到壳模型的可解子模型。 这使得有可能将壳模型中的耦合方案与相应的集体模型相关联，并将两个模型的对称性限制联系起来。一个挑战是处理不相容的对称性和耦合方案竞争的情况。 在上一个资助期内，通过专注于目前流行的量子相变，取得了相当大的进展，这种相变发生在存在竞争动力学对称性的系统中。 通过引入准动力学对称性的概念，我们已经观察到并解释了竞争的动力学对称性中的一个往往占主导地位。 为了利用这一观察结果，我们正在开发一种新的量子多体理论方法，没有预定义的基础，旨在处理具有准对称性的系统以及具有对称性的系统。

A central goal is completion of a two-volume book on the Fundamentals of Nuclear Models with an experimentalist, J.L. Wood. A primary objective of this book is to establish the experimental and mathematical foundations of the models and theories of nuclear structure so that subsequent developments can build upon them. This long-term project, now nearing completion, also ensures that the overall objectives of ours research programs remain in focus. It also serves to identify critical gaps in the data and the theory, that can be filled. Thus, John Wood is a leader of an experimental research team, using ISAC at the Triumf laboratory, for which I am a consulting member. On the theory side, a major part of my program has been to give the macroscopic collective models a microscopic expression in terms of interacting nucleons. Thus, the collective and shell models are seen as complementary and the intuition gained from one is used to guide applications of the other. For example, a pedagogical development of the collective model in terms of multipole moments instead of the historical shape coordinates, raises the status of the collective model from a liquid-drop model to a solvable submodel of the shell model. This makes it possible to associate coupling schemes in the shell model with corresponding collective models and relate the symmetry limits of the two models. A challenge, is to handle situations in which incompatible symmetries and coupling schemes are in competition. Considerable progress was made during the last grant period by focusing on the presently popular quantum phase transitions that occur in systems for which there are competing dynamical symmetries. We have observed and explained, by introducing the concept of quasi-dynamical symmetry, that one among competing dynamical symmetries tends to dominate. To take advantage of this observation, we are developing a new approach to quantum many-body theory, without predefined bases, that is designed to handle systems with quasi-symmetries as well as those with symmetries.