粒子-振动耦合方案中的平均场之外
Beyond the mean field in the particle-vibration coupling scheme
摘要：
能量密度泛函理论是原子核结构研究中最常用的方法之一。它是基于这样的假设，即基态的能量仅是密度分布的函数。该方法是非常成功的有效力的方法，特别是Skyrme或Gogny力，在复制核结合能和其他整体性质沿整个质量表。尽管在这种情况下密度泛函被正式表示为有效力的哈特里-福克平均场，但相应的单粒子态通常并不能很好地再现这种现象。为了克服这个困难，已经开发了一种策略，其中调整有效力以直接再现单粒子能量，试图保持基态能量足够好地再现。另一种解决这一问题的方法是引入平均场涨落，即原子核系统的集体振动，以及它们对单粒子动力学和结构的影响。这是粒子-振动耦合模型的基础。本文提出了一种基于格林函数方法的质点-振动耦合模型的形式化理论。该理论扩展到现实的有效力，宏观粒子振动耦合模型和（微观）核场论。它是形式化的函数导数方法的多体理论。设计了单粒子自能和声子传播子的图解展开式。颗粒振动耦合模型的关键方面进行了分析一般。最低阶的扩展的应用程序，并进行了讨论。
英文摘要：
The Energy Density Functional theory is one of the most used methods developed in nuclear structure. It is based on the assumption that the energy of the ground state is a functional only of the density profile. The method is extremely successful within the effective force approach, noticeably the Skyrme or Gogny forces, in reproducing the nuclear binding energies and other bulk properties along the whole mass table. Although the Density Functional is in this case represented formally as the Hartree-Fock mean field of an effective force, the corresponding single-particle states in general do not reproduce the phenomenology particularly well. To overcome this difficulty, a strategy has been developed where the effective force is adjusted to reproduce directly the single particle energies, trying to keep the ground state energy sufficiently well reproduced. An alternative route, that has been developed along several years, for solving this problem is to introduce the mean field fluctuations, as represented by the collective vibrations of the nuclear system, and their influence on the single particle dynamics and structure. This is the basis of the particle-vibration coupling model. In this paper we present a formal theory of the particle-vibration coupling model based on the Green' s function method. The theory extends to realistic effective forces the macroscopic particle-vibration coupling models and the (microscopic) Nuclear Field Theory. It is formalized within the functional derivative approach to many-body theory. An expansion in diagrams is devised for the single particle self-energy and the phonon propagator. Critical aspects of the particle-vibration coupling model are analysed in general. Applications at the lowest order of the expansion are presented and discussed.
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