Theoretical Study of Nuclear Large-Amplitude Collective Motions based on Self-Consistent Mechanism

在组成核子之间的强相互作用的影响下紧密结合的原子核，已知表现出高度非线性的集体运动。本项目的目标是建立一个基于孤立多体系统固有的自洽机制的大振幅集体运动理论；即为孤立有限量子多体系统建立一种新的非线性动力学特性理论。我们将简略地介绍一下我们的成就的范围。完成了基于自洽场的大振幅集体运动理论的发展，并确定了最优集体子空间，在该子空间中可以描述大振幅核集体运动的产生和发展，其适用性远远超过线性近似。此外，从子空间中运动的稳定性出发，给出了集体模态跃迁和耗散的定量判据。自洽有效相互作用的理论是在集体激励发生时，在平均场的变化中施加严格的自洽性。由此导出的高阶有效相互作用表征了核系统的非线性粒子-集体耦合特征，并在实际核的数值应用中得到了改进的玻色子展开和曲轴理论的证实。从第一个原理开始，提出了一种更基本的方法来推导与集体激励自洽的有效相互作用。发现高阶相关和相互作用的起源与集体运动的非线性密切相关。一个原子核的图象变成了一个更一般的孤立强子多体系统的图象，特别是当中间能量探针被用来研究一个核系统的状态时。提出了包含子自由度的自洽相对论强子多体系统的理论，并证明了由子自由度引起的效应是非常重要的。综上所述，除了超出预期的成就外，本项目中提出的许多作品实际上是非常独特和原创的，并且会找到更多可能的扩展和应用。少

A nucleus, tightly bound under the influence of strong interactions acting between constituent nucleons, is known to exhibit highly nonlinear collective motions. The goal of this Project is to develop a theory for large-amplitude collective motions based on the self-consistent mechanism inherent to the isolated many-body system; in other words to construct a new theory of nonlinear dynamics characteristic to an isolated finite quantal many-body system. The scope of our achievements will be briefly sketched.The development of a theory for a large-amplitude collective motion based on the self consistent field has been completed, and the optimal collective subspace has been determined in which generation and development of the large-amplitude nuclear collective motions can be described with applicability far beyond that in a linear approximation. Furthermore, the quantitative criteria for transition and dissipation of the collective mode is proposed in terms of the stability of the motion … More in the subspace.A theory for the self-consistent effective interactions has been developed by imposing strict self-consistency in the change of an average field when collective excitations take place. The higher-order effective interactions thus derived represent nonlinear particle-collective couplings characteristic to a nuclear system, and they have been confirmed in the numerical application to realisticnuclei in terms of the improved boson expansion and the cranking theory.A more fundamental approach to derive effective interactions which are self-consistent to collective excitations has been set forth starting from the first principle. The origin of higherorder correlations and interactions has been found to be closely related to non-linearity of collective motions.A picture of a nucleus becomes that of a more general isolated hadronic many-body system especially when intermediate energy probes are used to study the state of a nuclear system. The development of a theory of a self-consistent relativistic hadronic many-body system has been initiated including pionic degrees of freedom, and the effects originated from pionic degrees of freedom are shown to be quite important.In summary, without metioning the accomplishments that are better than expected, many of the works set forth in this Project in fact are quite unique and original and will find more possible extensions and applications. Less