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，紧密束缚的原子核表现出高度的非线性集体运动。该项目的目标是发展一种基于孤立多体系统固有的自洽机制的大幅度集体运动的理论，换句话说，构建一种孤立的有限量子多体系统的非线性动力学特征的新理论。我们将简要介绍我们所取得的成果的范围。基于自洽场的大振幅集体运动理论的发展已经完成，并确定了可以描述大振幅核集体运动的产生和发展的最佳集合子空间，其适用性远远超出了线性近似。此外，根据运动…的稳定性，提出了集体模的跃迁和耗散的定量判据在子空间中，通过在发生集体激发时平均场的变化中施加严格的自洽，发展了一种自洽有效相互作用的理论。由此得到的高阶有效相互作用代表了核系统的非线性粒子-集体耦合的特征，并根据改进的玻色子展开和曲折理论在对现实核的数值应用中得到了证实。从第一原理出发，提出了一种更根本的方法来获得与集体激发自洽的有效相互作用。高阶关联和相互作用的起源已经被发现与集体运动的非线性密切相关。原子核的图像变成了更一般的孤立的强子多体系统的图像，特别是当使用中能探测器来研究核系统的状态时。自洽相对论强子多体系统理论的发展已经开始，其中包括轻子自由度，而轻子自由度的影响被证明是相当重要的。综上所述，尽管没有提及比预期更好的成果，本项目中的许多工作实际上是相当独特和原创的，并将找到更多可能的扩展和应用。较少

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