Microscopic Study of Non-Linear Collective Motions in Yrast Region of Medium-Heavy Nuclei

本项目的目的是建立一个理论框架，以重新规范中重核弹性区内的运动学和动力学非调和效应，并利用该理论分析低自旋态和高自旋态的集体运动。当从低自旋区一侧靠近时，1。在球面基向量的基础上，采用Dyson玻色子映射方法分析了低自旋区域的集体运动。我们建立了dyson型自洽集体坐标方法的理论，可以说，这是一种将非线性耦合效应重正化为集体坐标的动态玻色子展开理论。利用这一理论，我们分析了Sm同位素的形状转变现象。当从高自旋区一侧接近时，3。为了统一描述旋转、振动和旋转对准的单准粒子模式，我们在变形基向量的基础上建立了“旋转壳模型+ RPA +准粒子-振动-旋转耦合模型”。利用该模型，我们研究了超高自旋态准粒子旋转带的超变形、配对相变和E2-M1相变的异常。为了处理软变形效应，我们将玻色子映射方法推广到能够重归一化高阶耦合效应，并将其应用于不明确摆动运动的描述。除此之外，我们还成功地开发了量子力学中角动量耦合代数处理的计算机程序。这些程序将在量子物理的许多领域非常有用。

The purpose of the present project is to establish the theoretical framework to renormalize the kinematical and dynamical anharmonicity effects in the yrast region of medium-heavy nuclei, and to analyze the collective motions in both the low and high spin states using this theory.As approaches from the side of low-spin region,1. We analyzed the collective motions in the low-spin region by using the Dyson boson mapping method on the basis of spherical basis vectors.2. We established the theory of the Dyson-type self-consistent-collective-coordinate method, which is, so to say, a dynamical boson expansion theory to renormalize non-linear coupling effects into collective coordinates. Using this theory, we analyzed the shape transition phenomena in the Sm isotopes.As approaches from the side of high-spin region,3. to make a unified description of rotation, vibration and rotation-aligned single-quasiparticle mode, we established a "rotating shell model + RPA + quasiparticle-vibration-rotation coupling model" on the basis of deformed basis vectors.Using this model, we investigated the super-deformed rotational bands, pairing phase transitions, and anomalies of E2-M1 transitions in the quasiparticle-rotation bands in the very high spin states.In order to treat soft-deformation effects, we generalized the boson mapping method to be capable to renormalize higher-order coupling effects, and applied it to the description of unclear wobbling motion.In addition to these, we were successful to develop the computer programs for algebraic manipulation of angular momentum coupling in quantum mechanics. These programs would be very useful in the many fields of quantum physics.