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Particle correlation of novel quantum states

新型量子态的粒子关联

基本信息

批准号：
10440120
负责人：
MATSUZAWA Michio
金额：
$ 4.86万
依托单位：
The University of Electro-Communications
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

Employing the approach of hyperspherical coordinates, we investigate particle correlations of novel quantum states of Coulomb three-body system including exotic particles. The hyperspherical approach is based on the adiabatic approximation as hyper radius which measures the size of the systems is treated as an adiabatic parameter. Electron correlation is investigated in the model electron-impact problem in which the target hydrogen atom interacts with the incident electron only by monopole. It is found that the threshold law shows an exponential form related to the local instability of the ridge motion. This approach is also extended to electron-impact ionization of the collinear Z=1/4 model atom. Slightly above the ionization limit, ab initio calculation reveals a distinct dip due to the short-range dynamics. In the middle of 1990, the hyperspherical elliptic (HSE) coordinates was introduced which is suitable for treating the Coulomb three body systems with arbitrary mass ratios. At first, HSE harmonics are investigated which are the eigenfunctions of the generalized angular operator by separating the variables in the HSE coordinates. This harmonics are related to the Heun equation. An efficient method is developed to construct HSE harmonics for application for the Coulomb three body problems. An approximate symmetry of the Coulomb three body problemis is found which leads to the approximate separability of the hyperspherical adiabatic eigenvalue problem in HSE coordinates and to the set of HSE quantum numbers. This enables us to establish the rapidly convergent expansion of the HSE basis set and to get the highly reliable estimates of the energy levels for Coulomb three body systems. The conventional HS method is also applied to study electron correlation of triply excited states of atoms. Metastability of of atoms under the application of half cycle pulse is also studied based on the model of harmonic oscillator.

利用超球坐标方法，研究了含有奇异粒子的库仑三体系统新量子态的粒子关联。超球方法是基于绝热近似的超半径，它衡量的系统的大小被视为一个绝热参数。在电子碰撞模型中，靶氢原子与入射电子仅发生相互作用。结果表明，阈值规律与脊运动的局部不稳定性有关，呈指数形式。这种方法也被推广到共线Z=1/4模型原子的电子碰撞电离。稍高于电离极限，从头计算揭示了一个明显的下降，由于短程动力学。1990年中期，超球椭圆坐标（HSE）被引入，它适用于处理任意质量比的库仑三体系统。首先，通过分离HSE坐标中的变量，研究了广义角算符的本征函数HSE调和函数。这个谐波与Heun方程有关。提出了一种构造HSE调和函数的有效方法，并应用于库仑三体问题。本文发现库仑三体问题的一个近似对称性，从而得到超球绝热本征值问题在HSE坐标系下的近似可分性和HSE量子数集。这使我们能够建立HSE基组的快速收敛展开，并得到库仑三体系统能级的高度可靠的估计。本文还将传统的HS方法用于研究原子三重激发态的电子关联。基于谐振子模型，研究了半周期脉冲作用下原子的亚稳性。