Particle correlation of novel quantum states

利用超球坐标的方法，研究了含外来粒子的库仑三体系统新量子态的粒子关联。超球面方法是基于绝热近似，而测量系统大小的超半径被视为绝热参数。研究了目标氢原子仅通过单极子与入射电子相互作用的模型电子碰撞问题中的电子关联。研究发现，与脊运动的局部失稳有关的阈值律呈指数形式。这种方法也推广到共线Z=1/4模型原子的电子碰撞电离。略高于电离极限，从头算出一个明显的下降，由于短程动力学。1990年中期，引入了适用于处理任意质量比的库仑三体系统的超球椭圆坐标（HSE）。首先，通过分离HSE坐标中的变量，研究了广义角算子的特征函数HSE谐波。这个谐波与Heun方程有关。针对库仑三体问题，提出了一种构造HSE谐波的有效方法。发现了库仑三体问题的近似对称性，从而得到了超球面绝热特征值问题在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基集的快速收敛扩展，并获得库仑三体系统的高度可靠的能级估计。传统的HS方法也被用于研究原子三激发态的电子相关。在谐振子模型的基础上，研究了半周脉冲作用下原子的亚稳态。

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.