In order to make the theoretical calculation feasible , we first obtain an analytical formalism of partial integrals with respect to the coordinates of the core and target in the phase - shift functions and their cross terms of scattering matrix elements , if the density distributions of the core and target are fitted to a few gaussian forms . then the rest multidimensional integrals with respect to the impact parameter and coordinates of halo nucleons are performed by a monte carlo method 为使理论计算变得可行，我们在核芯和靶核密度采用多个高斯分布拟合的情况下，解析求解了各个散射矩阵元中的光学相移函数及交叉项含有的与晕核核芯、靶核密度分布有关的积分;同时对与碰撞参数和晕核子坐标有关的积分(八重以上，并且积分维数随晕核子数很快增加)采用蒙特卡洛方法计算。
Abstract : the effect of correction of self - consistent potential on electronic structure in simple cubic nanocrystal particles is calculated by means of the green ' s function method in the tight - binding approximation , taking only the nearest neighbor matrix elements into account . the numerical results show that the electronic energy spectrum is shifted , the chemical potential is not equal to the atomic energy level , the electronic density at each lattice point is changed , and the variation of electronic density at surface lattice point is the largest 文摘:在紧束缚近似下，只计及最近邻的矩阵元，采用格林函数计算了自洽势修正对简立方纳米晶体颗粒的电子结构的影响，发现电子能谱发生了移动，化学势不等于格点原子能级，各格点的电子密度也发生了变化，其中以表面格点的电子密度变化最大。
Firstly , with the help of angular momentum coupling theory , the hamiltonian for multi - electron adorns is rewritten in terms of spherical tensors . the advantage of this form is that the radial , angular and spin parts are separated completely , which makes it easy to calculate the angular matrix elements by means of irreducible tensor . secondly , theoretical expressions of the relativistic corrections including the relativistic mass correction , the darwin correction terms , the electron - electron contact terms and the orbit - orbit interaction which contribute to the non - relativistic energy for two - electron atom are theoretically derived in the lsmlms scheme 具体内容包括：首先，借助角动量耦合理论，将多电子原子哈密顿算符中的自旋-自旋、自旋-其它轨道以及轨道-轨道相互作用全部改用球张量表示，这种球张量形式的优点在于已将原子哈密顿算符中的径向、角向和自旋部分完全分开，从而便于计算矩阵元，而且角向矩阵元可以方便地利用不可约张量理论来进行计算。
In a word , a new method that theoretically calculates the relativistic corrections and the fine structure of the energy levels in two - electron atom , including the atomic hamiltonian expressed by spherical tensors , the calculation of the angular matrix elements and the summations over spin of the various interactions in the atomic hamiltonian , and the approximate calculation of the radial matrix elements , has been provided in this thesis 总之，本文为双电子原子能级的相对论修正和精细结构的理论计算提供了一种新的方法，包括原子哈密顿算符的球张量表示方法、原子哈密顿中各种相互作用项的角向矩阵元和自旋求和的计算方法，以及径向矩阵元的近似计算方法
In this thesis , a semi - classical model of the force on an atom is used to describe the motion of a two - level atom interacting with a standing wave laser field . the velocity dependent force and momentum diffusion are derived through optical bloch equations by using the matrix form of the continued fraction technique . by investigating the dynamic properties of atoms in laser field , we can control and manipulate the mechanical motion of an atom 本文利用半经典理论，从二能级原子在激光驻波场中所满足的运动方程出发，推导出密度矩阵元所满足的递推关系，利用矩阵连分数方法求解出密度矩阵元，从而求出依赖于原子运动速度的光压力与动量扩散系数，通过讨论原子在激光场中的动力学行为，为原子在激光场中被囚禁、形成原子列阵以及可控制的量子态，从而为量子信息处理提供理论基础。
In this paper , the current states of research about the basic theory of stationary state perturbation method are firstly reviewed , on base of them , and studied some physics issues mainly about hydrogen atom . the stark effect of the energy level ( n = 4 ) of hydrogen atom is calculated and the stark effect of three dimensional hydrogen atom is discussed by the use of the parabolic coordinates , then the perturbative matrix elements for each energy level are given 本文首先综述了关于定态微扰论基本理论的研究现状，在此基础上利用定态微扰论对某些物理问题，主要是对氢原子问题展开了研究，计算了氢原子n = 4能级的斯塔克效应，并利用抛物线坐标法求解了三维氢原子的斯塔克效应，给出了氢原子斯塔克效应中微扰矩阵元的普遍公式。
