核电荷分布对类氢原子基态能量计算的影响

在高斯型核电荷分布模型中,分别采用基于B样条的Notre Dame和Dual-Kinetic-Balance基组求解类氢体系的Dirac方程。通过对所得的基态能量和点电荷分布模型的结果以及实验测量值进行比较,发现核电荷分布效应对结果具有重要影响,其相对修正随原子序数Z的增加而逐渐显著。当Z=100时,相对修正能达到10^−3。并在近核区域给出了两种模型下计算的波函数。当Z增加时,波函数的差别也逐渐明显。不同于其他将B样条应用于电子与原子核的长程相互作用计算的工作,此工作成功地将B 样条方法推广到了短程相互作用的研究。     

核电荷分布对类氢原子基态能量计算的影响（英文）

在高斯型核电荷分布模型中,分别采用基于B样条的Notre Dame(ND)和Dual-Kinetic-Balance(DKB)基组求解类氢体系的Dirac方程.通过对所得的基态能量和点电荷分布模型的结果以及实验测量值进行比较,发现核电荷分布效应对结果具有重要影响,其相对修正随原子序数Z的增加而逐渐显著.当Z=100时,相对修正能达到10-3.并在近核区域给出了两种模型下计算的波函数.当Z增加时,波函数的差别也逐渐明显.不同于其他将B样条应用于电子与原子核的长程相互作用计算的工作,此工作成功地将B样条方法推广到了短程相互作用的研究.     

氢原子基态能量的简化计算

本文从氢原子的相对论能量和测不准关系出发，简化计算了氢原子的非相对论与相对论的基态能量，并和分别用精确的薛定谔理论与狄拉克理论计算的结果一致．     

高压类氢原子的能量与极化率计算

 为了探讨压力对类氢原子结构与性能的影响，本文采用类氢原子关闭在一半径为r₀的球壳内的模型，计算其能量与极化率随球壳半径r₀与相应压力的变化规律，给出了数值表和相应的曲线。     

类氢原子能级与轨道半径的计算

从氢原子的基本模型出发,归纳分析了几种类氢原子能级和轨道半径的计算方法.     

类氢原子椭圆轨道的动能、势能和能级

利用椭圆的几何性质确定类氢原子的轨道，并计算其能级。     

类氢氖基态电离势随等离子体温度密度的变化

采用自洽场离子球模型,研究类氢氖基态1s的电离势随等离子体电子温度及电子密度的变化规律,计算得到基态电离势的百分偏移量随等离子体电子密度的变化关系,拟合结果表明两者的对数值满足很好的线性关系.该结果对计算等离子体电离态分布及光谱模拟具有一定意义.     

高压类氢原子能量与极化率的另一种计算

 本文采用新的试探波函数，对于关闭在半径为r₀球壳内的类氢原子模型，计算了其能量和极化率随球壳半径r₀和相应压强的变化规律。同文献[1]的结果相比，有明显的改善。     

类Li与类Be离子基态能量的简便计算公式

由双参数变分法导出类Ｌｉ与类Ｒｅ离子基态能量近似计算公式，该公式计算简便且具有很高精度。     

类钠离子激发态能级的计算

本文采用HFS法计算了Na、Mg~ 、Al~( )的ls~(2-)2P~6nl(n≤14.l≤7)所有激发态的能级。发现能级的计算值和实验值的相对误差先是随n的增大而迅速减小,然后缓慢变化并趋于一个相当小的“稳定值”。根据这一规律可以更准确地预言未知的较高能级值。     

相邻类氢离子电离能关系的研究

根据类氢离子电离能的实验值和相邻元素电离能的相关约束方程,定量地建立了各元素类氢离子电离能与核电荷数的较为精确的递推关系.其推算结果与实验值的相对误差小于0.001%,与相对论自洽场方法计算的结果相比,其相对误差也小于0.001%.     

Influence of the image charge effect on the hydrogen-like impurity-bound polaron in a spherical quantum dot in the presence of an electric field

We have investigated the influence of an external electric field on the binding energies and polaronic shifts of the ground and some first few excited states of a hydrogenic impurity in a spherical quantum dot by taking into account the image charge effect. By using Landau–Pekar variational method the general analytical expression is obtained for the impurity bound-polaron energies. It has been numerically identified the conditions (electric field, nominal radius of quantum dot, etc.) in which the bound-polaron states can be existence in GaAs quantum dot. We have shown that the polaronic shifts in the binding energy of 1s-like state are the same in cases with and without image charge effect while they for 2s-like state are not coincide and have different monotonic behavior versus confinement potential. Electron–phonon interaction lifts the degeneracy of the 2px-, 2py-, and 2pz-like states of a donor impurity and reduces their binding energies.     

Probabilistic calculations on the ground state of the harmonic oscillator

A comparison is made between the approaches of Nelson and of Lewis and Davies to quantum probability, using calculations made on the harmonic oscillator. Calculation of the joint distribution of position shows an expected difference in the approaches. The time the particle takes to hit an absorbing counter put in the system is calculated to first order, in both theories, and the results again differ.     

等离子体屏蔽效应对Ar~(16+)基态和激发态能级的影响

基于Rayleigh-Ritz变分原理,发展了一套处理弱耦合等离子体环境中多电子原子(离子)非相对论能量及其相对论修正的解析方法.通过考虑电子间交换相互作用以及内外壳层电子的屏蔽效应,计算了Ar~(16+)基态1s~2~1S、单激发态1sns~(1,3)S (n=2—5), 1snp~(1,3)P (n=2—5)和双激发态2snp~1P (n=2—5)非相对论能量及其相对论修正值(包括质量修正、单体和双体达尔文修正以及自旋-自旋接触相互作用项),讨论了等离子体屏蔽效应对能级的影响.结果表明:相对论质量修正和第一类达尔文修正占主导,比其他相对论修正项高出三个数量级.此外,等离子体屏蔽效应具有明显的态选择性,屏蔽效应对外壳层电子的影响大于内壳层电子,随着等离子体屏蔽参数的增加,外壳层电子轨道向外延展,激发态越高,延展程度越大.     

德拜势中类氢原子能级近似解析式与幂级数求解

对德拜势(Debye)中类氢原子的能级问题采用Rayleigh-Schrdinger微扰展开,给出了能级的一阶修正与原子能级的近似解析式.同时,采用波函数幂级数解法,求得了德拜势下相关的递推关系.在此基础上,利用能量自洽法,求出了相当于二阶修正的德拜势下类氢原子的能级值,并就其计算结果与数值解进行了比较.同时,讨论了相应的临界束缚能态与截断条件.     

The influence of Debye plasma on the ground state energies of exotic systems

The effect of plasma environment on the ground state energies of exotic systems ppμ, ddμ and ttμ has been analyzed within a generalized three-body formalism using multi-term correlated basis sets. The Debye screening model of the plasma has been adopted for such a study. The binding energies of p with pμ, d with dμ and t with tμ have been estimated for a range of values of the Debye screening parameters. The systems tend toward instability for increased screening. The effect of particle correlation has been investigated in detail and is found to play an important role for the stability in these systems.     

A set of inequalities between the ground state energies of many-body systems

The energy E_N of a system of N identical pairwise-interacting particles of mass M is shown to satisfy the inequalities

where N > n ? 2. These inequalities generalize the Stenschke result E ₃(M) ? 3E ₂(3M/2). They hold for Bose or Fermi systems in any number of dimensions, and are shown to be the strongest possible of this type. Further extensions are made to the case where the potential is varied instead of the mass, or where both are varied together.     

Electric-field effect on shallow impurity ground state in nanowire superlattice

We have developed a variational formalism to analyze the effect of electric field on the donor ground state in a nanowire superlattice with cylindrical cross-section. The trial function is taken as a product of the free-electron ground state wave function with an envelope function that is a solution of a differential equation arising from the Schrödinger variational principle. We establish a close relationship between the donor ground state energy and density of charge induced by the unbound electron at the point of donor location. Also, we show that electric field applied along the crystal growth direction can easily shift the peak position of the free-electron density distribution from the central well toward one of the nanowire ends, providing a variation of the average electron-ion separation and a considerable alteration of the donor ground state energy.     

Impurities potential effect on the charge density wave dynamics in one-dimensional systems

In this work, we present in the weak pinning case the numerical simulation results of the one-dimensional deformable charge density wave (CDW) properties considering the potential amplitude fluctuations effect generated by different impurity types randomly distributed in the lattice. When the electric field approaches threshold value ET, the static equilibrium characteristic time τ and the polarization PCDW become large and seem to diverge at critical field Ecr from below ET following a power law [1−(E/Ecr)]^−α where α is an impurity dependant critical exponent. This divergence indicates that the CDW depinning can be described in terms of a dynamical critical phenomena, where the critical field Ecr plays the role of a transition temperature as in ordinary phase transitions. In agreement with several experimental results, we show that the electric current density JCDW and electric conductivity σCDW follow respectively a power law β[(E/ET)−1] and (ET/E)ν[(E/ET)−1] where β and ν are critical exponents. This results are analogous to these obtained in the case of one impurity type.