氦原子基态能量的Hylleraas变分计算

本文给出了基于Hylleraas波函数变分计算氦原子基态非相对论能量的详细过程,得到了含参数的基态能量表达式,并编写了相应的Mathematica程序来完成变分,计算所得的基态能量的理论值和实验数据符合得很好,误差小于0.04‰.由于计算过程直观简单,在教学过程中亦可采用.     

氦原子基态能量的Roothaan-Hartree-Fock计算

采用包含两个斯莱特基的"双ζ"函数说明了利用自洽场法求解基态氦原子Roothaan-Hartree-Fock方程的数值过程,计算得基态能量为-2.862 568 Hartree.利用基态的对称性,提出了通过求解泊松方程来计算库仑算符的方法,给出了交叠矩阵和单电子算符的矩阵元,并对自洽的标准作了讨论.     

氦原子基态的斯塔克效应

用微扰与变分相结合的方法计算了氦原子基态的斯塔克效应，通过计算发现这种方法简便直观，尤其适用于低激发态且电子数不太多的原子．     

四参数法计算氦原子基态能级研究

在求解氦原子径向Schr dinger方程时,设计了含有四参数的基态波函数,推导出含有四参数的氦原子基态能级表达式,分别采用Matlab 7.0最优化运算和Monte-Carlo法,计算了氦原子的基态能量,得到了相应的波函数.将计算结果与其它文献采用变分法所得计算值及实验值进行了比较,结果表明:这种方法不仅计算简便有效,准确性较高,而且所得氦原子基态空间波函数自动满足空间对称性的要求.     

氦原子低激发态的精细结构

利用变分法得到的氦原子低激发态1s2p能级的波函数，在考虑在氦原子自旋轨道相互作用的情况下，计算出1s2p能级的精细结构，与实验值比较，较为接近。     

氦原子及类氦离子基态能量的经验公式

通过对氦原子和类氦离子电离能数据的分析 ,找到了一个能够快速计算类氦体系基态能量的经验公式 ,验算了一些类氦离子 (Z=2— 1 5 )的基态能量 ,与实验测量值符合得很好。除了 Li 和 Be 的基态能量的相对偏差为 0 .4 46 %外 ,其他的都低于 0 .4 %。     

氦原子基态能量的组态相互作用计算

将基态氦原子的波函数取作1s2和1s2s两个组态函数的叠加,利用组态相互作用方法解析计算了氦原子基态的非相对论能量.计算结果表明,考虑激发态1s2s与基态的相互作用,可以获得0.029 38Hartree的基态能量修正.本文的解析组态相互作用方法可作为量子力学教学的有益补充.     

氩原子基态波函数和能量的解析计算

以第一性原理和变分原理为基础,给出了氩原子基态波函数的一种解析表达式,计算了基态氩原子(含类氩离子)的能量,导出了所涉及的所有积分的解析表达式.对氩原子,所得到的能量理论值与实验值的相对误差为0.22%.     

The effect of Coulomb interaction on particle-antiparticle correlation function

正Dear Editors,The quantitative interpretation of the particle and antiparticle correlation results depends critically on understanding the role of Coulomb interaction of the measured pairs of particles with each other,as well as the Coulomb interaction of the pair with the system of remaining particles[1-7].The     

The ground state energy of a Bose gas with Coulomb interaction

LetH _N be the 2N particle Hamiltonian $$\begin{array}{*{20}c} {H_N = \sum\limits_{i = 1}^{2N} {( - \Delta _\iota ) + \sum\limits_{i< j = 1}^N {\left| {x_i - x_j } \right|^{ - 1} + } \sum\limits_{i< j = 1}^N {\left| {x_{i + N} - x_{j + N} } \right|^{ - 1} } } } \\ { - \sum\limits_{i,j< j = 1}^N {\left| {x_i - x_{j + N} } \right|^{ - 1} ,} } \\ \end{array} $$ whereΔ _i is the Laplacian in the variablex _i ∈?³, 1≦i≦2N. The operatorH _N is assumed to act on wave functionsΨ(x ₁, ...,x _N ;x _N+1, ...,x _2N ) which are symmetric in the variables (x ₁, ...,x _N ) and (x _N+1, ...,x _2N ). SupposeΨ is supported in a setΛ ^2N , whereΛ is a cube in ?³. It is shown that if a normalized wave functionΨ can be written as a product of two wave functions $$\psi (x_1 ,...,x_N ;x_{N + 1} ,...,x_{2N} ) = \psi _1 (x_2 ,...,x_N )\psi _2 (x_{N + 1} ,...,x_{2N} ),$$ and the density of particles inΛ is constant, then 〈Ψ|H _N |Ψ〉≧?CN ^7/5 for some universal constantC.     

The ground state energy of a Bose gas with Coulomb interaction II

LetH _N be the quantum mechanical Hamiltonian for a neutral system of 2_N charged particles, each of unit charge. The HamiltonianH _N is assumed to act on wave functions inL ²(^6N ) which satisfy Bose statistics. It is shown that if the kinetic energy of is sufficiently small, then |H _N |–CN ^7/5 for some universal constantC.Research supported by U.S. National Science Foundation Grant DMS 8600748     

On the F-center ground state wave function

We present a type of isotropic envelope for the F-center ground state wave function, suggested by ENDOR experimental data. We discuss it within a moment analysis of the experimental F-absorption spectrum.     

Radial correlation of the helium atom in the ground state

An expression for the binding energies of electrons in the ground state of an atom is derived on the basis of the Bohr–Sommerfeld quantization rule within the Thomas–Fermi model. The validity of this relation for all elements from neon to uranium is tested within a more perfect quantum-mechanical model with and without the inclusion of relativistic effects, as well as with experimental binding energies. As a result, the ordering of electronic levels in filled atomic shells is established, manifested in an approximate atomic-number similarity. It is proposed to use this scaling property to analytically estimate the binding energies of electrons in an arbitrary atom.     

PuCO基态分子的结构与势能函数

在相对论有效原子实势近似下,用B3LYP密度泛函方法计算优化出PuCO分子基态的结构参数,离解能和力常数.用多体项展式方法导出PuCO分子基态(AX～G67A″)的分析势能函数,获得的势能面正确地复现出PuCO分子的平衡结构特征.     

PdPbH分子的结构与势能函数

在相对论有效原子实势近似下,用密度泛函理论的B3LYP方法,对钯和铅采用LANL2DZ基函数,氢原子采用6-311 G**全电子基函数,对PdPb、PdPbH分子的结构进行优化.计算表明:PdPb分子的基态为X1∑ ,键长RPdPb=0.24536 nm,离解后Pd原子处于基态(单重态)而Pb原子处于激发态(单重态),离解能为3.107686 eV,引入开关函数拟合得到Murrell-Sorbie势能函数;PdPbH分子最稳态为Cs构型,电子组态为X2A′,键长RPdPb=0.2547 nm,RPdh=0.15919 nm,键角∠PbPdH=64.7856°,离解能De=4.79 eV.由微观过程的可逆性原理分析了分子的可能离解极限,并用多体项展开式理论方法分别导出基态PdPb和PdPbH分子的势能函数,其等值势能面图准确的再现了PdPb和PdPbH分子的结构特征和离解能,由此讨论了Pd Pb H分子反应的势能面静态特征.     

Wave packet theory of Coulomb scattering

Potential scattering in a Coulomb field is treated in a wave packet formalism. The Rutherford law is derived from the off energy shell CoulombT-matrix avoiding the usual divergencies due to the long range Coulomb potential.