Transport coefficients for deeply inelastic scattering from the Feynman path integral method

Friction and diffusion coefficients can be derived simply by combining statistical arguments with the Feynman path integral method. A transport equation for Feynman's influence functional is obtained, and transport coefficients are deduced from it. The expressions are discussed in the limits of weak, and of strong coupling.     

New framework for the Feynman path integral

The well-known Fourier integral solution of the free diffusion equation in an arbitrary Euclidean space is reduced to Feynmannian integrals using the method partly contained in the formulation of the Fresnelian integral. By replacing the standard Hilbert space underlying the present mathematical formulation of the Feynman path integral by a new Hilbert space, the space of classical paths on the tangent bundle to the Euclidean space (and more general to an arbitrary Riemannian manifold) equipped with a natural inner product, we show that our Feynmannian integral is in better agreement with the qualitative features of the original Feynman path integral than the previous formulations of the integral.     

Absolute electron scattering cross sections for the CF2 radical

Using a crossed electron-molecular beam experiment, featuring a skimmed nozzle beam with pyrolytic radical production, absolute elastic cross sections for electron scattering from the CF2 molecule have been measured. A new technique for placing measured cross sections on an absolute scale is used for molecular beams produced as skimmed supersonic jets. Absolute differential cross sections for CF2 are reported for incident electron energies of 30-50 eV and over an angular range of 20-135 deg. Integral cross sections are subsequently derived from those data. The present data are compared to new theoretical predictions for the differential and integral scattering cross sections, as calculated with the Schwinger multichannel variational method using the static-exchange and static-exchange plus polarization approximations.     

Total cross sections for electron scattering from sulfur compounds

The original additivity rule method cannot give good results for electron scattering from SO,SO2,SO2Cl2,SO2ClF,and SO2F2 molecules at low energy,because the electron-molecule scattering is simply reduced to electron-atom scattering.Considering the difference between the bound atom in a molecule and the corresponding free atom,the original additivity rule is revised.With the revised additivity rule,the total cross sections for electron scattering from these molecules are calculated over a wide energy range below 3000 eV and compared with the available experimental and theoretical data.A better agreement between them is obtained.     

Total electron scattering cross sections for carbon dioxide at low electron energies

Absolute total electron scattering cross sections for carbon dioxide have been measured at low electron energies using a photoelectron source. The measurements have been carried out at 27 electron energies varying from 0.91–9.14 eV with an accuracy of ±3%. The cross sections obtained in the present experiment have been compared with other measurements and theoretical computations.     

On the calculation of scattering cross sections from absorption cross sections

A dispersion-type relation between photon scattering and absorption cross sections is derived. It is shown that the relation gives the correct scattering cross section in the low and high frequency limits, and is consistent with the Kramers-Heisenberg formula in the vicinity of a resonance. The practical application of the relation is illustrated by calculations of the scattering cross section and refractive index of He and Ne at STP and dry air at 1200°K from known absorption cross section data. The method is useful for obtaining scattering cross sections, polarizabilities, and refractive indices at elevated temperatures.     

Logarithmically accurate total cross sections of fast electron scattering by atoms

A simple analytical formula for the total integrated cross section of fast electron scattering by atoms is obtained. This formula, being logarithmically accurate, is derived from the approximate rule of sum that does not take into account exchange effects in the atomic wave function (Hartree approximation). It is shown that exchange effects can be neglected in that scattered electron energy range where the first Born approximation is valid. The results of calculation for He, Ne, and Ar atoms agree well with experimental data.     

Feynman path integral and ordering rules on discrete finite space

The Feynman path integral is constructed for systems whose configuration space is a discrete finite set. The construction is based on the operator formulation of quantum mechanics on a finite discrete space. We derive connections between operators and introduce the analogue of the^*-multiplication for discrete symbols.     

Total cross sections for electron scattering from well-known and exotic molecules

In this review paper, scattering of intermediate to high energy electrons on well-known as well as exotic molecular targets is considered. The ‘additivity rule’ and its modifications for calculating various total cross sections are discussed against the background of an extensive experimental data. The theory succeeds at high impact energies (E _i>100 eV). Tentative upper and lower limits of e-molecule ionization cross sections are identified. Fitting formulas to represent total cross sections as functions of energy are also given.     

光子与相对论麦克斯韦分布电子散射截面的蒙特卡罗计算方法

高温全电离等离子体的辐射输运问题中,光子与电子的Compton散射与逆Compton散射是其中重要的特性,光子与相对论麦克斯韦电子散射的描述及截面的计算非常复杂且费时.本文提出了一种用于模拟计算光子与相对论麦克斯韦速度分布电子散射截面的蒙特卡罗计算方法.给出了各步骤的具体实现办法,推导了对应的计算公式,研究了相对论电子速率抽样方法,编写了光子与相对论电子散射的微观截面的蒙特卡罗计算程序.开展了高温全电离等离子体中,不同能量光子与不同温度电子散射的微观散射截面计算和分析.模拟计算结果显示,在电子温度低于25 keV情况下,本文方法与多重数值积分方法的计算结果非常接近;但随着电子温度继续升高,二者差异逐渐增大并较明显,经分析,可能是本文方法目前的电子速率抽样偏差所致,希望将来能够找到更好的相对论电子速率抽样方法以克服此缺陷.     

低能电子与氮分子碰撞振动激发动量迁移截面的研究

采用作者改进的振动密耦合方法和基于量子力学从头计算的静电势、交换势、相关极化势,研究了低能电子与N₂振动激发散射动量迁移截面. 计算结果与试验符合较好. 关键词： 动量迁移截面 低能电子 分子碰撞 振动激发     

运用球高斯分布极化势研究低能电子与H2 分子碰撞的振动激发动量迁移散射截面

用最近改进的球高斯分布(distributed spherical Gaussian,DSG)极化势模型,在振动密耦合框架下和基于量子力学从头计算的静电势、交换势的基础上,研究了低能电子与H₂分子碰撞振动激发的动量迁移散射截面(momentum transfer cross section,MTCS).通过包含18个振动波函数、5个分波和16个分子对称性,得到了0<E≤10 eV时收敛性很好的ν=0→ν'=0,1,2,3等几个振动跃迁通道和总的MTCS,并与其他实验和理论得到的值进行了比较和分析. 关键词： 2分子碰撞')" href="#">H₂分子碰撞 动量迁移散射截面 振动激发 球高斯分布极化势     

Target-spin effects on elastic scattering cross sections

It is shown, using a simple model and empirical results, that the odd-even differences in the scattering of He ions from ⁵⁹Co and ⁶⁰Ni can be explained as due to the scattering from the quadrupole moment which is allowed for the odd target nucleus but not the even.     

Differential cross sections for electron scattering by polar molecules. Elastic scattering and vibrational excitation

By use of the effective range theory for electron scattering by polar molecules differential cross sections for elastic scattering by HCN and LiF molecules and for vibrational excitation of water molecules are calculated.     

低能电子与N2分子碰撞的振动共振激发散射截面的密耦合研究

使用经孙卫国教授改进后的振动密耦合散射方法和基于量子力学从头计算得到的静电、交换与极化散射作用势,研究了低能电子与N2分子的振动激发散射截面.研究表明在振动密耦合计算中使用18个振动波函数和12个分波数目,可以得到收敛的0→5,1→5等高激发散射的积分和微分截面.     

A semi-empirical formula for total cross sections of electron scattering from diatomic molecules

A fitting formula based on the Born approximation is used to fit the total cross sections for electron scattering by diatomic molecules (CO, N₂, NO, O₂ and HCl) in the intermediate- and high-energy range. By analyzing the fitted parameters and the total cross sections, we found that the internuclear distance of the constituent atoms plays an important role in the e-diatomic molecule collision process. Thus a new semi-empirical formula has been obtained. There is no free parameter in the formula, and the dependence of the total cross sections on the internuclear distance has been reflected clearly. The total cross sections for electron scattering by CO, N₂, NO, O₂ and HCl have been calculated over an incident energy range of 10–4000 eV. The results agree well with other available experimental and calculation data.     

低能电子与H_2分子碰撞振动激发动量迁移散射截面的研究

采用振动密耦合方法及基于量子力学从头计算的静电势、交换势和相关极化势,研究了低能电子与H2分子碰撞振动激发的动量迁移散射截面.通过包含18个振动波函数、8个分波和16个分子对称性,得到了收敛性很好的ν=0→ν′=0,1,2,3,4等几个振动跃迁通道的动量迁移散射截面值,并在入射电子能量1eVE≤10eV时给出了比以前的理论研究更为合理的总的动量迁移散射截面.