Total cross sections for electron scattering from fluoromethanes: A revised additivity rule method

The additivity rule for electron-molecule scattering is revised by considering the difference between the free atom and the bound atom in the molecule.The total cross sections for electron scattering from fluoromethanes(CF4,CF3H,CF2H2,and CFH3) are calculated in an energy range from 100 eV to 1500 eV by the revised additivity rule.The present calculations are compared with the original additivity rule results and the available experimental data.Better agreement with each other is obtained.     

Classical Description of Intense Field Stabilization Dynamics of 1D Model Atom

Abstract In this paper classical nonlinear dynamics approaches are used to study the intense field stabilization (IFS) for ID model atom according to differential equation (DE) and map approximation (MA). The exact stability boundary and region of I-period fixed points in the parameter space of field strength and frequency are obtained, and the results of MA are in excellent agreement with those of DE. The electrons dynamical behavior in phase space is investigated and the IFS mainly occurring in high frequency regime is confirmed. The stabilization phenomenon connected with the stable fixed points is also examined. In particular it is shown that this phenomenon depends on tightly the KAM tori. It can be predicted that the stabilization probability is just the fraction of initial electrons confined by the KAM tori.     

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.     

Additivity rule for electron--molecule total cross section calculations at 50--5000eV: a new geometrical approach

Taking into consideration the changes of the geometric shielding effect in a molecule as the energy of incident electrons varies, this paper presents an empirical fraction, which depends on the energy of incident electrons, the target＇s molecular dimension and the atomic and electronic numbers in the molecule. Using this empirical fraction, it proposes a new formulation of the additivity rule. Employing the new additivity rule, it calculates the total cross sections of electron scattering by C2H4, C6H6, C6H14 and C8H18 over the energy range from 50 to 5000eV. In order to exclude the calculation deviations caused by solving the radial Schrodinger equation of electron scattering by atoms, here the atomic cross sections are derived from the experimental total cross section results of simple molecules （H2, O2, CO） via the inversion algorithm. The quantitative total cross sections are compared with those obtained by experiments and other theories, and good agreement is obtained over a wide energy range, even at energy of several tens of eV.     

一种考虑几何屏蔽效应的计算“电子-分子”散射总截面的可加性规则修正方法

在考虑分子内原子间的几何屏蔽效应随电子入射能量变化的基础上, 提出了一种能够在中、高能区准确计算“电子-分子”散射总截面的可加性规则修正方法. 利用这一修正后的可加性规则并使用“电子-C, H, O, N原子”散射总截面的实验数据, 在50—5000 eV内计算了电子被NO, N₂O, NO₂和C₂H₆分子散射的总截面, 且将计算结果与实验结果及其他理论结果进行了比较. 结果表明, 利用这一方法修正过的可加性规则进行计 关键词： 电子散射 可加性规则 总截面 几何屏蔽效应     

Additive Invariant Functionals for Dynamical Systems

We consider the problem of defining completely a class of additive conservation laws for the generalized Liouville equation whose characteristics are given by an arbitrary system of first-order ordinary differential equations. We first show that if the conservation law, a time-invariant functional, is additive on functions having disjoint compact support in phase space, then it is represented by an integral over phase space of a kernel which is a function of the solution to the Liouville equation. Then we use the fact that in classical mechanics phase space is usually a direct product of physical space and velocity space (Newtonian systems). We prove that for such systems the aforementioned representation of the invariant functionals will hold for conservation laws which are additive only in physical space; i.e., additivity in physical space automatically implies additivity in the whole phase space. We extend the results to include non-degenerate Hamiltonian systems, and, more generally, to include both conservative and dissipative dynamical systems. Some applications of the results are discussed.     

Absolute differential, elastic integrated and moment transfer cross sections for electron--OCS collisions at intermediate and high energies

A complex optical model potential modified by incorporating the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds between atoms in a molecule, is firstly employed to calculate the absolute differential, elastic integrated and moment transfer cross sections for electron scattering by OCS over the incident energy range from 200 to 1000\,eV using the additivity rule model at Hartree--Fock level. The calculated results are compared with those obtained by experiment and other theories wherever available, and good agreement is obtained over a wide energy range. It is shown that the additivity rule model together with the modified potential is completely suitable for calculating the absolute differential, elastic integrated and moment transfer cross sections of electron scattering by molecules such as OCS.     

中高能正电子被CO，HCl，NH3及SiH4散射的总截面

利用可加性规则，使用Hartree-Fock波函数，采用由束缚原子概念修正过的复光学势(由静电势、极化势及吸收势三部分组成)，在30—3000eV内对正电子被CO，HCl，NH₃和SiH₄散射的总截面进行了计算，且将计算结果与实验结果及其他理论计算结果进行了比较.结果表明，利用被束缚原子概念修正过的复光学势及可加性规则进行计算，所得结果与实验结果的符合程度要比利用未被束缚原子概念修正的复光学势及可加性规则进行计算得到的结果好很多.因此，在复光学势中采用束缚原子概念可提高正电子被分子散射的总截面的计算准确度. 关键词： 正电子散射 可加性规则 束缚原子 总截面     

Free energy of multiple overlapping chains

How accurate is pair additivity in describing interactions between soft polymer-based nanoparticles? Using numerical simulations we compute the free energy cost required to overlap multiple chains in the same region of space, and provide a quantitative measure of the effectiveness of pair additivity as a function of chain number and length. Our data suggest that pair additivity can indeed become quite inadequate as the chain density in the overlapping region increases. We also show that even a scaling theory based on polymer confinement can only partially account for the complexity of the problem. In fact, we unveil and characterize an isotropic to star-polymer crossover taking place for large number of chains, and propose a revised scaling theory that better captures the physics of the problem.     

30-3000eV的正电子被O2、H2O及CH4散射的总截面计算

使用可加性规则，在Hartree-Fock水平上计算了30-3000eV的正电子被三个分子（O2、H2O及CH4）散射的总截面。计算正电子被三个分子散射的总截面时，首次使用了被束缚原子概念修正过的复光学势（这一复光学势考虑了分子中两个原子间的电子云重叠效应）。将正电子被这三个分子散射的总截面计算结果与实验结果及其它理论计算结果进行了比较，结果显示出在30-3000eV内，文中的计算结果与实验结果及其它理论计算结果具有较好的一致性。因此，可加性规则与修正后的复光学势相结合，完全适用于正电子被分子散射的总截面的计算。     

中、高能电子被SO2分子散射的微分截面、动量转移截面及弹性积分截面

在考虑分子内成键原子间的电子云重叠效应的基础上, 提出了一种能够准确计算“中、高能电子-分子”散射的微分截面、动量转移截面及弹性积分截面的修正势方法. 利用可加性规则、使用Hartree-Fock波函数并采用被这一方法修正过的复光学势, 在100—1000eV内对电子被SO₂分子散射的微分截面、动量转移截面及弹性积分截面进行了计算, 并将计算结果与实验及其他理论结果进行比较. 结果表明, 利用这一修正过的复光学势及可加性规则获得的微分截面比利用未修正的复光学势及可加性规则得到的结果准 关键词： 可加性规则 微分截面 动量转移截面 电子散射     

中高能电子被甲烷及氯代甲烷散射的总截面

利用可加性规则，使用HartreeFock波函数，采用由束缚原子概念修正过的复光学势（由静 电势、交换势、修正极化势及吸收势这四部分组成），在较大的能量(30—5000eV)范围内对 电子被甲烷及氯代甲烷（CH₄，CCl₄，CHCl₃，CH₂Cl₂和CH ₃Cl）散射的总截面进行了计算，且将计算结果与实验结果及其他理论计算 结果进行 了比较.结果表明，利用被束缚原子概念修正过的复光学势及可加性规则进行计算，所得结 果的精度要比利用未被束缚原子概念修正的复光学势及可加性规则进行计算得到的结果好很 多.因此，在复光学势中采用束缚原子概念可提高电子被分子散射的总截面的计算准确度. 关键词： 电子散射 可加性规则 束缚原子 总截面     

Local charge compensation in the quark-cascade jet-production model

The charge correlations and the local charge compensation mechanism in rapidity space for quark jets are analysed in the framework of the quark-cascade jet-production model. The calculated results are compared with those observed experimentally in antineutrino-nucleon processes, and for the short range charge correlations observed ine ⁺ e ⁻ annihilation experiments. The results appear consistent with the quark-cascade model. The treatment of Snider (1975) is essentially based on Chew and Pignotti (1968). Pinskyet al (1973) showed the similarity of multiperipheral and Muller-Regge concepts.     

Scattering of e± from N2 in the energy range 1 eV–10 keV

The differential, integrated elastic, inelastic, total, momentum transfer, viscosity, and ionisation cross sections for electron and positron scattering from the homonuclear diatomic nitrogen molecule over an incident energy range of 1?eV–10?keV are calculated using the additivity rule. Dirac partial wave analysis is employed to calculate the cross sections of the constituent atoms of molecules, using a complex optical model potential (OPM). Comparison of our results of the additivity rule with the available experimental data and other theoretical predictions is presented. Our findings produce reasonable results in intermediate and high energies.     

一种计算中、高能电子被分子散射总截面的修正势方法

在考虑分子内成键原子间的电子云重叠效应的基础上，提出了一种能够在中、高能区准确计算“电子-分子”散射总截面的修正势方法.利用可加性规则及Hartree-Fock波函数，使用这一修正过的复光学势，在30—5000eV内对电子被4个等电子(Z=18)分子(HCl，H₂S，PH₃和SiH₄)散射的总截面进行了计算，并将理论计算值与实验结果及其他理论值进行了比较.结果表明，利用这一修正过的复光学势及可加性规则进行计算，所得理论值与实验结果更为接近. 关键词： 电子散射 总截面 可加性规则 束缚原子     

深度非弹性散射中QCD-瞬子末态的熵及热平衡性质

在蒙特-卡洛产生器 QCDINS 产生的瞬子参与的e-P深度非弹性散射事件中,用$r$ 排序法得到瞬子末态和喷注样本。研究了 R\'enyi熵$H_2$在快度空间中的标度性和相加性。在瞬子末态中观察到了 $H_2$ 随着相空间尺度的减小展现出来的渐进标度性。相比之下,喷注的$H_2$在相空间尺度减小时呈现出饱和趋势。而且,在瞬子末态中还观察到在不同快度位置的窄窗口中$H_2$的相加性很好地成立。这些结果表明,在瞬子参与的深度非弹性散射中的瞬子末态达到了局域平衡。     

Scaling Equation for Invariant Measure

An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.     

Charged-particle multiplicity distributions in different rapidity windows in 800 GeV proton-nucleus interactions

Multiplicity distributions of charged particles produced in interactions of 800 GeV protons with emulsion nuclei in various rapidity windows are presented. The data is also analyzed separately for the forward and the backward hemispheres, for rapidity windows of different widths. It is found that the Negative Binomial Distribution (NBD) describes well the multiplicity distribution of secondary particles in various rapidity windows and also in both the hemispheres. We have compared the NBD parameters, in both the hemispheres, at 200 GeV and 360 GeV, with those at 800 GeV. The behaviour of NBD parameters in rapidity windows of different widths and for different targets has also been studied. Received: 30 August 2001 / Accepted: 28 January 2002     

The Structure of State Space with Respect to Imbedding

The entanglement of formation as well as the conditional entropy can be used to define leaves in the state space, given by the linear superposition of their extremal points. Examples, where these leaves can be found and can be used to calculate the entanglement respectively the conditional entropy are presented. The definition of entanglement is generalized to infinite systems and allows again to find a leaf structure. Finally we remark on the additivity property of both expressions, offering a counter example to the additivity of the conditional entropy.     

Dynamic shadow effect in the energy loss of protons

Summary The nonrelativistic quantum-mechanical approach for the stopping power has been developed by means of the Glauber-Franco approximation for the inelastic-scattering amplitude. It takes into account excitation and ionization processes in the amorphous target by heavy charged particles. The calculations of the stopping power of protons in H and He targets are in excellent agreement with the available experimental data due to the effect of nuclear dynamic blocking (shadow) and the rescattering processes by the electrons of the target atom. Formulae of the stopping-power calculations, taking into account individual atom shell effects, have been derived. On this basis, the case of violation of Bragg’s additivity rule is discussed.