Electron scattering from nonlinear molecules using multicentre wavefunction expansions

Summary The scattering of slow electrons by polyatomic molecules is studied within a full quantum formulation of the problem, and the wavefunctions of the target molecular bound electrons are obtained from a multicentre expansion (MCE) of Gaussian-type orbitals (GTOs) within the single-determinant Hartree-Fock (HF)-SCF scheme. It is shown that the scattering calculations require the solution of radial coupled equations where the interaction is obtained as a further multipolar expansion at the target centre of mass (c.o.m.), while the relevant numerical procedures are discussed for systems like SiH₄, GeH₄ and CF₄. The ensuing interaction coefficients are used to carry out convergence studies of the scattering cross-sections, over a broad range of energies, in the case of silane targets. The results are found to be rapidly converging for such a system, while the different behaviour expected for other targets is also analysed and explained.     

Comments on the capture cross-section of electrons in silver bromide grains

The values in the range of 10⁻¹⁵ cm² to 10⁻¹⁴ cm² have been reported by various authors for the capture cross-section of electrons at the traps in silver bromide grains. In this paper we have given a suitable value of this cross-section which is used for computing the track characteristics in nuclear emulsions (e.g. effective ionization, probability of development, grain density and mean gap length) and the ratio of the rate constant of recombination and trapping. Theoretical results agree well with the experimental observations and the available data of other workers and give a convincing support to our choice of this cross-section parameter.     

一类二阶线性变系数常微分方程的常系数化解法

利用线性方程对自变量的变换以及对未知函数的线性变换的不变性，导出一类二阶线性变系数常微分方程系数化的充要条件及所需的变换，给出求这类方程的显示解的简便方法。     

关于多电子体系的投影算符的注记

按照群论方法对多电子体系的对称化投影算符进行了讨论，并用投影算符和升降算符推出多电子的自旋态。     

Multistability in the laser cooling of atomic beams

Summary We describe the interaction of a beam of two-level atoms with multiple laser beams propagating in the opposite direction. The lasers are frequency-chirped in order to remain close to resonance and they continuously decelerate the atoms by radiation pressure. In a deterministic treatment, the average atomic velocity exhibits multistability cycles as a function of the chirping rate. A statistical (Fokker-Planck) treatment shows the corresponding splitting of the atomic velocity distribution into well-separate, quasi-monokinetic bunches of atoms. In the laboratory reference frame, multistability shows up through the increasingly decelerated motion of these atomic bunches. Analytical results are presented, as well as numerical simulations for a beam of cesium atoms, both in the laboratory frame and in the non-inertial frame. The conditions for the observation of multiple cooling with frequency-chirped lasers are discussed. A comparison with standard chirped cooling is outlined. Possible applications are indicated.     

Temperature and electric field dependences of the mobility of electrons in vertical transport in GaAs/Ga<Subscript>1−<Emphasis Type="Italic">y</Emphasis></Subscript>Al<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript>As barrier structures containing quantum wells

The mobility of electrons in vertical transport in GaAs/Ga_1−y Al _y As barrier structures was investigated using geometric magnetoresistance measurements in the dark. The samples studied had Ga_1−y Al _y As (0 ≤ y ≤ 0:26) linearly graded barriers between the n⁺-GaAs contacts and the Ga_0:74Al_0:26As central barrier, which contain N _w (=0, 2, 4, 7 and 10) n-doped GaAs quantum wells. The mobility was determined as functions of (i) temperature (80–290 K) at low applied voltage (0.01–0.1 V) and (ii) applied voltage (0.005–1.6 V) at selected temperatures in the range 3.5–290 K. The experimental results for the temperature dependence of low-field mobility suggest that space-charge scattering is dominant in the samples with N _w =0 and 2, whereas ionized impurity scattering is dominant in the samples with N _w =4, 7 and 10. The effect of polar optical phonon scattering on the mobility becomes significant in all barrier structures at temperatures above about 200 K. The difference between the measured mobility and the calculated total mobility in the samples with N _w =4, 7 and 10, observed above 200 K, is attributed to the reflection of electrons from well-barrier interfaces in the quantum wells and interface roughness scattering. The rapid decrease of mobility with applied voltage at high voltages is explained by intervalley scattering of hot electrons.      

Energy and angular distributions of backscattered electrons from collisions of 5 keV electrons with thick Al,Ti, Ag,W and Pt targets

The energy and angular distributions of backscattered electrons produced under the impact of 5 keV electrons with thick Al, Ti, Ag, W and Pt targets are measured. The energy range of backscattered electrons is considered between E _B = 50 eV and 5000 eV. The angle of incidence α and take-off angle θ are chosen to have values α = 0 and 10 and θ = 100, 110 and 120 respectively. The measured energy spectra are compared with the available theoretical models for α = 0 and 10. The elastic peak intensity of backscattered electrons is found to be a function of angle of incidence, take-off angle and atomic number of the target material. The considered theories are reasonably in good agreement with experiment for the energy spectra of the backscattered electrons having their reduced energies ∈ (= E _B/E ₀) in the range of 0.20 to 1.00.      

Geometric shielding corrections for total cross section calculations of electron scattering by CH4, C2H6, C2H3F3, C2H4, C2F4, C2Cl4 and C2Cl2F2 from 30–5000?eV

To quantify the changes in the geometric shielding effect in a molecule as the incident electron energy varies, an empirical fraction, which represents the total cross section contributions of shielded atoms in a molecule at different energies, is presented. Using this empirical fraction, the total cross sections for electron scattering by CH₄, C₂H₆, C₂H₃F₃, C₂H₄, C₂F₄, C₂Cl₄ and C₂Cl₂F₂ are calculated over a wide energy range from 30 to 5000 eV by the additivity rule model at the Hartree-Fock level. The quantitative total cross sections are compared with those obtained by experiment and other theories where available. Good agreement is attained above 100 eV.