(e,2e) Spectroscopy of ethane

The 400-eV and 1200-eV non-coplanar symmetric (e, 2e) reaction has been used to measure the momentum distributions of electrons in the individual valence orbitals of ethane as well as to measure the complete separation energy spectra in the valence region. The shapes and relative magnitudes of the momentum distributions agree well with those calculated using the plane wave off-shell impulse approximation and double zeta basis molecular orbital wave functions. The ground state of C₂H₆⁺ is shown to be 1e_g^?1, with the vertical ionization potential being 12.25 ± 0.1 eV. Considerable structure due to configuration interaction is observed in the separation energy region 29–55 eV. Much of this structure can be assigned to the 2a_1g orbital.     

Direct observation of distorted wave effects in ethylene using the (e,2e) reaction

We report here the direct measurements of electron momentum distributions for ethylene using the (e,2e) reaction at different impact energies from 400 to 2400 eV. The "turn up" effects in the (e,2e) cross sections of the 1b(3g) orbital compared with the plane-wave impulse approximation calculations were observed at low and high momentum regions, and such discrepancies become smaller with the increase of the impact electron energies. It is suggested that the observed discrepancies are due to the distorted-wave effects in molecules, while appropriate theoretical calculations using distorted waves in molecules could not be achieved until now.     

Study of (e, 2e) process on potassium at 6 eV—60 eV above threshold in second-order Born approximation

The standard distorted wave Born approximation (DWBA) method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target. Second-order DWBA calculations have been preformed to investigate the triple differential cross sections (TDCS) of coplanar doubly symmetric (e, 2e) collisions for alkali target potassium at excess energies of 6 eV-60 eV. Comparing with the first-order DWBA calculations before, the present theoretical model improves the degree of agreement with experiments, especially for backward scattering angle region of TDCS. This indicates that the present second-order Born term is capable to give a reasonable correction to DWBA model in studying coplanar symmetric (e, 2e) problems in low and intermediate energy range.     

Theoretical calculation of triple differential cross sections of 3s orbital of argon in coplanar symmetric （e, 2e） reaction

The triple differential cross section for the low-energy electron impact ionization of inner-valence 3s orbital of argon has been calculated using the modified distorted wave Born approximation in coplanar symmetric energy-sharing geometry. Satisfactory agreement between theory and experiraent is achieved when the polarization and post-collisional interaction (PCI) are included in the calculations. It is shown that the polarization and PCI effects play a very important role in the case of argon at low incident energies.     

电子碰撞原子(e,2e)反应的复极化势

研究包括连续通道等非处理通道的复极化势对(e,2e)碰撞过程三重微分截面的影响,即将耦合通道光学势方法得到的复极化势附加到畸变波玻恩近似方法的畸变势中,在靶态的HF近似下,计算了Ar原子和Ne原子在非共面对称几何条件下(e,2e)反应的三重微分截面.对于较高的入射能量,在实验的误差范围内,计算结果与电子动量谱的实验数据符合较好,复极化势的影响很小;对于较低的入射能量,复极化势的作用明显增大. 关键词： 复极化势 (e;2e)反应 三重微分截面 电子动量谱     

On the exchange repulsion between beryllium atoms

Assuming the wave functions for free atoms in the form of the closed-shell SCF determinants, the first-order interaction energy for a system of three ground-state beryllium atoms has been computed. The decomposition of two and three-body interaction energies into individual, intershell contributions has been proposed. The results show that only the electrostatic energy is well approximated by the interaction of outer shells. For the two and three-body exchange energies this approximation is reliable only in the region of small orbital overlap. It has also been found that the three-body contribution to the interaction energy is considerably greater than in the case of the interaction of helium atoms.     

Quantum mechanics: cleaning up metaphysical baggage

The dynamic electronic structure of atoms and molecules can be directly observed by means of the (e, 2e) reaction, which measures the distribution of energies and momenta of two electrons in coincidence after a knockout reaction initiated by an electron beam of known momentum incident on a molecular gas target. The molecular state for each event is identified by the electron separation energy. The recoil momentum for each event is known from the difference of measured initial and final momenta. It has been verified that values of this momentum are equal under suitable conditions to the momentum of the electron in the target immediately before knockout. Thus the spherically-averaged electron momentum distribution for each molecular orbital is measured. This is directly related to molecular orbitals calculated by the methods of quantum chemistry. Properties obtained by this method for different types of molecules are discussed.     

共面双对称条件下电子碰撞Ar原子单电离的一阶扭曲波Born近似

在共面双对称几何条件下,利用一阶扭曲波Born近似计算了中低能电子碰撞Ar原子(3p壳层电子)单电离的三重微分截面,并与最近的实验数据做了比较.结果表明,对于Ar原子,当入射电子能量比电离阈高40 eV以上,随着入射能量的增加,binary和recoil碰撞机理逐渐占据支配地位;在近阈能量范围,上述碰撞机理不再处于支配地位,扭曲效应明显.要完备地描述中低能入射条件下Ar原子的电子碰撞电离过程,理论模型必须同时考虑多种散射机理.     

共面双对称几何条件下Ne原子(e,2e)反应的三重微分截面

利用标准一阶扭曲波玻恩近似方法(DWBA)计算了共面双对称几何条件下不同能量电子碰撞电离Ne原子的三重微分截面(TDCS),与Nixon和Murray[1]最新的实验测量数据进行比较.当入射电子能量较低时,理论计算结果和实验数据符合较差;而随着入射电子能量的增加,符合程度逐渐改善.     

共面双对称几何条件下Ne原子(e,2e)反应的三重微分截面

利用标准一阶扭曲波玻恩近似方法（DWBA）计算了共面双对称几何条件下不同能量电子碰撞电离Ne原子的三重微分截面(TDCS),与Nixon和Murray 最新的实验测量数据进行比较.当入射电子能量较低时,理论计算结果和实验数据符合较差;随着入射电子能量的增加,而符合程度逐渐改善.     

Study of （e, 2e） process on potassium at 6 eV-60 eV above threshold in a second-order Born approximation

The standard distorted wave Born approximation(DWBA) method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target.Second-order DWBA calculations have been preformed to investigate the triple differential cross sections(TDCS) of coplanar doubly symmetric(e,2e) collisions for the alkali target potassium at excess energies of 6 eV-60 eV.Compared with the previous first-order DWBA calculations,the present theoretical model improves the degree of agreement with experiments,especially for the backward scattering angle region of TDCS.This indicates that the present second-order Born term is capable of giving a reasonable correction to the DWBA model in studying coplanar symmetric(e,2e) problems in low and intermediate energy ranges.     

On the low energy limit of reflection and sticking coefficients in atom surface scattering. I. Short range forces

The elastic scattering of atoms and molecules by solid surfaces is treated in a nonperturbative way using the single particle Green's function of the scattered particles. For sufficiently short ranged interactions the elastic reflection coefficient is found to approach unity in the limit of zero energy of the incident particles. Unitarity then implies zero total reaction coefficient including the sticking coefficient. The findings of the first order distorted wave Born approximation are thus generalized. The result is not in contradiction to the experimental observation of sticking coefficients increasing with decreasing energy, since quantitative approximate calculations show that the limit is reached only at extremely low energies.     

The determination of the dynamic structures of atoms and molecules using the (e, 2e) reaction

In the (e, 2e) experiment a beam of electrons intersects a beam of slowly moving atoms or molecules, and pairs of emerging electrons are detected, in coincidence, at measured energies and angles. The momentum transfer distribution is closely related to the single-particle momentum distribution for a particular quantum state of the scattering molecule. The relative cross sections for different quantum states contain information about the relationship of single-particle orbitals to the many-body wave-function. The theoretical basis for interpretation is presented and shown to be self-consistent. The results for several experimental studies of atomic and molecular structure are analysed and the potential for further studies is discussed.     

Extracting Structure Parameters of Dimers for Molecular Tunneling Ionization Model

We determine structure parameters of the highest occupied molecular orbital(HOMO)of 27 dimers for the molecular tunneling ionization(so called MO-ADK)model of Tong et al.[Phys.Rev.A 66(2002)033402].The molecular wave functions with correct asymptotic behavior are obtained by solving the time-independent Schr(o|¨)dinger equation with B-spline functions and molecular potentials which are numerically created using the density functional theory.We examine the alignment-dependent tunneling ionization probabilities from MO-ADK model for several molecules by comparing with the molecular strong-field approximation(MO-SFA)calculations.We show the molecular PerelomovPopov-Terent'ev(MO-PPT)can successfully give the laser wavelength dependence of ionization rates(or probabilities).Based on the MO-PPT model,two diatomic molecules having valence orbital with antibonding systems(i.e.,Cl_2,Ne_2)show strong ionization suppression when compared with their corresponding closest companion atoms.     

High momentum range of electron momentum distributions investigated by means of high energy (e, 2e) collisions

High energy (8̃.5 keV) asymmetric coplanar (e, 2e) experiments are reported for the ionization of the 2s orbital of neon and 4s orbital of krypton. Corresponding electron momentum distributions are measured, with special emphasis being placed on the high momentum range where nodes and secondary maxima are predicted by Hartree-Fock wave functions. The present experimental results are compared with earlier ones at lower impact energy and with the factorized plane wave impulse approximation (PWIA) prediction. They give further evidence for the adequacy of this approximation at small electron momentum values. At high momenta, considerable improvement of the validity of the PWIA is observed with respect to the lower incident energy results, although ejection energy is smaller. Best agreement between experimental data and PWIA prediction is achieved when the scattering angle matches the Bethe ridge of the Bethe surface. The first minimum and secondary maximum of the electron momentum distribution are then experimentally observed for the first time. Trends are discussed in the measured momentum densities with reference to the scattering parameters.     

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.     

共面双对称几何条件下电子碰撞Na原子单电离的三重微分截面

应用参数化的最佳有效势方法, 推广三体库仑波模型(3C)及动力学屏蔽的三体库仑波模型(DS3C模型)于Na原子, 计算了共面双对称几何条件下, 电子碰撞Na原子单电离的三重微分截面(TDCS), 与最近Murray的测量数据、Hitawala等人的扭曲波近似(DWBA)及考虑极化 的扭曲波近似(DWBAP)的理论结果进行了比较. 发现, DWBA在低入射能量反映了实验结果, 而3C计算在低入射能量时失效, DS3C计算对其有所改善. 入射能量较高时DS3C及3C结果的角度分布优于DWBA, 能够较好地定性描述上述碰撞过程. 说明对于共面双对称几何条件下的电子碰撞多电子原子单电离过程, 出射道三粒子间的动力学关联效应是比较强的.     

Interpretation of intensities in electron-momentum and photoelectron spectroscopiesag

Relative intensities for the photoelectron reaction on atoms and molecules are not related to structure calculations in the same way as those for the noncoplanar symmetric (e, 2e) reaction. The photoelectron dipole matrix element is dependent on recoil momentum only through the unique relationship of recoil momentum to the photon energy and is much harder to calculate for chemically-interesting momenta. Relative intensities for binary (e, 2e) reactions are independent of total energy at high enough energies and strongly dependent on symmetry and recoil momentum, for which an intensity profile can be measured for values starting at zero. In comparing with structure calculations, binary (e, 2e) intensities for low recoil momentum may be compared directly with pole strengths in calculations of the one-electron Green's function. In the case of states within a single symmetry manifold the relative intensities will be independent of recoil momentum up to some maximum, usually at least a few atomic units.     

On a physical implementation of logical operators NOT and CNOT in a two-qubit quantum computer controlled by ultrashort optical pulses

It is shown that it is preferable to perform quantum computations on a system of two-level atoms with metastable states using optical dipole transitions that occur under the effect of ultrashort light pulses. It is suggested to measure the quantum information that is passed to qubits using Bloch, rather than pure, quantum states of two-level atoms. Moreover, the inversion of atoms can be used as the measure of quantum information. In order to describe the logical operators NOT and CNOT in the system of interacting two-level atoms (qubits), modified optical equations for the Bloch vectors of individual qubits are derived. These equations are solved in combination with field equations, without using the slowly varying amplitude approximation, for a small two-qubit system in the field of ultrashort intense optical pulses of arbitrary shape. A numerical analysis of the solution shows that it is possible to control the recording of information on individual qubits in a small quantum system of a dimension much smaller than the length of the optical wave by smoothly varying the irradiation conditions of qubits.