Coplanar (<Emphasis Type="Italic">e</Emphasis>, 3<Emphasis Type="Italic">e</Emphasis>) differential cross-section of He atom

We present in this paper the results of our calculation of five-fold differential cross-section (FDCS) for (e,3e) process on He atom in low momentum transfer and high electron impact energy in shake-off mechanism. The formalism has been developed in Born approximation using plane waves, Byron and Joachain as well as Le Sech and correlated BBK-type wave functions respectively for incident and scattered, bound and ejected electrons. The angular distribution of FDCS of our calculation is presented in various modes of coplanar geometry and comparison is made with the available experimental data. We observe that the present calculation is able to reproduce the trend of the experimental data. However, it differs in magnitude from the experiment. The present theory does not predict four-peak structure insummed mutual angle mode for lower excess ejected electron energies. We also discuss the importance of momentum transfer, post-collision interaction (PCI) and ion participation in the (e,3e) process in constant θ₁₂ mode     

Scaling of cross-sections for asymmetric (e, 3e) process on helium-like ions by fast electrons

An approximate simple scaling law is obtained for asymmetric (e, 3e) process on helium-like ions for double ionization by fast electrons. It is based on the equation (Z ^′3π) exp[-Z(r₁ + r₂)],Z′ = Z – (5/16) for ground state wave function of helium-like ions and Z^′2 scaling of energies. The scaling law is found to work very well if the lower energy electron is ejected along the momentum transfer direction and the other one is ejected in the opposite direction. It also works quite well if this electron is ejected within about 90° of the momentum transfer direction with the other electron going in the opposite direction. The scaling law becomes increasingly accurate as the target nuclear charge and the energy increase.     

Transition prediction for supersonic and hypersonic boundary layers on a cone with angle of attack

Transition prediction for boundary layers has always been one of the urgent problems waiting for a solution for the development of aero-space technology, yet there is no reliable and effective method due to the complexity of the problem. The e ^N method has been regarded as an effective method for the transition prediction of boundary layers. However, it heavily relies on experiment or experience. And in cases with three-dimensional base flow, for instance, the boundary layer on a cone with angle of attack, the result of its application is not satisfactory. The authors have found its cause and proposed the method for its improvement, which did yield the fairly satisfactory result for a given test case, and also did not rely so much on experiment or experience. However, before people can really apply this method to practical problems, more test cases have to be studied. In this paper, more test cases for the application of the improved e ^N method to problems of transition prediction of supersonic and hypersonic boundary layers on cones with angle of attack will be studied. The results are compared with those obtained by experiments and/or direct numerical simulations, confirming that the improved e ^N method is effective and reliable. We also find that there may be more than one ZARF for each meridian plane, and which one should be chosen for the e ^N method has been clarified. Supported by the National Natural Science Foundation of China (Grant Nos. 10632050 and 90716007), the Special Foundation for the Authors of National Excellent Doctoral Dissertations (Grant No. 200328), and the Foundation of Liu-Hui Center of Applied Mathematics of Nankai University and Tianjin University Contributed by ZHOU Heng     

Second-order eikonal corrections for

The first-order eikonal approximation is frequently adopted in interpreting the results of A(e,e^′p) measurements. Glauber calculations, for example, typically adopt the first-order eikonal approximation. We present an extension of the relativistic eikonal approach to A(e,e^′p) which accounts for second-order eikonal corrections. The numerical calculations are performed within the relativistic optical model eikonal approximation. The nuclear transparency results indicate that the effect of the second-order eikonal corrections is rather modest, even at Q²≈0.2 (GeV/c)². The same applies to polarization observables, left–right asymmetries, and differential cross sections at low missing momenta. At high missing momenta, however, the second-order eikonal corrections are significant and bring the calculations in closer agreement with the data and/or the exact results from models adopting partial-wave expansions.     

On the observation of the fine structure effect in non-relativistic (e, 2e) processes

The spin asymmetry arising in an (e,2e) process using spin-polarized incoming electrons with non-relativistic energies is shown to be dominated by the fine structure effect if a suitable kinematical regime is chosen. Calculations in the distorted wave Born approximation (DWBA) for both the triple differential cross-section and the spin asymmetry are presented for the inner shell ionization of argon. This process would provide an accessible target for existing experimental set-ups.     

L-shell ionization of atoms by relativistic electrons

A theoretical study of theL-shell ionization of atoms by relativistic electrons is made for atomic numbers in the range 47 to 92. A new potential model recently proposed by Das and Chakraborty dealing with atomic screening effect in a better way has been used. The results are in satisfactory agreement when compared with some available experimental results and also with the theoretical results of Scofield.     

A Possible New Value for the Electron Mass from g-Factor Measurements on Hydrogen-Like Ions

The mass of the electron in atomic units (m _e) represents the largest error contribution in an experiment to determine the g-factor of the electron bound in hydrogen-like carbon. Recent progress in the calculation reduces the uncertainty of the theoretical value to such a low value that m _e can be determined from a comparison of experimental and theoretical g-factors. The present preliminary value of the electron mass agrees with the accepted value but reduces the uncertainty by about a factor 2. This revised version was published online in July 2006 with corrections to the Cover Date.     

Transition prediction of a hypersonic boundary layer over a cone at small angle of attack—with the improvement of e<Superscript><Emphasis Type="Italic">N</Emphasis></Superscript> method

The problem of transition prediction for hypersonic boundary layers over a sharp cone has been studied in this work. The Mach number of the oncoming flow is 6, the cone half-angle is 5°, and the angle of attack is 1°. The conventional e ^N method is used, but the transition location so obtained is obviously incorrect. The reason is that in the conventional method, only the amplifying waves are taken into account, while in fact, for different meridians the decay processes of the disturbances before they begin to grow are different. Based on our own previous work, new interpretation and essential improvement for the e ^N method are proposed. Not only the amplification process but also the decay process is considered. The location, where by linear stability theory, the amplitude of disturbance wave is amplified from its initial small value to 1%, is considered to be the transition location. The new result for transition prediction thus obtained is found to be fairly satisfactory. It is also indicated that for the calculation of base flow, boundary layer equations can be used for a small angle of attack. Its computational cost is much smaller than those for DNS. Supported by the National Natural Science Foundation of China (Grant Nos. 10632050 and 90716007), the Special Foundation for the Authors of National Excellent Doctoral Dissertations (Grant No. 200328), and the Foundation of Liu-Hui Center of Applied Mathematics of Nankai University and Tianjin University     

Energy spectrum of ejected electrons in ionization of hydrogen atoms by electrons

Energy spectrum of ejected electrons in ionization of hydrogen atoms has been calculated following a multiple scattering theory of Das and Seal [15]. The results show peaks around two to three Rydbergs of energies of the ejected electrons, for incident electron energy of 250 eV and 500 eV, considered here, and for different combinations of the angular variables of the scattered and the ejected electrons, for scattering in a plane. The peaks are very similar to those observed in relativistic K-shell ionization of Ag atoms by electrons at 500 KeV energy [6]. The physical origin of these peaks may be traced to the second order scatterings, scattering first by the atomic nucleus (or the atomic electron) and then a second time by the atomic electron. These peaks are, however, absent in the first Born results. Experimental verification of the present results and theoretical calculation by some other well-known methods will be interesting.     

K-shell ionization of atoms and ions by relativistic projectiles

We evaluate the total cross section for the single K-shell ionization of atoms and ions by the impact of relativistic electrons. The study is performed to leading orders of the QED perturbation theory with respect to the parameters αZ and 1/Z. The results obtained are in good agreement with experimental data for different atomic targets. In the case of moderate values of the nuclear charge Z, the total cross section is described by a simple analytic formula. The K-shell ionization by relativistic heavy particles is also considered.     

内掺过渡金属非典型富勒烯M@C22(M=Sc, Ti, V, Cr, Mn, Fe, Co, Ni) 几何结构、电子结构、稳定性和磁性的密度泛函研究

采用密度泛函理论中广义梯度近似对非典型富勒烯C₂₂和过渡金属内掺衍生物M@C₂₂(M=Sc,Ti,V,Cr,Mn,Fe,Co和Ni)的几何结构和电子结构进行计算研究.发现非典型富勒烯C₂₂的基态结构是含有一个四碳环的单重态笼状结构.过渡金属原子的掺入明显提高了体系的稳定性. C-M键既有一定共价性又有一定离子性.磁性、能级图、轨道分布和态密度图分析表明: M原子的3d轨道和碳笼的C原子的原子轨道之间存在较强的轨道杂化. Ti, Cr, Fe和Ni内掺的结构出现磁性完全猝灭现象. Sc和碳笼间是弱反铁磁作用, V,Mn和Co与碳笼间是弱铁磁作用.     

Focusing of high-energy particles in the electrostatic field of a homogeneously charged sphere and the effective momentum approximation

The impact of the strongly attractive electromagnetic field of heavy nuclei on electrons in quasi-elastic (e, e') scattering is often accounted for by the effective momentum approximation. This method is a plane wave Born approximation which takes the twofold effect of the attractive nucleus on initial- and final-state electrons into account, namely the modification of the electron momentum in the vicinity of the nucleus, and the focusing of electrons towards the nuclear region leading to an enhancement of the corresponding wave function amplitudes. The focusing effect due to the attractive Coulomb field of a homogeneously charged sphere on a classical ensemble of charged particles incident on the field is calculated in the highly relativistic limit and compared to results obtained from exact solutions of the Dirac equation. The result is relevant for the theoretical foundation of the effective momentum approximation and describes the high-energy behavior of the amplitude of continuum Dirac waves in the potential of a homogeneously charged sphere. Our findings indicate that the effective momentum approximation is a useful approximation for the calculation of Coulomb corrections in (e, e') scattering off heavy nuclei for sufficiently high electron energies and momentum transfer.     

The Biot-Savart-Ampère law and the vacuum fieldB (3)

It is shown that the longitudinal vacuum fieldB ⁽³⁾ emerges from the Biot-Savart-Ampère law governing the motion of an electron with intrinsic spin moving at the speed of light, in which case the expression forB ⁽³⁾ is identical with that obtained from the Dirac equation of one electron accelerated to the speed of light by an electromagnetic field. Use of an O(3), non-Abelian, gauge geometry forB ⁽³⁾ identifies the quantized photon momentum appearing in the Dirac equation witheA ⁽⁰⁾, wheree is the charge on the electron andA ⁽⁰⁾ the amplitude of the vector potential. The condition =eA ⁽⁰⁾ can be obtained in turn from the relativistic Hamilton-Jacobi equation of an electron accelerated to the speed of light by an electromagnetic field.     

Recent KLOE results on hadron physics

The KLOE experiment at the Frascati e ⁺ e ^- collider DAFNE has completed this year its data taking. An integrated luminosity of 2.7fb^-1 has been collected mostly at the φ-resonance peak. A wide experimental program is in progress. The detection of φ radiative decays allows to study the properties of the lowest-mass scalar and pseudoscalar mesons and to obtain information on their structure. The main results are reviewed together with the prospects for low-energy e ⁺ e ^- physics at Frascati.     

Study of the 4He(e,e′d)pn Reaction

 The cross section for the ⁴He(e,e′d)pn reaction has been measured in parallel and in (q, ω)-constant kinematics for values of the three-momentum transfer of 406, 495 and 595 MeV/c, and for a range in missing momentum. Just above threshold this reaction can be characterized as a spin/isospin flip transition of the involved pn pair. By using two electron energies (576 and 370 MeV) the longitudinal and transverse structure functions could be separated. The cross sections turn out to be purely transverse, as expected for a spin/isospin flip transition. The data are well described by new covariant and current-conserving calculations that include the major final-state interaction effects. Received August 20, 1998; modified October 12, 1998; accepted for publication January 30, 1999     

First energy and angle differential measurements of e+e−-pairs emitted by internal pair conversion of excited heavy nuclei

We present the first energy and angle resolved measurements of e⁺e⁻-pairs emitted from heavy nuclei (Z≥ 40) at rest by internal pair conversion (IPC) of transitions with energies of less than 2 MeV as well as recent theoretical results using the DWBA method, which takes full account of relativistic effects, magnetic substates and finite size of the nucleus. The 1.76 MeV E0 transition in ⁹⁰Zr (⁹⁰Sr source) and the 1.77 MeV M1 transition in ²⁰⁷Pb (²⁰⁷Bi source) have been investigated experimentally using the essentially improved setup at the double-ORANGE β-spectrometer of GSI. The measurements prove the capability of the setup to cleanly identify the IPC pairs in the presence of five orders of magnitude higher β⁻ and γ background from the same source and to yield essentially background-free sum spectra despite the large background. Using the ability of the ORANGE setup to directly determine the opening angle of the e⁺e⁻–pairs (Θ_e+e−), the angular correlation of the emitted pairs was measured within the range covered experimentally (40°≤Θ_e+e−≤ 180°). In the ⁹⁰Zr case the correlation could be deduced for a wide range of energy differences E _Δ of the pairs (−530 keV ≤E _Δ≤ 530 keV). The ⁹⁰Zr results are in good agreement with recent theory. The angular correlation deduced for the M1 transition in ²⁰⁷Pb is in strong disagreement with theoretical predictions derived within the Born approximation and shows almost isotropic character. This is again in agreement with the new theoretical results. Received: 22 April 1997 / Revised version: 16 December 1997     

The relativistic density functional investigations on geometries, electronic and magnetic properties of Irn (n=1-13) clusters

<正>The Ir_n(n=1-13) clusters are studied using the relativistic density functional method with generalized gradient approximation.A series of low-lying structures with different spin multiplicities have been considered.It is found that all the lowest-energy Ir_n(n=4-13) geometries prefer non-compact structures rather than compact structure growth pattern.And the cube structure is a very stable cell for the lowest-energy Ir_n(n8) clusters.The second-order difference of energy,the vertical ionization potentials,the electron affinities and the atomic average magnetic moments for the lowest-energy Ir_n geometries all show odd-even alternative behaviours.     

Resolved photon processes

We review high-energy scattering processes that are sensitive to the hadronic structure of the photon, describing theoretical predictions as well as recent experimental results. These processes include deep-inelastic electron-photon scattering ate ⁺ e ⁻ colliders; and the production of jets, heavy quarks and isolated photons in the collision of real photons ate ⁺ e ⁻ colliders, as well as in photon-photon collisions atep colliders. We also comment on minijet based calculations of totalγp andγγ cross-sections, and discuss the possibility that future lineare ⁺ e ⁻ colliders might produce very large photon fluxes due to the beamstrahlung phenomenon; in the most extreme cases, we predict more than one hadronicγγ event to occur at every bunch crossing.     

Some consequences of neutral current systematics

Two kinds of general consequences of the ΔS=0 weak hadron neutral current independent of a gauge model are presented. Firstly are results which depend on the quark parton model. These involve bounds among neutrino inclusive cross-section and a bound onQ(Z, N) in terms of these inclusive cross-sections. Secondly are results which are independent of the quark-parton model and depend only on the SU(3) structure of the most general ΔS=0 neutral current. These tests of isopin and speciallyU-spin properties of the current are given forv+N→v+hadron+anything,v+N→v+baryon+meson ande ⁺ e ⁻→baryon+anti-baryon. In addition some conjectures are made with regard to the semi-inclusive neutrino-reactions using the quark parton model.