Nuclear isospin mixing and elastic parity-violating electron scattering

The influence of nuclear isospin mixing on parity-violating elastic electron scattering is studied for the even–even, N=Z nuclei ¹²C, ²⁴Mg, ²⁸Si, and ³²S. Their ground-state wave functions have been obtained using a self-consistent axially-symmetric mean-field approximation with density-dependent effective two-body Skyrme interactions. Some differences from previous shell-model calculations appear for the isovector Coulomb form factors which play a role in determining the parity-violating asymmetry. To gain an understanding of how these differences arise, the results have been expanded in a spherical harmonic oscillator basis. Results are obtained not only within the plane-wave Born approximation, but also using the distorted-wave Born approximation for comparison with potential future experimental studies of parity-violating electron scattering. To this end, for each nucleus the focus is placed on kinematic ranges where the signal (isospin-mixing effects on the parity-violating asymmetry) and the experimental figure-of-merit are maximized. Strangeness contributions to the asymmetry are also briefly discussed, since they and the isospin mixing contributions may play comparable roles for the nuclei being studied at the low momentum transfers of interest in the present work.     

9Be(3He,n)11C and 11B(3He,n)13N Reactions at Energies below Coulomb Barrier

Angular distributions have been measured for ⁹Be(³He, n)¹¹C and ¹¹B(³He, n)¹³N reactions for the neutron group leading to the ground state at E_3He = 0.90, 1.00, 1.20, 1.40 MeV and 1.70, 1.90 MeV respectively. To fit the experimental data, the theory of two nucleon stripping reactions below the Coulomb barrier has been considered. Taking Coulomb distorted wave functions for the interacting particles in the initial channel, a closed analytical form for the differential cross-section has been obtained. The other two cases using the plane wave Born approximation and the distorted wave Born approximation are also applied to the experimental data. The agreement between the Coulomb distorted wave calculations and the experimental data is better than with the PWBA and DWBA. The spectroscopic factors are extracted by fitting the experimental data with the theoretical calculations.     

Coulomb corrections for coherent electroproduction of vector mesons: Eikonal approximation

Virtual radiative corrections due to the long-range Coulomb forces of heavy nuclei with charge Z may lead to sizeable corrections to the Born cross-section usually used for lepton-nucleus scattering processes. An introduction and presentation of the most important issues of the eikonal approximation is given. We present calculations for forward electroproduction of rho-mesons in a framework suggested by the VDM (vector dominance model), using the eikonal approximation. It turns out that Coulomb corrections may become relatively large. Some minor errors in the literature are corrected.Received: 3 October 2003, Revised: 2 December 2003, Published online: 6 July 2004PACS: 25.30.-c Lepton-induced reactions - 25.30.Rw Electroproduction reactions - 13.40.-f Electromagnetic processes and properties - 25.30.Bf Elastic electron scattering     

Collisional deexcitation of exotic hydrogen atoms in highly excited states

The deexcitation of exotic hydrogen atoms in highly excited states in collisions with hydrogen molecules has been studied using the classical-trajectory Monte Carlo method. The Coulomb transitions with large change of principal quantum number n have been found to be the dominant collisional deexcitation mechanism at high n. The molecular structure of the hydrogen target is shown to be essential for the dominance of transitions with large Δn. The external Auger effect has been studied in the eikonal approximation. The resulting partial wave cross-sections are consistent with unitarity and provide a more reliable input for cascade calculations than the previously used Born approximation. Received 28 May 2002 Published online 15 October 2002 RID="a" ID="a"e-mail: thomas@physik.unizh.ch     

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.     

Double ionization and excitation ionization in the Compton scattering of high-energy photons for metastable states of heliumlike ions

Double ionization and excitation ionization in Compton scattering for heliumlike ions in metastable states are investigated. The electron energy distribution for double ionization and the total cross sections for both processes are calculated. The calculations are carried out in the zeroth order of perturbation theory with respect to electron-electron interaction, using Coulomb wave functions as the first approximation. The resulting equations are valid only in the high-energy nonrelativistic range. It is assumed that Z≫1, but αZ≪1 (Z is the charge of the nucleus, and α is the fine-structure constant). Zh. éksp. Teor. Fiz. 116, 1889–1902 (December 1999)     

Folding model analysis of the nucleus–nucleus scattering based on Jacobi coordinates

This paper presents the results of scattering of ¹⁶O+²⁰⁹Bi interaction near the Coulomb barrier. The interaction potential between two nuclei is calculated using the double folding model with the effective nucleon–nucleon (NN) interaction. The calculations of the exchange part of the interaction were assumed to be of finite-range and the density dependence of the NN interaction is accounted for. Also the results are compared with the zero-range approximation. All these calculations are done using the wave functions of the two colliding nuclei in place of their density distributions. The wave functions are obtained by the D-dimensional wave equation using the hyperspherical calculations on the basis of Jacobi coordinates. The numerical results for the interaction potential and the differential scattering are in good agreement with the previous works.     

后钙钛矿CaRhO3的电子结构和磁学性质的第一性原理研究

采用基于密度泛函理论的投影平面波方法,对后钙钛矿结构(Ppv)的CaRhO₃的电子结构和磁学性质进行了研究.广义梯度(GGA)近似下的计算表明,Ppv-CaRhO₃的基态为铁磁性半金属,Rh⁴⁺离子的磁矩大小为0.57μ_B,具有低自旋态构型;而考虑在位库仑作用修正的GGA+U计算,得到了与实验结果相符的反铁磁绝缘体基态,表明后钙钛矿结构中4d电子之间的关联效应对体 关键词： 电子结构 磁学性质 金属绝缘体转变     

Calculation by plane wave Born approximations of electron-impact ionization of silver and copper

The plane wave Born approximation is used to calculate total electron impact ionization cross section of silver and copper. Wavefunctions of the target and residual ions were modeled by non orthogonal Hartree-Fock and Dirac-Fock orbitals. The wave functions of the atom and residual ion are calculated with allowance for relaxation effects. The one-electron wavefunction of the continuous spectrum for the ejected electron is obtained using single-configuration Hartree-Fock and Dirac-Fock method. The orthogonalization of the ejected electron wave functions to all occupied orbitals of the target atom is performed. Results of calculations are compared to available experimental measurements and theoretical calculations performed by non relativistic one-electron PWBA, where the ejected electrons is modeled by the hydrogenic Coulomb wave function.     

Pair creation by internal conversion

In this report we describe the general theory of internal electron-positron pair conversion. Within the point nucleus approximation we derive analytical formulae for the differential pair conversion coefficient using Coulomb wave functions for the electron. Numerical calculations of the pair conversion coefficient for pointlike and extended nuclei for various multipolarities, transition energies and nuclear charges are presented and compared with Born approximation results and experimental data.     

Approximate scattering solutions of the dirac equation for electron-nucleus processes in light nuclei

Scattering solutions of the second-order Dirac equation for the case of the Coulomb potential and which are correct to first order in the coupling constantZe ²/hc are investigated and found to describe pure Coulomb scattering equally well as the Sommerfeld-Maue wave functions. Errors introduced by the use of these solutions are studied in a numerical calculation of cross sections for nuclear electric-quadrupole excitation by high-energy electrons. The use of these wave functions is suggested for simplified calculations of lowest-order Coulomb corrections to Born approximation results for various electron-nucleus processes.     

Absorption effects in halo-nucleus core or nucleon stripping reactions

Inclusive halo-nucleus core or nucleon stripping reactions are considered on the basis of a potential three-body model using the eikonal and adiabatic approximations. Clear analytical expressions for the cross sections of these reactions are obtained, and numerical calculations for ¹¹Be halo nucleus are performed. Constituent absorption by the target nucleus substantially influences the integral and differential (with respect to longitudinal momentum) nucleon stripping cross section. It is demonstrated that the differential core stripping cross section contains more complete information on the unperturbed wave function of the halo nucleus.     

On the ground state of the half-filled Hubbard model

We calculate the ground state of the half-filled Hubbard model and its energy by starting from a spindensity wave approximation and improving it by incorporating transverse spin fluctuations. The calculations are done by employing a projection method. The quality of the proposed approximation is particularly high for intermediate and large Coulomb repulsionU, where it exceeds considerably e.g. that of the Gutzwiller projected spin-density wave state. To ordert ²/U (wheret is the hopping matrix element), our approximation is shown to be equivalent to a recent Coupled Cluster calculation for the Heisenberg antiferromagnet. Finally we show how to ordert ²/U the linear spin-wave approximation for the Heisenberg antiferromagnet may be obtained.     

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.     

Bound state poles of the form factors in eikonal approximation and infinite component wave equations

We investigate the form factor in eikonal approximation for the whole region of momentum transfer t in electrodynamics and in φ³ theory, and determine the poles in the time-like region below the threshold. A covariant mass formula is obtained similar to the one derived from four point functions in eikonal approximation. The mass formula does not become imaginary for large values of the coupling constant. The relation to positronium Regge trajectory and infinite component wave equations is discussed.     

Calculation of the cross section of helium ionization by an electron impact with the formation of a helium ion in an excited state

The total cross sections of He and He⁺ ionization by an electron impact are calculated in the first Born approximation. Calculations of the matrix elements are carried out by the Fock-Dirac multiconfiguration relativistic method using an intermediate type of coupling with orthogonal functions of the initial and final states. A single-electron wave function of the continuous spectrum for an Auger electron is obtained using the Fock-Dirac single-configuration method. The results of the calculations performed with orthogonal and nonorthogonal wave functions of the initial and final states are compared. The ionization cross sections are calculated for cases in which a knock-on electron of the continuous spectrum is described by both the orthogonal and nonorthogonal wave functions with respect to the wave functions of the core electrons.     

H+,He2+与Li原子碰撞中电子俘获总截面的程函近似计算

采用Li原子价电子的有效势对前置形式程函近似振幅公式进行了修正,提出有效势修正程函近似方法,并对H^＋和He²⁺与Li原子碰撞中的电子俘获总截面进行了计算,取得了与实验比较吻合的结果. 关键词：     

Long-range Coulomb forces in DIS: missed radiative corrections?

The Born approximation, one photon exchange, used for DIS (deep inelastic scattering) is subject to virtual radiative corrections which are related to the long-range Coulomb forces. They may be sizeable for heavy nuclei since Zα is not a small parameter. So far, these corrections are known only for two processes, elastic scattering and bremsstrahlung on the Coulomb field of a point-like target. While the former amplitude acquires only a phase, in the latter case also the cross-section is modified. Although the problem of Coulomb corrections for DIS on nuclei is extremely difficult, it should be challenged rather than “swept under the carpet”. The importance of these radiative corrections is questioned in the present paper. We show that, in the simplest case of a constant hadronic current, the Coulomb corrections provide a phase to the Born amplitude, therefore the cross-section remains the same. Inclusion of more realistic hadronic dynamics changes this conclusion. The example of coherent production of vector mesons off nuclei reveals large effects. So far a little progress has been made deriving lepton wave functions in the Coulomb field of an extended target. Employing available results based on the first-order approximation in Zα, we conclude that the Coulomb corrections are still important for heavy nuclei. We also consider an alternative approach for extended nuclear targets, the eikonal approximation, which we demonstrate to reproduce the known exact results for Coulomb corrections. Calculating electroproduction of vector mesons, we again arrive at a large deviation from the Born approximation. We conclude that one should accept with caution the experimental results for nuclear effects in DIS based on analyses done in the Born approximation. Received: 16 May 2001 / Accepted: 4 July 2001     

(π +,p) Reaction in12C

Hartree-Fock wave functions obtained from realistic nucleon-nucleon interaction are employed to calculate cross-sections for the reaction¹² C(π ⁺,p)¹¹ C(g.s.). These wave functions take into account central correlations between nucleons inside the nucleus. This itself is found to change the cross-section by more than an order of magnitude. The incoming pion is represented by a plane wave while proton-distortion is taken into account in the high-energy or semi-classical approximation, thereby determining the proton optical well parameters. These values agree well with those obtained by more conventional methods. Variation of the cross-section with the oscillator well parameter is also studied. Calculations have been made using the one-nucleon mechanism for the pion-absorption process.