Ionization of helium in positron collisions

A new Coulomb distorted-wave method with coupled-channel target functions is used to calculate total ionization cross-sections for helium in positron collisions. Besides Slater-like orbitals we use regular Coulomb wave packets in our configurational interaction basis to describe the target continuum. The incident positron energy was varied between the ionization threshold and 500 a.u. The results are in good agreement with experimental data and other theoretical calculations. Comparing to other sophisticated distorted wave methods our model is much easier to implement and gives accurate results. As a new feature we present ionization cross-sections where the He ⁺ ion remains in the 1s ground state or excited to the 2s or 2p state. As we know there are no experimental work done to determine such cross-sections. In the case of ionization followed by 2s or 2p excitation we compared our results with other calculations.Received: 18 February 2004, Published online: 15 April 2004PACS: 34.85. + x Positron scattering     

Elastic scattering of e∓ by Na atoms

ABSTRACT

The differential, integrated elastic, momentum transfer, viscosity and total cross-sections along with Sherman function for the elastic scattering of electrons and positrons by sodium atoms have been calculated within the framework of complex projectile–atom optical potential model at the impact energies 0.1 ≤ E_i ≤ 10⁴ eV for both the projectiles. The relativistic Dirac partial wave techniques, with accurate analytical charge densities, are used to obtain the scattering amplitudes. The present results produce satisfactory agreement with the experimental measurements and other theoretical calculations available in the literature.     

Effect of distortion in electron impact excitation in Coulomb-projected Born approximation

We have calculated total and differential cross-sections for 1s →ns (n = 2, 3, 4) electron impact excitation of hydrogen and hydrogenic ions at various energies in Coulomb-projected Born approximation. Distortion due to static interactions, target polarization and exchange effects has been incorporated in the initial channel. The present calculations have been compared with other theoretical and experimental results.     

Two-electron excitation in helium-like ions by electron impact

Calculation of cross-sections for the two-electron excitation in helium-like ions by electron impact employing Coulomb-Born-Oppenheimer (CBO) approximation is presented. Analytical expressions for the differential and total scattering cross-sections without using partial wave expansion of the wavefunction reported earlier have been used. The total and differential scattering cross-sections for each of the excitations 1s ^{2 1} S* → 2s ^{2 1} S ^e , 2s2p ^1.3 P ⁰, 2p ^{2 1} S ^e ,³ P ^e,¹ D ^e in Be²⁺ and B³⁺ are computed. Results for Li⁺ reported earlier are also included for comparison.     

Two Coulomb waves theory for direct excitation

A theoretical model of Dewangan, in which the total scattering wave function is approximated by a distorted wave containing two Coulomb wave functions, is discussed and its relation with the Brauner-Briggs-Klar model for ionization is examined. An important feature of the theory is that it includes a second Born amplitude naturally and in addition, contains, albeit approximately, both real and imaginary parts of all higher order Born terms. The theory is applied to study the 1s→2s excitation of hydrogen by electrons in the energy range 54.4 to 400eV. The differential and integral cross sections predicted by the theory are compared with the results of other theories and experimental data at 54.4eV and a good agreement is found.     

Formation of ground and excited hydrogen atoms in proton–potassium inelastic scattering

The inelastic scattering of proton with a potassium atom is treated for the first time as a three-channel problem within the framework of the improved coupled static approximation by assuming that the ground (1s state) and the excited (2s state) hydrogen formation channels are open for seven values of total angular momentum, ? (0≤?≤6) at energies between 50 and 500 keV. The Lipmann–Swinger equation and the Green’s function iterative numerical method are used to calculate iterative partial and total cross-sections. This can be done by calculating the reactance matrix at different values of the considered incident energies to obtain the transition matrix that gives partial and total cross-sections. Present results are in reasonable agreement with previous results.     

Differential Cross-Section for Excitation of Helium by Electron from Field Theoretic View Point

Cross-section for excitation of helium from ground state to 2s singlet state is computed by field theoretic methods. Comparisons are made with experimental and Born cross-sections. Field theoretic cross-section is found to be in good agreement with experimental results for all ejection angles.     

Study of Bohr–Mottelson with minimal length effect for Q-deformed modified Eckart potential and Bohr–Mottelson with Q-deformed quantum for three-dimensional harmonic oscillator potential

Bohr–Mottelson Hamiltonian on the γ-rigid regime for Q-deformed modified Eckart and three-dimensional harmonic oscillator potentials in the β-collective shape variable was investigated in the presence of minimal length formalism and Q-deformed of the radial momentum part. By introducing new wave function and using the Q-deformed potential concept in Bohr–Mottelson Hamiltonian in the minimal length formalism, the un-normalized wave function and energy spectra equation were obtained by using the hypergeometric method. Meanwhile, the Bohr–Mottelson Hamiltonian in the presence of the quadratic spatial deformation to the momentum in collective shape variable was investigated using transformation of a new variable such as the Schrodinger-like equation with shape invariant potential. The energy equation and un-normalized wave function were obtained using the hypergeometric method. The results showed that the Bohr–Mottelson equations with different energy potentials and different deformation forms in the radial momentum reduced to the similar Schrodinger-like equation with the modified Poschl–Teller potential.     

Positron-hydrogen charge-exchange scattering

The positron hydrogen charge-exchange problem has been investigated using the three-particle scattering formulation. 1s and 2s intermediate states of hydrogen atom have been taken into account for calculation of second order matrix elements. The effect of 2s term is to decrease total cross-section as compared to the results involving 1s state only. The total cross-sections results are compared with results of other calculations in the energy region 1.5 to 10 Ry.     

Nucleon matrix elements and baryon masses in the Dirac orbital model

Using the expansion of the baryon wave function in a series of products of single-quark bispinors (Dirac orbitals), the nonsinglet axial and tensor charges of a nucleon are calculated. The leading term yields g _A = 1.27 in good agreement with experiment. Calculation is essentially parameter-free and depends only on the strong coupling constant value α _s . The importance of lower Dirac bispinor component, yielding 18% to the wave-function normalization is stressed. As a check, the baryon decupletmasses in the formalism of this model are also computed using standard values of the string tension σ and the strangequark mass m _s ; the results being in a good agreement with experiment. The text was submitted by the authors in English.     

A trial wave function to study of the structure of the molecular dd μ ion

This paper provides a new effort to study of the ddμ structure. The present work is numerically performed using a new trial wave function to the ddμ system in configuration of coupled channels. The present results of energies are more accurate than those of our previous work. The obtained results of formation rates are close to results published by Yu.V. Petrov et al. and giving strong indications that the trial wave function is good enough in determining the resonance states of the mentioned ionic molecule.     

Photoionization of the ground1 S e and twenty lowest excited states of the Ne-like Fe16+

TheR-matrix method is used to calculate cross-sections for the photoionization of Ne-like Fe¹⁶⁺ from ground 2s ²2p ⁶¹ S ^e and excited states belonging to 2s2p ⁶ 3l and 2s ²2p ⁵ 3l configurations. Configuration interaction wavefunctions are used to represent two target states of Fe¹⁷⁺ ion retained in theR-matrix expansion. The cross-sections are obtained as a function of kinetic energy (ε _k) of the ejected electron from 10 to 24 Ry. For low kinetic energy the cross-sections show series of Rydberg states which converge onto² S ^e threshold Fe¹⁷⁺. The calculations are carried out in the LS coupling.     

Wave propagation in carbon nanotube intramolecular junctions: finite element calculations

The dispersion of longitudinal and transverse waves in (n,0)–(2n,0) intramolecular junctions (IMJs) are investigated using an atomistic finite element method (FEM). The transient responses of IMJs with different connection types subjected to harmonic incident wave were modelled using three-dimensional elastic beams of carbon bonds and point masses. The linkage between the force-field constants of molecular mechanics and input parameters of beam and mass elements was established through the molecular structural mechanics approach. The wave dispersion simulated by FEM shows good agreement with that of the non-local elastic model in a wide frequency range up to the terahertz region. It is shown that both the microstructure of conical part (connection part) and the coupling of longitudinal vibration and transverse vibration brought by the conicity play important roles in the dispersion of longitudinal and transverse wave in a single-walled IMJ. The amplitude decay of longitudinal wave depended on the distance propagating; the wavelength and the structure in connection part are examined. The results show that the dispersion of the decay of the wave amplitude in IMJ with less pentagon–heptagon defects has a better agreement with analytical results of macroscopic conical shell.     

Perturbation theory for isotropic velocity-dependent potentials: Bound-states case

Starting from the time-independent Schr?dinger equation we develop formulae for the changes in the bound-state energies in the presence of an isotropic, velocity-dependent perturbing potential. The corresponding changes in the wave functions are also obtained. Unlike the case of the standard perturbation theory, determination of the changes in the energy and the wave function of a state only requires knowledge of the unperturbed ground-state wave function in addition to the perturbing potential. Evaluations of the energy changes and the corresponding wave functions are given for two examples in the s-wave case.     

Design of Sandwich Transducer Based on the Equivalent Length Algorithm

The sandwich transducer structure is comprised of three components along its main axis: the back metal cap, piezoelectric ceramic stack and the horn. The purpose of this work is to present a simplified method, referred as the equivalent length algorithm, to design the actuator parameters including each segment length and the resonance frequency f_s. The actuator length L and the propagation wavelength λ along its main axis satisfy the standing wave theory. So, define an equivalent length coefficient for each part of the actuator, and then the sandwich structure is regarded as a single material cylindrical rod with equivalent length L′. According to the standing wave theory, the equivalent length L′ of the actuator can be determined with the given resonance frequency f_s, or vice versa. The phase length of each part of the actuator in the standing wave is optimized freely in the design procedure. The actual length of each part of the actuator is determined by the equivalent length coefficient. Finally, the resonance frequencies of three given actuators are calculated with this method. They are compared with those obtained through Ansys simulation and those measured by an impedance analyzer. The results show agreement.     

Elastic scattering of electrons and positrons by cadmium atoms

ABSTRACT

The differential, integrated elastic, total and momentum transfer cross sections along with Sherman function for the elastic scattering of electrons and positrons by cadmium atoms have been evaluated from the partial wave solution of the Dirac relativistic scattering equations for a projectile-atom complex potential at the energy range 6.4 eV < E < 1.0 keV. For various scattering quantities, a comparison of our results exhibits better agreement with the experimental data than the other available theoretical values.     

Electron transfer in proton-hydrogen collisions in dense semi-classical hydrogen plasma

Quantum mechanical calculations have been accomplished to study the dynamics of the reaction: p + H(1s) → H(nlm) + p in dense semi-classical hydrogen plasma. Interactions among the charged particles in plasma are represented by a pseudopotential which takes care of the collective effects at large distances and quantum effect of diffraction at small distances. Various capture cross sections are computed for the incident proton energy lying within 10 to 500 keV by applying a distorted wave method which uses a variationally determined closed-form wave function of hydrogen atom. Moreover, an inclusive study is made to explore the effects of screening of plasma and quantum diffraction on various capture cross sections for a wide range of thermal Debye length and de Broglie wave length. It has been found that various cross sections suffer considerable changes due to varying Debye length and de Broglie wave length.     

Using Short Wave Visible–Near Infrared Reflectance Spectroscopy to Predict Soil Properties and Content

In this study, short wave visible–near infrared reflectance spectroscopy was evaluated for prediction of diverse soil properties related to four different soil series of several regions in Jiangxi, China. A total of 240 soil samples were collected for the calibration (n = 168) and prediction (n = 72) sets. The used wavelength range of short wave visible–near infrared reflectance spectroscopy is 325–1075 nm. Partial least squares regression and back propagation neural network were used to develop models for soil properties such as organic matter and extractable forms of calcium, magnesium, and potassium. Performance of these models was also compared and analyzed. The input of back propagation neural network was the first six principal components resulted from the principal component analysis and the optimal number of latent variables obtained from partial least squares regression. The overall results showed that the performance of partial least squares regression model was inferior to all back propagation neural network models. The best prediction was obtained with latent variables as input of back propagation neural network model for organic matter (determination coefficient = 0.84 and relative predictive determinant = 2.38), which was classified as very good model predictions. The prediction of calcium, magnesium, and potassium was classified as fair (determination coefficient = 0.56–0.68 and relative predictive determinant = 1.51–1.61), where quantitative predictions were considered possible. It is recommended to adopt latent variables as input for back propagation neural network model predicting soil properties with short wave visible–near infrared reflectance spectroscopy. In conclusion, short wave visible–near infrared reflectance spectroscopy was variably successful in estimating soil properties and showed potential for substituting laboratory analyses.