Relativistic Convergent Close-coupling Method Research Articles

Cross sections for electron scattering from atomic gallium

Abstract The relativistic convergent close-coupling method was applied to calculate cross sections for electron scattering on atomic gallium. The integrated and momentum-transfer cross sections for elastic scattering are presented from the 4 s 2 4 p 4P 1 / 2 , 3 / 2 electronic states for incident energies between 0.03 eV and 1000 eV. Integrated excitation cross sections are also presented from these initial states to the 4 s 2 4 [ d , f ] , 4 s 2 5 [ s , p , d ] , 4 s 2 6 [ s , p ] and 4 s 2 7 s manifolds, as well as cross sections for excitation of the 4 s 2 4 p 2P 1 / 2 state to the 4 s 2 4 p 2P 3 / 2 state. Estimates were presented for the total single ionisation cross section and total cross section for scattering on gallium in the 4 s 2 4 p 2P 1 / 2 , 3 / 2 states, including direct ionisation from the 4p, 4s and 3d electrons, and excitation-autoionisation contributions from the 4s and 3d electrons. The estimated total single ionisation cross section was found to agree well with existing experimental data.

Electron impact excitation of Sn^{2+}

The relativistic convergent close-coupling method is applied to calculate integrated cross sections for the electron-impact excitation of Sn^{2+}. Cross sections have been calculated for excitations to all states in the 5s5p, 5p^2, 5s6s and 5s5d manifolds from the ground state for projectile electron energies ranging from 24 eV to 500 eV. The total discrete inelastic scattering cross section is also presented.Graphical abstract

Electron scattering cross sections for the ground and excited states of tin

A comprehensive set of cross sections for electron scattering from the ground and first four excited states of tin has been calculated using the Relativistic Convergent Close-Coupling method. Elastic scattering, momentum transfer, total scattering, and total-inelastic scattering cross sections have been produced for the 5p23P0,1,2, 1D2 and 1S0 states of atomic tin over a projectile energy range of 0.1 eV to 1000 eV. Over the same projectile energy range, state-resolved cross sections for excitations to the 5p2, 5p6s, 5p5d and 5p6p manifolds from the ground and first four excited states of tin are presented. Total single-ionisation cross sections have been calculated which account for the direct ionisation of electrons in the valence 5p and closed 5s shells, as well as indirect contributions from excitation auto-ionisation. These ionisation cross sections are presented for projectile energies up to 1000 eV. Maxwellian rate coefficients have been calculated for all studied transitions over electron temperatures ranging from 0.5 eV to 200 eV and fitted with simple formulas. The fit coefficients are tabulated for use in modelling applications.

Cross Sections for Electron Scattering from Atomic Tin

The relativistic convergent close-coupling method is applied to calculate cross sections for electron scattering from atomic tin. We present integrated and momentum-transfer cross sections for elastic scattering from the ground and the first four excited states of tin for projectile energies ranging from 0.1 to 500 eV. Integrated and selected differential cross sections are presented for excitation to the 5p2, 5p6s, 5p5d and 5p6p manifolds from the ground state. The total ionisation cross sections are calculated from the ground and the first four excited states, accounting for the direct ionisation of the 5p valence shell and the closed 5s shell and the indirect contributions from the excitation–autoionisation. The presented results are compared with previous theoretical predictions and an experiment where available. For the total ionisation cross sections, we find good agreement with the experiment and other theories, while for excitation cross sections, the agreement is mixed.

Calculation of electron scattering on atomic silver

We report on the application of the relativistic convergent close-coupling method to electron scattering from silver atoms. Differential and integrated cross sections are presented for elastic scattering and excitation to a number of low-lying excited states for energies ranging from 0.1 to 200 eV. The total and ionisation cross sections and elastic spin asymmetry parameters are also presented, and we find potentially large relativistic effects for elastic scattering at low energies. The results are compared with experiments where available, and somewhat variable agreement is found.

Spin asymmetries for electron-thallium scattering calculated with the relativistic convergent close-coupling method

Spin asymmetries for elastic and inelastic scattering of electrons from thallium are presented. Thallium is a heavy target (Z = 81) and the spin asymmetries can be caused by relativistic effects (spin-orbit interactions) in addition to exchange effects.

Elastic scattering of electrons by europium and ytterbium atoms

The method of relativistic optical potential is applied to studying elastic scattering of electrons by europium and ytterbium atoms in a wide range of collision energies up to 2 keV. The angular dependences of the scattering differential cross sections and the energy dependences of the scattering integral (total, elastic, momentum transfer, and viscosity) cross sections are calculated in both spin-polarized and spin-unpolarized approximations. It is shown that the spin-polarized approximation should be used to calculate the scattering cross sections at energies below 10 eV for a europium atom. The low-energy scattering of an electron by a europium atom is characterized by P-, D-, and F-wave shape resonances. For an ytterbium atom, the calculated cross sections are in good agreement with available experimental data and with those obtained by calculation in terms of the relativistic convergent close-coupling method.

Calculation of the relativistic rise in electron-impact-excitation cross sections for highly charged ions

Exact relativistic plane-wave Born (RPWB) matrix elements of the M\o{}ller interaction are incorporated in the ``analytic Born subtraction technique'' and employed in the relativistic convergent close-coupling method. Application to the calculation of high-energy electron-impact-excitation cross sections of highly charged hydrogenlike ions demonstrates the ``Bethe rise,'' an effect that is manifest in Bethe's original 1932 work on relativistic high-energy, electron-impact excitation. The result represents an improvement over Bethe's relativistic high-energy theory developed in the 1930s in that (i) both target and projectile electrons are represented relativistically with Dirac spinor wave functions and (ii) the dipole approximation plus additional assumptions are not employed in the RPWB scattering amplitude of the M\o{}ller interaction.

Nonperturbative electron-ion-scattering theory incorporating the Møller interaction

Relativistic distorted-wave studies by Fontes et al. [Phys. Rev. A 47, 1009 (1993)] demonstrated that the generalized Breit interaction (equivalently, the M$\o{}$ller interaction) can affect electron-impact excitation cross sections of hydrogenlike ${\mathrm{U}}^{91+}$ by more that 50$%$ in comparison to calculations that employ the Coulomb interaction alone. We present calculations that investigate the effects of both the M$\o{}$ller interaction and close coupling in the calculation of electron-impact excitation cross sections. Electron scattering from ${\mathrm{U}}^{91+}$ is used as a test case. The relativistic convergent close-coupling (RCCC) method is nonperturbative and we emphasize the restrictions and subsequent limitations associated with employing the M$\o{}$ller interaction in the RCCC method.

Relativistic convergent close-coupling method calculation of the spin polarization of electrons scattered elastically from zinc and mercury

We present spin-asymmetry parameters (Sherman functions) for elastic electron scattering on zinc and mercury atoms calculated using the relativistic convergent close-coupling method for quasi-two-electron atoms above an inert core. The results for mercury are in excellent agreement with experiment across a wide range of energies. Similarly for zinc, we find excellent agreement between theory and experiment for energies below $9.0$ eV. However, at $11.0$ eV there is a discrepancy between theory and experiment, most likely due to a resonance excitation of a core electron.

Relativistic and Close-Coupling Effects in the Spin Polarization of Low-Energy Electrons Scattered Elastically from Cadmium

The measurements of the Sherman function in elastic electron-cadmium scattering by Bartsch et al. [J. Phys. B 25, 1511 (1992)] have been in serious disagreement with scattering theories for nearly two decades. The recently developed relativistic convergent close-coupling method is applied to the problem and found to be in excellent agreement with experiment over the complete energy range measured. The unusually rapid variation in the spin asymmetry parameter in the vicinity of 4 eV projectile energy is now explained in terms of unitarity of the close-coupling formalism.

Relativistic convergent close-coupling method applied to electron scattering from mercury

We report on the extension of the recently formulated relativistic convergent close-coupling (RCCC) method to accommodate two-electron and quasi-two-electron targets. We apply the theory to electron scattering from mercury and obtain differential and integrated cross sections for elastic and inelastic scattering. We compared with previous nonrelativistic convergent close-coupling (CCC) calculations and for a number of transitions obtained significantly better agreement with the experiment. The RCCC method is able to resolve structure in the integrated cross sections for the energy regime in the vicinity of the excitation thresholds for the $(6s6p){ }^{3}{P}_{0,1,2}$ states. These cross sections are associated with the formation of negative ion (${\mathrm{Hg}}^{\ensuremath{-}}$) resonances that could not be resolved with the nonrelativistic CCC method. The RCCC results are compared with the experiment and other relativistic theories.

Relativistic convergent close-coupling method: Calculation of electron scattering from hydrogenlike ions

We report on the extension of the recently formulated relativistic convergent close-coupling (RCCC) method to include the Breit and M\o{}ller interactions. The inclusion of these relativistic effects ensures that the RCCC method is now capable of calculating electron scattering excitation and ionization cross sections for highly charged ions. We have calculated the polarization of the Lyman-${\ensuremath{\alpha}}_{1}$ x-ray line emitted by hydrogenlike ${\text{Ti}}^{21+}$, ${\text{Ar}}^{17+}$, and ${\text{Fe}}^{25+}$ ions excited by electron impact. We find that account of Breit relativistic corrections is important to resolve the discrepancy between experiment and theoretical calculations. For the much heavier hydrogenlike ${\text{U}}^{91+}$ ion where the M\o{}ller interaction becomes important we present the estimate of the polarization of the Lyman-${\ensuremath{\alpha}}_{1}$ x-ray line and performed a calculation of the total ionization cross section.

Relativistic Convergent Close-Coupling method for excitation and ionization processes in electron collisions with atoms and ions

We have used relativistic Convergent Close-Coupling method to perform calculations of electron scattering from cesium and gallium atoms. Differential, integrated and ionization cross sections and spin asymmetries have been calculated from 1 to 500 eV and compared with available experimental data and results of other calculations.

Inclusion of the Breit interaction in the relativistic convergent close-coupling method

Recently the non-relativistic convergent close-coupling method has been extended into the relativistic domain [1]. When applied to electron impact collision processes for highly charged hydrogen-like ions, the RCCC method that utilizes relativistic kinematics and the Coulomb interaction in the absence of QED Breit and Møller corrections is suitable for target ions with atomic number Z up to Z ≈ 30. For Z larger than 30, such QED corrections become significant and must be included in the calculations. We have modified the RCCC computer code accordingly and report the results for Z = 100 selected excitation cross sections and for U91+ ionization cross sections which were found to be in good agreement with previous calculations of Fontes et al.[2].

Electron scattering from atomic gallium

Theoretical study of electron scattering from the 4P1/2 ground state of gallium atoms is reported. We have used relativistic convergent close-coupling method to obtain cross sections for elastic scattering and excitations of the 4P3/2, 5S1/2, 5P1/2,3/2 and 4D3/2,5,2 states for incident electron energies ranging from 0.1 to 500 eV. Comparison of our results with recent theoretical estimates that have been used in plasma modeling shows significant discrepancies for all considered transitions.

Relativistic convergent close-coupling method: Calculations of electron scattering from cesium

We present a detailed formulation of the relativistic convergent close-coupling (RCCC) method which is based on the solution of the Dirac equation describing electron scattering from quasi-one-electron atoms. A square-integrable Dirac $L$ spinor basis has been used to obtain a set of target states representing both the bound and continuum spectra of the target. A set of momentum-space coupled Lippmann-Schwinger equations for the $T$ matrix is then formulated and solved. We use spin asymmetries, particularly those that are identically zero in a nonrelativistic formulation, to check the accuracy of the RCCC method and find good agreement with experiment on a broad energy range.

Fully Relativistic Convergent Close-Coupling Method for Excitation and Ionization Processes in Electron Collisions with Atoms and Ions

We report the development of the fully relativistic convergent close-coupling method based on the solution of the Dirac equation. A complete square-integrable Dirac L-spinor basis is used to obtain a set of target states spanning the target discrete and continuous positive- and negative-energy spectra. The present implementation is for quasi-one-electron atoms whose electronic configuration corresponds to the first column of the periodic table. By way of example, we consider elastic scattering of 7 eV electrons on the ground state of cesium, where the full set of spin asymmetries (A1, A2, Ann) has been measured. Excellent agreement with experiment is found.