Relativistic Convergent Close-coupling Research Articles

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 Cadmium: Theory and Experiment

Results from the application of optical potential, relativistic optical potential, relativistic convergent close-coupling, and binary encounter Bethe models to electron scattering from gas-phase cadmium are presented. In particular, integral cross sections for elastic scattering, summed discrete electronic-state excitation, and ionization scattering processes are reported over an extended incident electron-energy range. Total cross sections are constructed by taking their sum. Measurements are presented for elastic scattering and for excitation to the 51P1 state. The theoretical and experimental results are compared to previous calculations and measurements. Recommended electron cross-section datasets are constructed over an incident electron energy range of 0.01–10 000 eV.

Electron-impact excitation of the (4d105s)S1/22→(4d95s2)D3/22 and (4d105s)S1/22→(4d106s)S1/22 transitions in silver: Experiment and theory

We present angle-differential and angle-integrated cross sections for electron-impact excitation of the ($4{d}^{10}5s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}(4{d}^{9}5{s}^{2})\phantom{\rule{0.16em}{0ex}}^{2}D_{3/2}$ and $(4{d}^{10}5s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}(4{d}^{10}6s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}$ transitions in atomic silver. Experimental data for four incident electron energies between 10 and 60 eV are compared with predictions from our relativistic distorted wave (RDW) and nonrelativistic atomic optical potential models. Agreement between our measured and calculated data is only fair, although in the case of the RDW it is seen to improve with increasing incident electron energy. However, only for the $(4{d}^{10}6s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}$ excitation process, agreement of our measured data with earlier relativistic convergent close coupling results from McNamara et al. [J. Phys. B 51, 085203 (2018)] was, with a few exceptions, typically observed to be very good, to within the uncertainties on the data.

Recommended Cross Sections for Electron–Indium Scattering

We report, over an extended energy range, recommended angle-integrated cross sections for elastic scattering, discrete inelastic scattering processes, and the total ionization cross section for electron scattering from atomic indium. In addition, from those angle-integrated cross sections, a grand total cross section is subsequently derived. To construct those recommended cross-section databases, results from original B-spline R-matrix, relativistic convergent close-coupling, and relativistic optical-potential computations are also presented here. Electron transport coefficients are subsequently calculated, using our recommended database, for reduced electric fields ranging from 0.01 Td to 10 000 Td using a multiterm solution of Boltzmann’s equation. To facilitate those simulations, a recommended elastic momentum transfer cross-section set is also constructed and presented here.

Cross sections for electron scattering from atomic lead

We applied the relativistic convergent close-coupling and the Dirac B-spline R-matrix methods to electron scattering from lead atoms. Differential and integrated cross sections are presented for elastic scattering and excitations from the ground state to the 6p7s, 6p7p, and 6p6d manifolds for energies ranging from 1 to 100 eV. The momentum-transfer, ionisation, and total scattering cross sections are also presented. Our results are compared with experimental data and previous theoretical predictions where available. Generally good agreement is found between the two theories and experiment, though some renormalisation of experiment is suggested.

Calculation of the polarization of light emitted during electron-impact excitation ofBa+

The measurements of Crandall et al. [Phys. Rev. A 10, 141 (1974)] for the polarization of light emitted during electron-impact excitation of ${\mathrm{Ba}}^{+}$ are in significant disagreement with relativistic distorted wave scattering theory calculations of Sharma et al. [Phys. Rev. A 83, 062701 (2011)]. The relativistic convergent close-coupling (RCCC) method is applied to the problem and the discrepancy between theory and experiment is resolved across the full range of energies measured. Furthermore, the oscillations in the polarization fraction measurements at low energies near threshold are reproduced by the RCCC calculations and linked to the formation of autoionizing states of neutral Ba.

Relativistic convergent close-coupling calculation of inelastic scattering of electrons from cesium

We present fully relativistic convergent close-coupling calculations of differential cross sections, spin-asymmetries, and Stokes parameters for inelastic electron-cesium scattering at intermediate energies. Comparison is made with the differential cross section and spin asymmetry measurements of Baum et al. [Phys. Rev. A 70, 012707 (2004)] and the Stokes parameter measurements of Slaughter et al. [Phys. Rev. A 75, 062717 (2007)]. Comparison is also made with previous semirelativistic and nonrelativistic theories. With a relatively high atomic number for cesium ($Z=55$) we find surprisingly excellent agreement between the relativistic, semirelativistic, and nonrelativistic theories for most observables. The overall agreement with the measurements is very good, with isolated discrepancies for some observables.

Calculation of the circular-polarizationP3Stokes parameter for electron-silver scattering

We present relativistic convergent close-coupling (RCCC) calculations of the ${P}_{3}$ circular light polarization Stokes parameter for atomic silver associated with the radiative decay of the electron-impact excited $(4{d}^{10}5p){\phantom{\rule{0.28em}{0ex}}}^{2}{P}_{3/2}$ state. The results are compared with the recent measurements of Jhumka et al. [Phys. Rev. A 87, 052714 (2013)]. We find excellent agreement between the RCCC results and experiment across the full energy range of measurements. We also find that relativistic effects have a weak influence on the calculation of ${P}_{3}$ in the energy range considered.

Relativistic convergent close-coupling calculation of spin asymmetries for electron-thallium scattering

The measurements of Bartsch et al (1992 J. Phys. B: At. Mol. Opt. Phys. 25 1511) of the left‐right spin asymmetry for elastic and inelastic scattering of polarized electrons from unpolarized indium atoms are compared with corresponding relativistic convergent close-coupling (RCCC) calculations over the full range of energies (1‐14 eV) and 5p 2 P o/2 → 5p 2 P o/2 ,5 p 2 P o/2 → 5p 2 P o/2 ,5 p 2 P o/2 → 6s 2 S1/2 and 5p 2 P o/2 → 6s 2 S1/2 transitions. There is very good agreement between theory and experiment for elastic scattering spin asymmetries. Some discrepancies still exist between the RCCC results and experiment for excited state spin asymmetries.

Breit interaction effect on the polarization of the Lyman-α1 x-ray line emitted by hydrogen-like ions excited by electron impact

The relativistic convergent close-coupling (RCCC) method has been used to resolve the discrepancy between theory and experiment for the polarization of the Lyman-α1 x-ray line emitted by hydrogen-like Ti21+, Ar17+ and Fe25+ ions excited by electron impact. We find that account of Breit relativistic corrections is important to resolve the discrepancy between experiment and theoretical calculations.

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 calculation of spin asymmetries for electron–indium scattering

The measurements of Bartsch et al (1992 J. Phys. B: At. Mol. Opt. Phys. 25 1511) of the left–right spin asymmetry for elastic and inelastic scattering of polarized electrons from unpolarized indium atoms are compared with corresponding relativistic convergent close-coupling (RCCC) calculations over the full range of energies (1–14 eV) and 5p 2Po1/2 → 5p 2Po1/2, 5p 2Po1/2 → 5p 2Po3/2, 5p 2Po1/2 → 6s 2S1/2 and 5p 2Po3/2 → 6s 2S1/2 transitions. There is very good agreement between theory and experiment for elastic scattering spin asymmetries. Some discrepancies still exist between the RCCC results and experiment for excited state spin asymmetries.

Differential cross sections and electron impact coherence parameters for elastic electron scattering from laser-excited 138Ba

We have measured and calculated differential cross sections and the P3 collision Stokes parameter for elastic electron scattering from the laser-excited (…6s6p 1P1) and cascade-populated (…6s5d 3D1, 2) levels of barium at 5, 10, and 20 eV impact energy. Measurements were performed using a crossed-beam apparatus, where excited-state atomic targets were prepared with resonant laser radiation incident on the electron–atom interaction region. Calculations were performed in the convergent close-coupling (CCC), relativistic CCC, and optical-model potential approximations. We present measured and calculated partial differential cross sections, which relate to differential cross sections and electron impact coherence parameters through the target state anisotropy introduced by the laser geometry.

Calculations of electron scattering from cadmium

Electron scattering from the ground state of cadmium atoms has been investigated theoretically using the convergent close-coupling, relativistic convergent close-coupling, relativistic optical potential, and relativistic distorted-wave methods. Elastic and inelastic differential cross sections, Stokes parameters, and spin-asymmetry parameters have been calculated and compared with available experimental and theoretical results. We find, in general, very good agreement between the theories and experiment.

Polarization of the Lyman-α1 X-ray line emitted by hydrogen-like Ti21+, Ar17+, and Fe25+ ions excited by electron impact1This review is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

We present a review of the relativistic convergent close-coupling (RCCC) method and describe how it has been used to resolve the discrepancy between theory and experiment for the polarization of the Lyman-α1 X-ray line emitted by hydrogen-like Ti21+, Ar17+, and Fe25+ ions excited by electron impact. We find that taking account of Breit relativistic corrections is important to resolve the discrepancy between experiment and theoretical calculations.

Electron-impact coherence parameters for electron-impact excitation of laser-excited 174Yb (…6s6p 3P1)

We have measured and calculated the P3 collision Stokes parameter for electron-impact collisional de-excitation to the ytterbium (…6s6p 3P1) level from the higher-lying 1P1, 3D1, 2, 3 and 3S1 levels for 20 eV residual energy. These processes are the time-reverse of the experimentally measured processes, where an impact energy of 20 eV was used to collisionally excite the 3P1 target, prepared by resonant laser pumping. Measurements were performed using a crossed-beam apparatus, where excited-state atomic targets were produced using resonant laser radiation incident on the electron–atom interaction region. Calculations were performed in the relativistic convergent close-coupling, convergent close-coupling and relativistic distorted-wave approximations. The theoretical calculations show that the h electron-impact coherence parameter (EICP) is equal to 1/2, independent of the scattering angle. We use this result to present the L⊥ EICP for the (…6s7s 3S1)→(…6s6p 3P1) collision process.

Differential cross sections for electron-impact excitation of laser-excited 174Yb (…6s6p 3P1)

We have measured and calculated electron-impact excitation cross sections from the laser-excited Yb (…6s6p 3P1) level to the higher-lying Yb (…6s6p 1P1), (…6s5d 3D1, 2, 3) and (…6s7s 3S1) levels at 20 eV impact energy. Measurements were performed using a crossed-beam apparatus, with resonant laser radiation incident on the electron–atom interaction region, providing excited-state atomic targets. Calculations were performed in the relativistic convergent close-coupling (RCCC), convergent close-coupling (CCC), and relativistic distorted-wave (RDW) approximations. We present measured and calculated partial differential cross sections (), which relate to differential cross sections and electron-impact coherence parameters through the target state anisotropy introduced by the laser geometry. Using theoretical predictions of the h electron-impact coherence parameter, we present the differential cross section for the 3P1–3S1 excitation.

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.