Distorted-wave Cross Sections Research Articles

Electron-impact single ionization for N+ ion

ABSTRACT Electron-impact single ionization from levels of the ground configuration of the N+ ion is presented. Study analyses direct and indirect processes of the ionization. Convergence of the excitation-autoionization cross-sections is ensured by taking excitations up to shells with the principal quantum numbers n ≤ 10. The potential of the ionizing ion is used in the study. The scaled distorted wave cross-sections show a fairly good agreement with measurements. The study shows a presence of metastable states in the ion beams of experiments.

Nuclear excitation of Th229 induced by laser-driven electron recollision

Previously we proposed a new approach of exciting the $^{229}\mathrm{Th}$ nucleus using laser-driven electron recollision [Wang, Zhou, Liu, and Wang, Phys. Rev. Lett. 127, 052501 (2021)]. The current article is aimed at elaborating the method by explaining further theoretical details and presenting extended new results. The method has also been improved by adopting the electronic excitation cross sections calculated recently by Tkalya [Tkalya, Phys. Rev. Lett. 124, 242501 (2020)]. The new cross sections are obtained from Dirac distorted-wave calculations instead of from Dirac plane-wave calculations as we used previously. The distorted-wave cross sections are shown to be 5 to 6 orders of magnitude higher than the plane-wave results. With the excitation cross sections updated, the probability of isomeric excitation of $^{229}\mathrm{Th}$ from electron recollision is calculated to be on the order of ${10}^{\ensuremath{-}12}$ per nucleus per (femtosecond) laser pulse. The dependency of the excitation probability on various laser parameters is calculated and discussed, including the laser intensity, the laser wavelength, and the laser pulse duration.

Electron-impact single, double, and triple ionization of B+

Electron-impact single, double, and triple ionizations are investigated for the ${\mathrm{B}}^{+}$ ion. The direct and indirect ionization processes are studied for the single and double ionization. Good agreement with measurements for the single and double ionization is obtained when the scaled distorted-wave cross sections are used to study the collisional ionization and excitation processes. It is shown that ionization-excitation-autoionization and excitation-ionization-autoionization processes have to be introduced to the total double ionization to explain the measurements. The triple ionization is investigated by considering the direct double ionization with the subsequent autoionization.

Electron-impact ionization of the Pb atom

Electron-impact ionization cross sections are calculated for the ground configuration of the Pb atom. Time-dependent close-coupling cross sections for the direct ionization of the 6s and 6p subshells leading to single ionization are calculated with and without a polarization potential. Configuration-average distorted-wave cross sections for the direct ionization of the 6s and 6p subshells leading to single ionization are also calculated with and without a polarization potential. We find the time-dependent close-coupling cross sections using a polarization potential to be in good agreement with convergent-close-coupling cross sections using a polarization potential. The total direct ionization cross sections are compared to two sets of experimental measurements. The differences between the direct ionization cross sections and the experimental measurements are mainly due to indirect ionization cross sections coming from the 6s^2 6p^2 rightarrow 6s 6p^3 excitation followed by autoionization.Graphic

Electron impact single ionization for Si atom

Single ionization by electron impact is studied in the Si atom by performing level-to-level calculations. Direct and indirect processes of the ionization are investigated for all levels of the ground configuration. It is demonstrated that cross sections are heavily dependent on the initial level for which the ionization is considered. The cross sections of the indirect process differ by more than a factor of two for the lowest and highest levels of the ground configuration. The scaled distorted wave cross sections are used to explain experimental data. Modeling shows that ∼70% of the atoms in the beam belong to the levels of the 3P term. The cross sections and Maxwellian rate coefficients are tabulated for the electron-impact collisional ionization and excitation–autoionization processes.

Transition densities and form factors in the triangular α -cluster model of C12 with application to C12+α scattering

Densities and transition densities are computed in an equilateral triangular $\ensuremath{\alpha}$-cluster model for $^{12}\mathrm{C}$, in which each $\ensuremath{\alpha}$ particle is taken as a Gaussian density distribution. The ground state, the symmetric vibration (Hoyle state), and the asymmetric bend vibration are analyzed in a molecular approach and dissected into their components in a series of harmonic functions, revealing their intrinsic structures. The transition densities in the laboratory frame are then used to construct form factors and to compute distorted-wave Born approximation inelastic cross sections for the $^{12}\mathrm{C}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$ reaction. The comparison with experimental data indicates that the simple geometrical model with rotations and vibrations gives a reliable description of reactions where $\ensuremath{\alpha}$-cluster degrees of freedom are involved.

Electron-impact ionization of Fe3+

SynopsisElectron-impact ionization cross sections are studied for levels of the ground and first excited con-figurations of the Fe3+ ion. Convergence for the excitation-autoionization cross sections due to excitations to the high-nl shells is investigated. Single configuration and configuration interaction methods are used in the study. Scaling is applied to the distorted wave cross sections of the excitation-autoionization and collisional ionization processes.

Electron-impact single ionization ofFe3+from the ground and metastable states

Single ionization by electron impact of the ${\mathrm{Fe}}^{3+}$ ion is investigated using the Dirac-Fock-Slater approximation for the levels of the ground and first-excited $3{d}^{4}4s$ configuration. Contributions from direct ionization (DI) and excitation-autoionization (EA) processes are taken into account. The scaled distorted-wave (DW) cross sections for DI and excitation by electron impact are used to analyze the experimental data. The study demonstrates the importance of correlation effects for the EA process. Good agreement with experimental data reveals that currently available DW cross sections and, therefore, the corresponding Maxwellian rate coefficients for electron-impact ionization process in ${\mathrm{Fe}}^{3+}$ are overestimated and their usage may lead to wrong predictions for charge state distribution in plasma.

Spectroscopic diagnostics of low-pressure inductively coupled Kr plasma using a collisional–radiative model with fully relativistic cross sections

A collisional–radiative (C–R) model for krypton plasma using fully relativistic distorted-wave cross sections for electron excitations was developed. The model was applied to the characterization of inductively coupled Kr plasma with cylindrical geometry over the pressure regime 1–50 mTorr. Radially averaged emission intensities from transitions of Kr (4p55p → 4p55s) in the range 500–900 nm were recorded at 17 cm from the planar RF-driven coil, with the plasma operated in the inductive regime (H mode). The measured emission intensities were then fitted by varying the electron density, ne, and electron temperature, Te, in the C–R model. At both low and high pressures, variations of the electron density by over two orders of magnitude had only a minor role on the relative emission intensities. On the other hand, Te values deduced from the comparison between experiment and model decreased from 6.7 to 2.6 eV as pressure increased from 1 to 50 mTorr. These results are found to be in good agreement with the effective electron temperature determined from Langmuir probe measurements and the predictions of a model based on the particle balance equation of charged particles.

Collisional-radiative model for non-Maxwellian inductively coupled argon plasmas using detailed fine-structure relativistic distorted-wave cross sections

Our recently developed collisional-radiative model which included fine-structure cross sections calculated with a fully relativistic distorted-wave method [R.K. Gangwar, L. Sharma, R. Srivastava, A.D. Stauffer, J. Appl. Phys. 111, 053307 (2012)] has been extended to study non-Maxwellian inductively coupled argon plasmas. We have added more processes to our earlier collisional-radiative model by further incorporating relativistic distorted-wave electron impact cross sections from the 3p54sJ = 0, 2 metastable states, (1s3, 1s5 in Paschen’s notation) to the 3p55p (3pi) excited states. The population of various excited levels at different pressures in the range of 1–25 mTorr for an inductively coupled argon plasma have been calculated and compared with the recent optical absorption spectroscopy measurements as well as emission model results of Boffard et al. [Plasma Sources Sci. Technol. 19, 065001 (2010)]. We have also calculated the intensities of two emission lines, 420.1 nm (3p9 → 1s5) and 419.8 nm (3p5 → 1s4) and compared with measured intensities reported by Boffard et al. [J. Phys. D 45, 045201 (2012)]. Our results are in good agreement with the measurements.

Argon plasma modeling with detailed fine-structure cross sections

Our recently reported fully relativistic distorted-wave electron-impact cross sections from the ground and metastable states of argon to various excited fine-structure levels are incorporated in a collisional-radiative model to obtain the population densities for the 3p54s and 3p54p (1s and 2p) fine-structure manifolds for low temperature argon plasmas. Excitation cross sections from the two 3p54s J = 1 resonance levels, 1s2 and 1s4, to the higher lying 2p fine-structure manifold as well as for transitions among individual levels of the 1s and 2p manifolds are also calculated and included in the present model which were not fully considered in any earlier model. Our results for the population densities of the 1s and 2p levels show good agreement with recent measurements. The variation of population densities of all the 1s and 2p levels with electron temperature and density are presented. We have also calculated and compared the intensities for the 750.38 nm (2p1 → 1s2) and 696.54 nm (2p2 → 1s5) lines with recently reported experimental results. The present work suggests that the inclusion of a complete fine-structure description of the electronic processes occurring in the plasma is important for a collisional radiative model, which includes separate 1s and 2p levels.

Electron-impact ionization of moderately charged atomic ions in excited states

Nonperturbative $R$-matrix and perturbative distorted-wave methods are used to calculate electron-impact ionization cross sections for ${\mathrm{C}}^{3+}$ in excited states. Convergence studies for the cross sections of the $1{s}^{2}5s$ excited configuration reveal that both the $R$-matrix and distorted-wave methods need fairly high ejected electron angular momenta. Reasonable agreement is found between the converged $R$-matrix and distorted-wave cross sections. Thus, the use of the computationally less demanding distorted-wave method as a tool for the $n$ scaling of excited-state ionization cross sections appears to be reasonable for atomic ions with charge $q\ensuremath{\geqslant}3$.

Radial Secondary Electron Dose Profiles and Biological Effects in Light-Ion Beams Based on Analytical and Monte Carlo Calculations using Distorted Wave Cross Sections

To speed up dose calculation, an analytical pencil-beam method has been developed to calculate the mean radial dose distributions due to secondary electrons that are set in motion by light ions in water. For comparison, radial dose profiles calculated using a Monte Carlo technique have also been determined. An accurate comparison of the resulting radial dose profiles of the Bragg peak for (1)H(+), (4)He(2+) and (6)Li(3+) ions has been performed. The double differential cross sections for secondary electron production were calculated using the continuous distorted wave-eikonal initial state method (CDW-EIS). For the secondary electrons that are generated, the radial dose distribution for the analytical case is based on the generalized Gaussian pencil-beam method and the central axis depth-dose distributions are calculated using the Monte Carlo code PENELOPE. In the Monte Carlo case, the PENELOPE code was used to calculate the whole radial dose profile based on CDW data. The present pencil-beam and Monte Carlo calculations agree well at all radii. A radial dose profile that is shallower at small radii and steeper at large radii than the conventional 1/r(2) is clearly seen with both the Monte Carlo and pencil-beam methods. As expected, since the projectile velocities are the same, the dose profiles of Bragg-peak ions of 0.5 MeV (1)H(+), 2 MeV (4)He(2+) and 3 MeV (6)Li(3+) are almost the same, with about 30% more delta electrons in the sub keV range from (4)He(2+)and (6)Li(3+) compared to (1)H(+). A similar behavior is also seen for 1 MeV (1)H(+), 4 MeV (4)He(2+) and 6 MeV (6)Li(3+), all classically expected to have the same secondary electron cross sections. The results are promising and indicate a fast and accurate way of calculating the mean radial dose profile.

Study of inner-shell excitation processes from N(1s) orbitals in N2O molecules by electron impact

A combination of the iterative Schwinger variational method with the distorted-wave approximation is applied to study excitations of a core-level electron in a triatomic molecule by electron impact. More specifically, we report calculated differential and integral cross sections for the X1Σ+ → 1,3Π(2σ → 3π) and X1Σ+ → 1,3Π(3σ → 3π) transitions in N2O in the 415–900 eV incident energy range. The RI(1:3) ratios, obtained via dividing the distorted-wave integral cross sections for transitions leading to the singlet core-excited states by those leading to triplet states, are also reported. The generalized oscillator-strength profiles for the singlet transitions have also been calculated at the incident energy of 3400 eV. The comparison of these quantities with the available theoretical and experimental data reported in the literature is encouraging.

Rydberg transitions for positron-hydrogen collisions

e+ + H(ns) ↦e+ + H(n′s) transitions for arbitrary n and n′ have been studied using the distorted-wave formalism in the momentum space [Ghoshal and Mandal, Phys. Rev. A 72, 032714 (2005)]. The distorted-wave scattering amplitudes have been written in a simple closed analytical form. A detailed study has been made on differential and total cross sections in the energy range 20–300 eV. Resonance-like behaviour of the differential cross section has been observed in the the region of lower scattering angles for high Rydberg transitions. To the best of our knowledge the distorted-wave results for differential and total cross sections for such arbitrary transitions are reported for the first time in the literature.

Resonance contributions to collision strengths for transitions between magnetic sublevels in highly charged ions by impact with an electron beam

A fully relativistic approach is described for obtaining the resonance contribution to the cross sections for transitions between magnetic sublevels in highly charged ions due to impact with an electron beam. We derive the relativistic distorted-wave cross section for the ion in a lower N-electron magnetic sublevel to capture a directive electron and form a doubly excited $(N+1)$-electron magnetic sublevel. Also the autoionization rate from this magnetic sublevel to an N-electron magnetic sublevel is derived. The resonances are then treated as the two-step process of electron capture followed by autoionization to the final sublevel with the effects of autoionization to a different final level or radiative decay of the doubly excited sublevels included. These resonance contributions are added to the relativistic distorted-wave results for the ``direct'' contribution to give the complete cross section. Numerical results expressed in terms of the collision strengths are calculated and studied for He-like oxygen and iron and for Be-like oxygen. These are of interest for electron beam ion trap experiments and population alignment analysis.

Time-dependent close-coupling calculations for the electron-impact ionization of carbon and neon

A time-dependent close-coupling method is used to calculate the electron-impact ionization cross section for the outer 2 p subshell of both carbon and neon atoms. The inner 1s and 2s subshells are treated using pseudopotentials, while interaction with the remaining 2 p core electrons is handled in a configuration-average approximation. When the time-dependent ionization cross section for the 2 p subshell of carbon is combined with distorted-wave ionization cross sections for the 2 s subshell, the resulting total cross section is in reasonable agreement with previous experimental measurements. However, when the time-dependent ionization cross section for the 2 p subshell of neon is combined with distorted-wave ionization cross sections for the 2 s subshell, the resulting total cross section is substantially higher than all previous experimental measurements. Further LS term-dependent distorted-wave ionization cross sections for the 2 p subshell of neon suggest the need for extending the time-dependent close-coupling method to include a full Hartree-Fock interaction with the remaining 2p core electrons. PACS number~s!: 34.80.Kw

A distorted-wave study for core-excitation processes in CO2 by electron impact

In the present work, the distorted-wave approximation (DWA) is applied for the first time to study core-level excitations in molecules by electron impact. More specifically, we have calculated differential and integral cross sections for the X1Σg+→1,3Πu (carbon 1s 2σg→2πu) transitions in CO2 in the 320–800eV incident energy range. The frozen-core generalized oscillator strengths (GOS) for the transition leading to singlet excited states calculated using both the DWA and the first Born approximation (FBA) at 1290eV are also reported. Our calculated DWA GOS are in general 20% lower than the corresponding FBA, results which seem to indicate that the FBA is not valid at that incident energy. Moreover, we have also calculated the ratios between the distorted-wave integral cross sections for the transitions leading to the triplet and the singlet excited states as a function of incident energy. The comparison of these data with the experimental ratio R(3A:1A) obtained by dividing the intensities of the autoionizing electrons from the same excited states in the 320–800eV range is encouraging.

Relativistic distorted-wave excitation cross sections of F-like selenium by electron collision

RDWB procedures were applied to study the excitation cross sections induced by electron collision for F-like selenium. code was used for atomic structure calculations. By approaching from the `post' form approximation, it was possible to overcome the complexity involved in using non-orthogonal orbits. From the multipole expansion of the inter-electron potential used, it was found justifiable to add a correction term to the exchange Slater integrals due to the non-orthogonal orbitals. Comparisons are made of the resulting cross sections for excitation from the three low-lying levels as calculated using 113-level and 279-level MCDF configuration expansion both between themselves as well as with existing data. More than 10% in difference has been found in these comparisons.

Electron-Impact Ionization of Atomic Ions in the NaIsoelectronic Sequence

A database is assembled which contains electron-impact ionizationrate coefficients for selected atomic ions in the Na isoelectronicsequence. The rate coefficients are obtained from a Maxwellianconvolution of distorted-wave cross sections which include directionization of the 2p and 3s subshells, as well as inner-shellexcitations from the 2s and 2p subshells leading to autoionization.These excitation-autoionization contributions can be large for manyNa-like atomic ions. To assist modeling efforts of moderately denseplasmas, the rate coefficients are resolved as to the final state ofthe ionization process. A sample database file is presented forFe15+. The complete database will reside in electronic format the Controlled Fusion Atomic Data Center at ORNL(http://www-cfadc.phy.ornl.gov/data_and_codes/).