Electron-impact Excitation Cross Sections Research Articles

Relativistic plane-wave Born theory and its application to electron-impact excitation

An exact treatment of the relativistic plane-wave Born (RPWB) cross section for electron-impact excitation is provided for an arbitrary atom or ion. This result represents an improvement over the cross section obtained from the widely used Bethe high-energy theory developed in the 1930s. The results obtained from this RPWB approach can be applied to a broad class of problems in fundamental electron-impact scattering theory. As an illustration, the approach is used to approximate the high-$\ensuremath{\ell}$, partial-wave contribution in more accurate calculations of the excitation cross section, a problem which has been lacking a fully relativistic treatment for more than $20\phantom{\rule{0.3em}{0ex}}\text{years}$.

An investigation of Fe XVI emission lines in solar and stellar extreme-ultraviolet and soft X-ray spectra

New fully relativistic calculations of radiative rates and electron impact excitation cross-sections for Fe XVΙ are used to determine theoretical emission-line ratios applicable to the 251-361 and 32-77 A portions of the extreme-ultraviolet (EUV) and soft X-ray spectral regions, respectively. A comparison of the EUV results with observations from the Solar Extreme-Ultraviolet Research Telescope and Spectrograph (SERTS) reveals excellent agreement between theory and experiment. However, for emission lines in the 32A 9 A portion of the soft X-ray spectral region, there are large discrepancies between theory and measurement for both a solar flare spectrum obtained with the X-Ray Spectrometer/Spectrograph Telescope (XSST) and for observations of Capella from the Low-Energy Transmission Grating Spectrometer (LETGS) on the Chandra X-ray Observatory. These are probably due to blending in the solar flare and Capella data from both first-order lines and from shorter wavelength transitions detected in second and third order. By contrast, there is very good agreement between our theoretical results and the XSST and LETGS observations in the 50-77 A wavelength range, contrary to previous results. In particular, there is no evidence that the Fe XVI emission from the XSST flare arises from plasma at a much higher temperature than that expected for Fe xvi in ionization equilibrium, as suggested by earlier work.

Excitation of K-shell electrons by electron impact

The universal scaling behavior for the electron-impact excitation cross sections of the 2s states of hydrogen- and helium-like multicharged ions is deduced. The study is performed within the framework of non-relativistic perturbation theory, taking into account the one-photon exchange diagrams. Special emphasis is laid on the near-threshold energy domain. The parametrical relationship between the cross sections for excitation of multicharged ions with different number of electrons is established.

Excitation into3p55plevels from the metastable levels of Ar

Measurements of cross sections for electron-impact excitation out of the J=0 and J=2 3p{sup 5}4s metastable levels of argon into nine of the ten levels of the 3p{sup 5}5p manifold are presented in the energy range from threshold to 10 eV. A mixed target of atoms in both metastable levels was created by a hollow cathode discharge. Laser quenching was used to depopulate either one of the metastable levels, allowing separate measurements of the cross sections from each of the two metastable levels. Unlike the metastable excitation cross sections into 3p{sup 5}4p levels, the cross sections into the 3p{sup 5}5p levels are not found to be proportional to optical oscillator strengths.

Merged-beam measurements of absolute cross sections for electron-impact excitation ofS4+(3s2S1→3s3pP1)andS5+(3sS2→3pP2)

Absolute cross sections for electron-impact excitation of the dipole-allowed transitions S{sup 4+} (3s{sup 2} {sup 1}S{yields}3s3p {sup 1}P) and S{sup 5+} (3s {sup 2}S{yields}3p {sup 2}P) were measured near threshold using the merged electron-ion beams energy-loss technique. Although the magnitudes of the measured cross sections are in reasonable agreement with available theoretical data, the experimental data indicate that the contributions of dielectronic resonances in the near-threshold region are underestimated by these calculations.

Fe xiii emission lines in active region spectra obtained with the Solar Extreme-Ultraviolet Research Telescope and Spectrograph

Abstract Recent fully relativistic calculations of radiative rates and electron impact excitation cross-sections for Fe xiii are used to generate emission-line ratios involving 3s23p2–3s3p3 and 3s23p2–3s23p3d transitions in the 170–225 and 235–450 Å wavelength ranges covered by the Solar Extreme-Ultraviolet Research Telescope and Spectrograph (SERTS). A comparison of these line ratios with SERTS active region observations from rocket flights in 1989 and 1995 reveals generally very good agreement between theory and experiment. Several new Fe xiii emission features are identified, at wavelengths of 203.79, 259.94, 288.56 and 290.81 Å. However, major discrepancies between theory and observation remain for several Fe xiii transitions, as previously found by Landi and others, which cannot be explained by blending. Errors in the adopted atomic data appear to be the most likely explanation, in particular for transitions which have 3s23p3d 1D2 as their upper level. The most useful Fe xiii electron-density diagnostics in the SERTS spectral regions are assessed, in terms of the line pairs involved being (i) apparently free of atomic physics problems and blends, (ii) close in wavelength to reduce the effects of possible errors in the instrumental intensity calibration, and (iii) very sensitive to changes in Ne over the range 108–1011 cm−3. It is concluded that the ratios which best satisfy these conditions are 200.03/202.04 and 203.17/202.04 for the 170–225 Å wavelength region, and 348.18/320.80, 348.18/368.16, 359.64/348.18 and 359.83/368.16 for 235–450 Å.

Relativistic Distorted-Wave Calculations of Electron ImpactExcitation Cross Sections of Be-Like C2+ Ions

A fully relativistic distorted-wave program is developed based onthe Grasp92 and Ratip packages to calculate electron impact excitation(EIE) cross sections. As a first application of the program, the EIEcross sections of Be-like C2+ ions from the metastable 1s22s2p3P to 1s22p2 3P excitation and the inner-shell excitationsare calculated systematically. Meanwhile, the correlation effects oftarget states are discussed. It is found that the correlation effectsplay an important role in the low energy EIE cross sections. Anexcellent agreement is found when the results are compared with previouscalculations and recent measurements.

Electron impact excitation of molecules: Calculation of the cross section using the similarity function method and ab initio data for electronic structure

Electron impact excitation cross sections of dipole-allowed transitions in diatomic molecules have been evaluated using the similarity function method allowing one to express cross sections through the oscillator strength of the transition and some universal function of the reduced incident electron energy. The necessary characteristics of the molecular terms involved and transition dipoles were determined by ab initio electronic structure calculations using the multireference configuration interaction technique or relativistic multipartitioning many-body perturbation theory. The results of specific calculations performed for CO and NO in a reasonable agreement with the available experimental data and the results of comprehensive quantum-mechanical calculations.

High-energy electron-impact excitation process: The generalized oscillator strengths of helium

The high-energy electron impact excitation cross sections are directly proportional to the generalized oscillator strengths (GOSs) of the target (an atom or molecule). In the present work, the GOSs of helium from the ground state to $n\phantom{\rule{0.2em}{0ex}}^{1}S$, $n\phantom{\rule{0.2em}{0ex}}^{1}P$, $n\phantom{\rule{0.2em}{0ex}}^{1}D$ $(n\ensuremath{\rightarrow}\ensuremath{\infty})$ and adjacent continuum excited states are calculated by a modified $R$-matrix code within the first Born approximation. In order to treat the bound-bound and bound-continuum transitions in a unified manner, the GOS density (GOSD) is defined based on the quantum defect theory. The GOSD surfaces of $^{1}S$, $^{1}P$, and $^{1}D$ channels are calculated and tested stringently by the recent experiments. With the recommended GOSD surfaces with sufficient accuracy, the GOSDs (i.e., GOSs) from the ground state into all $n\phantom{\rule{0.2em}{0ex}}^{1}S$, $n\phantom{\rule{0.2em}{0ex}}^{1}P$, and $n\phantom{\rule{0.2em}{0ex}}^{1}D$ excited states of helium can be obtained by interpolation. Thus, the high-energy electron impact excitation cross sections of all these excited states can be readily obtained. In addition to the high-energy electron impact excitation cross sections, a scheme to calculate the cross sections in the entire incident energy range is discussed.

Near-threshold absolute angle-differential cross sections for electron-impact excitation of argon and xenon

Absolute angle-differential cross sections for electron-impact excitation of argon and xenon atoms to the lowest four np{sup 5}(n+1)s levels, and the 5p{sup 5}5d[7/2]{sub 3} level in xenon, have been measured and calculated as a function of electron energy up to a few eV above threshold at a fixed scattering angle of 135 degree sign . For argon, very good agreement is observed between the experimental data and predictions from a Breit-Pauli B-spline R-matrix (BSR) method, in which nonorthogonal orbital sets are used to optimize the target description. The agreement is still satisfactory for the more complex xenon target, suggesting that predictions from the BSR model should already be sufficiently accurate for many modeling applications. Nevertheless, the remaining discrepancies indicate the need for further refinement of the theoretical model.

Integral electronic excitation cross sections of hydrogen atom levels

Bombined results on the integral electron impact excitation cross sections of the 1s → 2s, 2p, 3s, 3p, and 3d transitions in the hydrogen atom obtained on the basis of the global approximation of all available data are presented. The parameters of a four-parameter approximation of the dependence of the excitation cross sections on the electron energy are calculated. Although the values of the cross sections reported in different papers differ by several times, the relative variance obtained by us for the 1s → 2s and 2p transitions is about 25%, while that for the 1s → 3s, 3p, and 3d transitions amounts to 30–40%, which corresponds to the real accuracy for these transitions reported to date. The data obtained on the basis of the global approximation seem to be more reliable than the data of any separate study.

Electron Impact Excitation Cross Section Measurement forn= 3 ton= 2 Line Emission in Fe17+to Fe23+

We have measured the electron impact excitation cross sections for the strong iron L-shell 3 {yields} 2 lines of Fe XVIII to Fe XXIV at the EBIT-I electron beam ion trap using a crystal spectrometer and NASA-Goddard Space Flight Centers 6 x 6 pixel array microcalorimeter. The cross sections were determined by direct normalization to the well established cross section of radiative electron capture through a sophisticated model analysis which results in the excitation cross section for the strong Fe L-shell lines at multiple electron energies. This measurement is part of a laboratory X-ray astrophysics program utilizing the Livermore electron beam ion traps EBIT-I and EBIT-II.

Cross-section and rate coefficient calculation for electron impact excitation, ionisation and dissociation of H2 and OH molecules

The weighted total cross-section (WTCS) theory is used to calculate electron impact excitation, ionisation and dissociation cross-sections and rate coefficients of OH, H2, OH+, H2 +, OH- and H2 - diatomic molecules in the temperature range 1500–15000 K. Calculations are performed for H2(X, B, C), OH(X, A, B), H2 +(X), OH+(X, a, A, b, c), H2 -(X) and OH-(X) electronic states for which Dunham coefficients are available. Rate coefficients are calculated from WTCS assuming Maxwellian energy distribution functions for electrons and heavy particles. One and two temperature (θe and θg respectively for electron and heavy particles kinetic temperatures) results are presented and fitting parameters (a, b and c) are given for each reaction rate coefficient: k(θ) = a (θb)exp (-c/θ).

Energy-Dependent Excitation Cross Section Measurements of the Diagnostic Lines of Fe XVII

By implementing a large-area, gain-stabilized microcalorimeter array on an electron beam ion trap, the electron-impact excitation cross sections for the dominant x-ray lines in the Fe XVII spectrum have been measured as a function of electron energy establishing a benchmark for atomic calculations. The results show that the calculations consistently predict the cross section of the resonance line to be significantly larger than measured. The lower cross section accounts for several problems found when modeling solar and astrophysical Fe XVII spectra.

Cross section database for carbon atoms and ions: Electron-impact ionization, excitation, and charge exchange in collisions with hydrogen atoms

A database has been constructed consisting of the recommended cross sections for electron-impact excitation and ionization of carbon atoms and ions C, C +–C 5+, as well as for charge exchange processes between carbon ions C +–C 6+ and hydrogen atoms. We have collected a large amount of theoretical and experimental cross section data from the literature, and have critically assessed their accuracy. The recommended cross sections, the best values for use, are expressed in the form of simple analytical functions. These are also presented in graphical form.

Electron scattering by magnesium: excitation of the 3s3p 1P1 state

Differential cross sections (DCS) for electron-impact excitation of the 3s3p 1P1 state in magnesium at incident electron energies E0 = 10, 15, 20, 40, 60, 80 and 100 eV have been measured and corresponding calculations carried out. Scattered-electron intensities were measured over a wide range of scattering angles (10°–150°) and normalized to the DCSs at 10° experimentally obtained by Filipović et al (2006 Int. J. Mass Spectrom. 251 66). Corresponding calculations have been conducted in the relativistic distorted-wave approximation. Integrated (integral, momentum transfer and viscosity) cross sections are determined by numerical integration of our DCSs. The results are analysed and compared with previous experimental data and theoretical calculations.

Low-energy elastic and inelastic scattering of electrons fromSO2using theR-matrix method

$R$-matrix method is used to calculate elastic differential, integral, and momentum transfer cross sections for electron-$\mathrm{S}{\mathrm{O}}_{2}$ collision. The electron-impact excitation cross sections for first seven low-lying electronic excited states of $\mathrm{S}{\mathrm{O}}_{2}$ molecule from the ground state of $\mathrm{S}{\mathrm{O}}_{2}$ molecule have been calculated for the first time. Sixteen low-lying electronic states of $\mathrm{S}{\mathrm{O}}_{2}$ molecule are included in the close coupling expansion of the wave function of the entire scattering system, which have vertical excitation energies up to $10.51\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Configuration-interaction (CI) wave functions are used to calculate these excitation energies. In our CI model, we keep the core 14 electrons frozen in doubly occupied molecular orbitals $1{a}_{1}$, $2{a}_{1}$, $3{a}_{1}$, $4{a}_{1}$, $1{b}_{1}$, $1{b}_{2}$, $2{b}_{2}$ and the remaining 18 electrons span the relevant active space: $5{a}_{1}$, $6{a}_{1}$, $7{a}_{1}$, $8{a}_{1}$, $9{a}_{1}$, $2{b}_{1}$, $3{b}_{1}$, $3{b}_{2}$, $4{b}_{2}$, $5{b}_{2}$, $6{b}_{2}$, and $1{a}_{2}$. Our calculated dipole moment of the ground state of $\mathrm{S}{\mathrm{O}}_{2}$ at its equilibrium geometry is $0.79\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$, which is in reasonable agreement with the corresponding experimental value $0.64\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ Our calculations detect one bound $\mathrm{S}\mathrm{O}_{2}{}^{\ensuremath{-}}$ state $(^{2}\mathrm{B}_{1})$ at the equilibrium geometry of $\mathrm{S}{\mathrm{O}}_{2}$ molecule. Both shape as well as core-excited shape resonances have been identified in the present work and are correlated with the experimental results on dissociative electron attachment study. A detailed analysis of resonances is provided. Cross sections are reported for the electron impact energy range $0--15\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. All cross section calculations are performed in the fixed-nuclei approximation at the experimental equilibrium geometry of the ground state of $\mathrm{S}{\mathrm{O}}_{2}$ molecule. We have also investigated dependence of resonances on the geometry of $\mathrm{S}{\mathrm{O}}_{2}$ molecule to probe the possible pathways for dissociation of resulting negative ion upon electron attachment. We have excellent agreement of differential, elastic integral, and momentum transfer cross sections calculated in the 16-state $R$-matrix approximation with the available experimental results for electron-impact energy range $0--15\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Our resonant peaks correlate well with the peaks observed in the study of dissociative electron attachment (DEA) of electron with $\mathrm{S}{\mathrm{O}}_{2}$ molecule.

Integral cross sections for electron-impact excitation of the 33S and 31S states of He near threshold

A joint experimental and theoretical study of near-threshold electron-impact excitation of the 33S and 31S states in helium is reported. A high-resolution electron spectrometer is used to study integral cross sections in the energy region of the n = 3 − 5 negative-ion resonances. Photons are detected from the decay of the two states and the observed intensities are normalized to theoretical predictions using a new B-spline R-matrix (close-coupling) method that allows for non-orthogonal orbitals to improve the target description. Remarkable agreement between experiment and theory is demonstrated in both the overall energy dependence of the cross section and the fine details of a wealth of resonance structures. A detailed list of the resonances in the individual partial waves, along with their widths, is presented.

Electronic structure and angular momentum coupling as reflected in electron excitation out of rare-gas metastable levels: Excitation cross sections of krypton

We present measurements of electron-impact excitation cross sections into levels of the $4{p}^{5}5p$ configuration from the $J=0$ and $J=2$ metastable levels of krypton. Metastable-atom targets were generated using two different sources, a hollow-cathode discharge and via charge-exchange collisions between a fast ${\mathrm{Kr}}^{+}$ beam and Cs atoms. The metastable atoms are excited to $4{p}^{5}5p$ levels by a monoenergetic electron beam and the fluorescence from the levels are used to determine the excitation cross sections. Laser quenching of the hollow-cathode target is used to separate the signal contributions from excitation of the two metastable levels. Like excitation from the metastable levels of Ar, cross sections for dipole-allowed excitations are generally larger than ones for dipole-forbidden excitations. Krypton differs from Ar and Ne, however, in having a larger spin-orbit coupling for the $4{p}^{5}$ core so that the energy levels of each excited configuration segregate into two tiers based on the value of the core angular momentum. Cross sections for dipole-allowed excitation with a change in the core angular momentum are not only much smaller than their core-preserving counterparts, but also have different energy dependence. The measured cross sections are compared with recent theoretical calculations and with previous experimental work.

Electron-impact excitation of the 3s3p 1P 1 state of magnesium: Electron scattering at small angles

Absolute differential cross sections for electron-impact excitation of the 3s3p 1P 1 state in magnesium at incident electron energies of E 0 = 10, 13, 15, 20, 40, 60, 80 and 100 eV have been experimentally derived and corresponding calculations have been carried out. The measurements are performed at small scattering angles from 2° to 14°. The forward scattering function method has been used for determination of the absolute values, except at E 0 ≤ 15 eV where the excitation function of the 3s3p 1P 1 state experimentally obtained by [D. Leep, A. Gallagher, Phys. Rev. A 13 (1976) 148] was utilized for normalization. The calculations have been performed in the relativistic distorted-wave approximation. The results are analyzed and compared with other available experimental data and theoretical calculations.