Distorted-wave Calculations Research Articles

State-selective influence of the Breit interaction on the angular distribution of emitted photons following dielectronic recombination

We report a measurement of $KLL$ dielectronic recombination in charge states from ${\mathrm{Kr}}^{+34}$ through ${\mathrm{Kr}}^{+28}$ in order to investigate the contribution of the Breit interaction for a wide range of resonant states. Highly charged Kr ions were produced in an electron-beam ion trap, while the electron-ion collision energy was scanned over a range of dielectronic recombination resonances. The subsequent $K\ensuremath{\alpha}$ x rays were recorded both along and perpendicular to the electron-beam axis, which allowed the observation of the influence of the Breit interaction on the angular distribution of the x rays. Experimental results are in good agreement with distorted-wave calculations. We demonstrate, both theoretically and experimentally, that there is a strong state-selective influence of the Breit interaction that can be traced back to the angular and radial properties of the wave functions in the dielectronic capture.

Effect of Exchange and Absorption Potential in the Distorted Wave Calculation of Electron Impact Excitation of Auto Ionizing State of Rubidium

A thesis is submitted in the partial fulfillment of the requirements for the award of the degree of Masters of Sciencein the School of Pure and Applied Sciences of Kenyatta University September, 2017

Scaling of collision strengths for highly-excited states of ions of the H- and He-like sequences

Emission lines from highly-excited states (n >= 5) of H- and He-like ions have been detected in astrophysical sources and fusion plasmas. For such excited states, R-matrix or distorted wave calculations for electron-impact excitation are very limited, due to the large size of the atomic basis set needed to describe them. Calculations for n >= 6 are also not generally available. We study the behaviour of the electron-impact excitation collision strengths and effective collision strengths for the most important transitions used to model electron collision dominated astrophysical plasmas, solar, for example. We investigate the dependence on the relevant parameters: the principal quantum number n or the nuclear charge Z. We also estimate the importance of coupling to highly-excited states and the continuum by comparing the results of different sized calculations. We provide analytic formulae to calculate the electron-impact excitation collision strengths and effective collision strengths to highly-excited states (n >= 8) of H- and He-like ions. These extrapolated effective collision strengths can be used to interpret astrophysical and fusion plasma via collisional-radiative modelling.

Energy levels, lifetimes and radiative data of Ba XXVI

We report an extensive and an elaborate theoretical study of atomic data for Ba XXVI by considering Singlet, Doublet and Triplet (SDT) electron excitations within N-shell and single excitations from N-shell to O-shell. We have calculated energy levels and lifetimes for lowest 110 fine structure levels by using Multi-configuration Dirac–Fock method (MCDF). We have also considered Quantum Electrodynamics (QED) and Breit corrections in our calculations. We have presented the radiative data for electric and magnetic dipole (E1, M1) and quadrupole (E2, M2) transitions among lowest 110 levels. We have made comparisons of our calculated excitation energies and EUV (Extreme Ultraviolet) transition wavelengths with experimentally observed energy levels and wavelengths and achieved good agreement. We have also computed energy levels by performing similar relativistic distorted wave calculations using Flexible Atomic Code (FAC). Additionally, we have provided new atomic data for Ba XXVI which are not published elsewhere in the literature. We believe that our results may be beneficial in fusion plasma research and astrophysical investigations and applications.

A coincidence study of electron and positron impact ionization of Ar (3p) at 1 keV

Distorted-wave calculations of the triple differential cross section (TDCS) are presented for electron and positron impact ionization of Ar(3p) in coplanar asymmetric geometry at an impact energy of 1 keV and are compared with a recent experiment. The experiment indicates that the positron TDCS is generally larger than the equivalent electron TDCS. It is shown that the magnitude of the TDCS is extremely sensitive to the energy of the ejected electron and that only when the cross section is averaged over energy do we get a reasonable agreement with experiment.

Dirac R-matrix and Breit–Pauli distorted wave calculations of the electron-impact excitation of W44+

With construction of ITER progressing and existing tokamaks carrying-out ITER-relevant experiments, accurate fundamental and derived atomic data for numerous ionization stages of tungsten (W) is required to assess the potential effect of this species upon fusion plasmas. The results of fully relativistic, partially radiation damped, Dirac R-matrix electron-impact excitation calculations for the ion are presented. These calculations use a configuration interaction and close-coupling expansion that opens-up the 3d-subshell; this does not appear to have been considered before in a collision calculation. As a result, it is possible to investigate the arrays, [3d104s2–3d94s24f] and [3d104s2–3d94s4p4d], which are predicted to contain transitions of diagnostic importance for the soft x-ray region. Our R-matrix collision data are compared with previous R-matrix results by Ballance and Griffin as well as our own relativistically corrected, Breit–Pauli distorted wave and plane-wave Born calculations. All relevant data are applied to the collisional-radiative modelling of atomic populations, for further comparison. This reveals the paramount nature of the 3d-subshell transitions from the perspectives of radiated power loss and detailed spectroscopy.

Calculation of energy levels, lifetimes and radiative data for La XXIX to Sm XXXIV

We present the most comprehensive atomic data for La XXIX to Sm XXXIV with single electron excitation from M-shell to N-shell and N-shell to higher shells. We have presented energy levels, lifetimes and radiative data using Multi-configuration Dirac–Fock (MCDF) method for the lowest 27 states belonging to the configuration 3d104l (l=0,1,2,3), 3d105l (l=0,1,2,3,4), 3d106l (l=0,1,2,3,4) and 3d94s2. We have also considered relativistic effects by incorporating quantum electrodynamics (QED) and Breit corrections. We have made comparisons of our presented results with available theoretical as well as experimental results and a good agreement is achieved. Further, we have also reported energy levels by performing distorted wave calculations with fully relativistic flexible atomic code (FAC). The calculations match well with MCDF results. Additionally, we have investigated the effect of nuclear charge on transition wavelength and radiative rates for strong Extreme Ultraviolet (EUV) transitions from n=4→4. We believe that our reported data in this work may be useful in various applications of lanthanide ions related to broad area of research such as applied physics, laser physics and astrophysics etc.

Relativistic Coulomb excitation inMg32near 200 MeV/nucleon with a thick target

Intermediate-energy Coulomb excitation of $^{32}\mathrm{Mg}$ using in-beam $\ensuremath{\gamma}$-ray spectroscopy with a relatively thick lead target was studied at a beam energy of 195 MeV/nucleon at the RIKEN Radioactive Isotope Beam Factory (RIBF). The angular distribution of the inelastic scattering was analyzed with distorted-wave calculations taking into account both the Coulomb and the nuclear excitation contributions. A $B(E2)$ value of 432(51) ${e}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{4}$ was extracted, which agrees with most of the previously reported results obtained at several tens of MeV/nucleon. Our investigation demonstrates that the electromagnetic properties of exotic nuclei can be studied with Coulomb excitation at beam energies of a few hundreds of MeV/nucleon, where a thicker target can be used to increase the excitation yields.

The theoretical studies on the electron-impact single ionization of Se3+

SynopsisWe have performed fully relatively level-to-level distorted-wave (LLDW) calculations for both direct ionization (DI) and excitation autoionization (EA) of ground state Se3+ ion using the flexible atomic code (FAC). Large EA contributions come from the excitations 4p to nl and 3d to nl. Our calculated total DI+EA cross section have been compared with the recent experimental results. It suggests that the contributions of resonace-excitation double-autoionization process (REDA) to electron impact single ionization of Se3+ at the near threshold are more than 25%.

Electron-impact ionization of tungsten ions

SynopsisElectron-impact ionization of tungsten ions has been measured in the energy range from threshold up to 1000 eV. Configuration-averaged distorted wave calculations were used to explain the experimental data.

Influence of excitations to high-nlshells for the ionization process in theW26+ion

It is shown that excitations from the ground configuration to high-$nl$ shells of the ${\text{W}}^{26+}$ ion have a large contribution to the electron-impact ionization process. Large-scale calculations for the excitations to over 900 configurations are performed using the Dirac-Fock-Slater approximation. The investigation includes subconfiguration-average and detailed level-to-level approaches. Our findings illustrate how important it is to study convergence of cross sections for the excitations to the high-$nl$ shells. The obtained results show that the excitations from the $4s$, $4p$, and $4d$ shells to the shells with the orbital quantum number $l=4$ dominate in the indirect process of the ionization. The excitation-autoionization cross sections make about 40% of the total ionization cross sections. Comparison between our data and previous configuration-average distorted-wave calculations for Maxwellian rate coefficients reveals large discrepancies for the direct and indirect parts of the ionization process.

41P1Zn excitation by 80-eV electrons

The electron-photon coincidence method in the coherence analysis version has been applied to characterize electron impact excitation of $4\phantom{\rule{4pt}{0ex}}{}^{1}{P}_{1}$ state of zinc atoms for 80 eV. The experimental values of the Stokes parameters and the electron impact coherence parameters are presented together with convergent close coupling theoretical data. Our results are compared with recently published relativistic distorted-wave approximation calculations.

Electron-impact excitation of silver

We measure the differential cross sections (DCSs) for the electron-impact excitation of the combined (two fine-structure levels) resonant $4{d}^{10}5p\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2,3/2}$ and $4{d}^{9}5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{2}D_{5/2}$ states in silver from the $4{d}^{10}5s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}$ ground state. A comparison with the predictions of the relativistic distorted-wave (RDW) approximation model is carried out. Relativistic distorted-wave calculations are performed for each level separately and are combined to compare with the measurements. Both the experimental and theoretical results are obtained at incident electron energies ${E}_{0}$ of 10, 20, 40, 60, 80, and 100 eV and scattering angles \ensuremath{\theta} from 10\ifmmode^\circ\else\textdegree\fi{} up to 150\ifmmode^\circ\else\textdegree\fi{} (experiment) and from 0\ifmmode^\circ\else\textdegree\fi{} to 180\ifmmode^\circ\else\textdegree\fi{} (calculations). Absolute values for the experimental DCSs are obtained by normalizing relative DCSs to theoretical RDW results at 40\ifmmode^\circ\else\textdegree\fi{} at all energies except at 10 eV, where we performed the normalization of the relative DCSs at 10\ifmmode^\circ\else\textdegree\fi{} to our previous small-angle experimental DCS values [S. D. To\ifmmode \check{s}\else \v{s}\fi{}i\ifmmode \acute{c}\else \'{c}\fi{} et al., Nucl. Instrum. Methods Phys. Res. Sect. B 279, 53 (2012)]. The integrated cross sections, which include integral ${Q}_{\mathrm{I}}$, momentum transfer ${Q}_{\mathrm{M}}$, and viscosity ${Q}_{\mathrm{V}}$ cross sections, are determined by numerical integration of the absolute DCSs.

Experimental and theoretical study of electron-impact ionization plus excitation of aligned H2

We report quadruple differential cross sections for electron-impact ionization of with simultaneous excitation of the ion which will immediately dissociate. The alignment of the molecule is determined by detecting the emitted proton. The first measurements of this type were recently reported (2013 Phys. Rev. A 88 062705). Here we report measurements with much better angular resolution using the COLTRIMS method. Experimental results are compared with molecular 4-body distorted wave calculations and reasonably good agreement between experiment and theory is found.

Collision rates for electron excitation of Mg V lines

Aims. Transition probabilities and electron impact excitation collision strengths and rates for astrophysically important lines in Mg V are reported. The 86 fine-structure levels of the 2s2p, 2s2p, 2p, 2s2p3s, 2s2p3p and 2s2p3d configurations are included in our calculations. The effective collision strengths are presented as a function of electron temperature for solar and other astrophysical applications. Methods. The collision strengths have been calculated using the B-spline Breit-Pauli R-matrix method for all fine-structure transitions among the 86 levels. The one-body mass, Darwin and spin-orbit relativistic effects are included in the Breit-Pauli Hamiltonian in the scattering calculations. The one-body and two-body relativistic operators are included in the multiconfiguration Hartree-Fock calculations of transition probabilities. Several sets of non-orthogonal spectroscopic and correlation radial orbitals are used to obtain accurate description of Mg V 86 levels and to represent the scattering functions. Results. The calculated excitation energies are in very good agreement with experiment and represents an improvement over the previous calculations. The present collision strengths show good agreement with the previously available R-matrix and distorted-wave calculations. The oscillator strengths for E1 transitions normally compare very well with previous calculations. The thermally averaged collision strengths are obtained by integrating total resonant and non-resonant collision strengths over a Maxwellian distribution of electron energies and these are presented over the temperature range log10 Te = 3.2−6.0 K.

Plasma rate coefficients for electron-impact ionization of Xeq+ ions (q = 8, …, 17)

Plasma rate coefficients (PRCs) for electron-impact single ionization of ground-state Xeq+ ions () in the temperature range 2 × 105 − 2 × 107 K have been derived from a combination of experimental cross-section data and results of distorted-wave calculations. For Xe8+ and Xe9+ new measurements were performed and thoroughly analyzed with respect to the contributions from different ionization mechanisms and the effects of long-lived excited states in the parent ion beams that had been employed in the experiments. In the same manner, previously published experimental data for the higher charge states were analyzed to extract the ground-configuration ionization cross sections and to derive the associated PRCs. The resulting temperature-dependent PRC functions were parameterized and the associated parameters are provided in tabular form. With the exception of Xe8+ the absolute uncertainties of the inferred rate coefficients are estimated to be For Xe8+ the uncertainties are due to the necessary correction for strong metastable-ion contributions to the measured cross sections.

R-matrix electron-impact excitation data for the Mg-like iso-electronic sequence

Aims. Emission lines from ions in the Mg-like iso-electronic sequence can be used as reliable diagnostics of temperature and density of astrophysical and fusion plasmas over a wide range of parameters. Data in the literature are quite lacking, there are no calculations for many of the ions in the sequence. Methods. We have carried-out intermediate coupling frame transformation R-matrix calculations which include a total of 283 finestructure levels in both the configuration interaction target and close-coupling collision expansions. These arise from the configurations 1s 2 2s 2 2p 6 3{s, p, d}nl with n = 4, 5, and for l = 0−4. Results. We obtain ordinary collision strengths and Maxwell-averaged effective collision strengths for the electron-impact excitation of all the ions of the Mg-like sequence, from Al + to Zn 18+ . We compare our results with those from previous R-matrix and distorted waves calculations, where available, for some benchmark ions. We find good agreement with the results of previous calculations for the transitions n = 3−3. We also find good agreement for the most intense transitions n = 3−4. These transitions are important for populating the upper levels of the main diagnostic lines.

Photoionization Processes of Ti XIX with J = 1

Breit–Pauli R-matrix and relativistic distorted-wave calculations are carried out for the photoionization of Belike Ti XIX ions at high energies. We calculate the photoionizaton cross sections in the energy region between the 1s 22s 2 S 1/2–1s 23d 2 D 5/2 threshold and many resonance energy levels and widths of 18 Rydberg series.

Gamow-Teller transitions in theA=40isoquintet of relevance for neutrino captures inAr40

Background: The Gamow-Teller response of $^{40}\mathrm{Ar}$ is important for the use of liquid argon as a medium for neutrino detection. An ambiguity about the Gamow-Teller strength for the excitation of ${1}^{+}$ states at 2290 and 2730 keV in $^{40}\mathrm{K}$ results in a significant uncertainty for neutrino capture rates. This ambiguity is caused by the large discrepancy observed between strengths extracted from $^{40}\mathrm{Ar}$($p$, $n$) charge-exchange data and the transition strengths for the analog transitions studied in the $\ensuremath{\beta}$ decay of $^{40}\mathrm{Ti}$.Purpose: This study was aimed at resolving the ambiguity between the results from the $^{40}\mathrm{Ar}$($p$, $n$) charge-exchange and $^{40}\mathrm{Ti}$ $\ensuremath{\beta}$-decay data.Method: Shell-model calculations in the $sd\text{\ensuremath{-}}pf$ shell with a new interaction (WBMB-C) were used to study differences between the structure of the transitions from $^{40}\mathrm{Ar}$ and $^{40}\mathrm{Ti}$. Distorted-wave Born approximation reaction calculations were used to investigate uncertainties in the extraction of Gamow-Teller strength from the $^{40}\mathrm{Ar}$($p$, $n$) data. New high-resolution data for the $^{40}\mathrm{Ar}$($^{3}\mathrm{He}$,$t$) reaction were used to gain further insight into the charge-exchange reaction mechanism and to provide more information to test the validity of the shell-model calculations.Results: The shell-model calculations showed that interference between amplitudes associated with $pf$ and $sd$ components to the low-lying Gamow-Teller transitions, in combination with a difference in Coulomb energy shifts for $^{40}\mathrm{Ar}$ and $^{40}\mathrm{Ti}$, can produce the differences on the scale of those observed between the $^{40}\mathrm{Ar}$ charge-exchange and $^{40}\mathrm{Ti}$ $\ensuremath{\beta}$-decay data. In combination with the difference in nuclear penetrability of the ($p$, $n$) and ($^{3}\mathrm{He}$,$t$) probes, the different contributions from amplitudes associated with transitions in the $pf$ and $sd$ shells are likely also responsible for the observed discrepancy between the ratio of the cross sections for the low-lying ${1}^{+}$ states in the $^{40}\mathrm{Ar}$($p$, $n$) and $^{40}\mathrm{Ar}$($^{3}\mathrm{He}$,$t$) data.Conclusions: On the basis of this study, it is recommended to use Gamow-Teller strengths extracted from the $^{40}\mathrm{Ar}$($p$, $n$) data, not the $^{40}\mathrm{Ti}$ $\ensuremath{\beta}$-decay data, for the calculation of neutrino capture rates. Further theoretical studies are required to achieve a consistent quantitative description for the energy differences between low-lying ${1}^{+}$ states in $^{40}\mathrm{K}$ and $^{40}\mathrm{Sc}$ and the experimentally observed Gamow-Teller strengths.

Atomic data for astrophysics: Ni XI

We present a new large-scale R-matrix scattering calculation for electron collisional excitation of Ni xi, carried out with the intermediate-coupling frame transformation method. The target includes all the main configurations up to n = 4, and is a significant improvement over earlier R-matrix (only three n = 3 configurations) and distorted-wave (DW) calculations. We find significant enhancements in the collision strengths of many of the strong transitions to the n = 3,4 levels. They are due to the resonances that arise within the present large-scale target. This results in significant increases in the predicted intensities of the UV and visible forbidden lines within the 3s 2 3p 5 3d configuration, the strong EUV lines that result from the decays of the 3s 2 3p 5 3d levels to the ground state, and the decays from the n = 4 levels, which are visible in the soft X-rays. We find good agreement between predicted and observed line intensities in the EUV. With the present atomic data, lines from Ni xi can reliably be used for plasma diagnostics. We also revise some level energies and suggest a few new possible identifications.