Relativistic Distorted-wave Calculations Research Articles

Electron impact excitation of bismuth

Abstract The present study investigates the electron impact excitation of bismuth from the ground state 6p3 4S3/2 to the excited state 6p27s 4P1/2. Motivated by the latest measurements by Marinković et al [J. Phys. B, 49 23 520 (2016)], relativistic distorted wave calculations are performed to obtain the differential and integrated cross sections for incident electron energies at 10, 20, 40, 60, 80, and 100 eVs. These results are compared with the available experimental data and a good agreement is observed. Our results represent the first theoretical work to provide such a comparison. Additionally, we report the generalized oscillator strengths derived from our calculated differential cross sections.

Fully relativistic distorted wave calculations of electron impact excitation of gallium atom: Cross sections relevant for plasma kinetic modeling

Electron impact excitation cross sections of neutral Ga are calculated using the relativistic distorted wave approximation with the aid of multiconfigurational Dirac-Fock wavefunctions. The cross sections are calculated from the fine structure resolved levels of the 4s24p manifold, i.e., from the ground 2P1/2 and the first excited state 2P3/2, to the fine structure resolved levels of the manifolds 4s24pdf, 4s4p2(4P1/2,4P3/2, and 4P5/2), 4s25spdf, 4s26spdf, 4s27spdf, and 4s28spdf for incident electron energies ranging from threshold to 500 eV. Where available, a comparison of the calculated oscillator strengths, transition probabilities, and cross sections with the previously reported results has been performed. The cross sections for the excitation from 4s24p2P1/2 to 4s24f, 4s4p2(4P1/2,4P3/2, and 4P5/2), 4s25f, 4s26f, 4s27df, and 4s28spdf and all the excitation cross sections from 4s24p2P3/2 are calculated and reported for the first time for a wide range of electron energies. Furthermore, the rate coefficients are also calculated using the present cross sections for an electron temperature varying from 0.5 to 5 eV. An analytic fitting of the calculated rate coefficients is provided to facilitate their inclusion in various plasma kinetic models.

Electron-Impact Excitation of the λ190.8 nm and λ179.9 nm Intercombination Lines in the Tl+ Ion

The results of experimental and theoretical studies on electron-impact excitation of the 6s6p P1° 3→6s2 S0 1 (λ190.8 nm) and 6s7s S0 1→6s6p P1° 3 (λ179.9 nm) intercombination transitions in the single-charged thallium ion are presented. The crossed-beams technique was used in combination with a spectroscopic method in the experiment. A distinct structure revealed in the cross-sections of both lines results from electron decay of atomic autoionizing states and radiative transitions from upper ionic levels. The dominant mechanism of the structure formation was the Coster–Kronig process. Relativistic distorted wave calculations were performed to obtain emission cross-sections for the above transitions. The absolute values of the cross-sections were found to be (0.25 ± 0.08) × 10−16 cm2 (λ190.8 nm) and (0.10 ± 0.04) × 10−16 cm2 (λ179.9 nm) at the electron energy of 100 eV.

Electron impact excitation of the Tl + ion: resonance and cascade transitions

Results of experimental and theoretical investigations into the electron-impact excitation of the resonance → 6s 2 1 S 0 (132.2 nm), as well as the cascade 6s7s 1 S 0 → (309.2 nm) and 6p 2 1 D 2 → (150.8 nm) spectral transitions from the ground 6s 2 1 S 0 level in the thallium ion, are presented. Crossed beams of electrons and Tl+ ions in combination with a spectroscopic method were used in the experiment. Measured cross sections have a distinct resonance structure arising mainly from the electron decay of atomic 5d 96s 26p 2, 5d 106s7s(1 S)np (n ⩾ 7), 5d 106s6d(1 D)np (n ⩾ 6), 5d 106s6d(1 D)nd (n ⩾ 6) and ionic 5d 96s 2 np, 5d 96s 2 nd, 5d 96snp (n ⩾ 6) autoionizing levels, as well as radiative transitions from the higher 6s7s 1 S 0, 6s6d 1 D 2, and 6p 2 1 D 2, 1 S 0 ionic levels. Relativistic distorted wave (RDW) calculations are performed to obtain the effective cross sections for the above transitions. The absolute values of the cross sections are found to be 1.39 × 10−16 cm2 at 300 eV for the λ132.2 nm resonance line, and 0.11 × 10−16 cm2 and 0.56 × 10−16 cm2 at 100 eV for the λ309.2 nm and λ150.8 nm lines, respectively. The contribution of the cascade transitions being studied to the effective cross section of the λ132.2 nm resonance line at the energy of 100 eV is about 30%. A calculation using the semi-empirical Van Regemorter formula is also performed to obtain the effective cross section of the resonance λ132.2 nm line. The absolute value of the cross section at 300 eV is found to be nearly the same as that given by the RDW calculation.

Probing for high-momentum protons in He4 via the He4(e,e′p)X reactions

Experimental cross sections for the He4(e,e′p)X reactions in the missing energy range from 0.017 to 0.022 GeV and up to a missing momentum of 0.632 GeV/c at xB=1.24 and Q2=2 (GeV/c)2 are reported. The data are compared to relativistic distorted-wave impulse approximation calculations for the He4(e,e′p)H3 channel. Significantly more events are observed for pm≥0.45 GeV/c than are predicted by the theoretical model, and striking fluctuations in the ratio of data to the theoretical model around pm=0.3GeV/c are possible signals of initial-state multinucleon correlations.5 MoreReceived 11 May 2019Revised 13 March 2022Accepted 14 April 2022DOI:https://doi.org/10.1103/PhysRevC.105.064003©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBreakup reactionsFew-body systemsNucleon-nucleon interactionsPropertiesA ≤ 5Nuclear Physics

Benchmarking intranuclear cascade models for neutrino scattering with relativistic optical potentials

The description of final-state interactions (FSI) in the large phase space probed in neutrino experiments poses a great challenge. In neutrino experiments, which operate under semi-inclusive conditions, cascade models are commonly used for this task, while under exclusive conditions FSI can be treated with relativistic optical potentials (ROP). We formulate conditions under which the ROP approach and cascade model can be directly compared. We feed the NEUT cascade with events from a relativistic distorted-wave impulse approximation calculation that uses the real part of an optical potential. Cuts on the missing energy of the resulting events are applied to define a set of events that can be directly compared to RDWIA calculations with the full optical potential. The NEUT cascade and ROP agree for proton kinetic energies $T_p > 150$ MeV for carbon, oxygen and calcium nuclei when a realistic nuclear density is used to introduce events in the cascade. For $T_p < 100$ MeV the ROP and NEUT cross sections differ in shape and differences in magnitude are larger than 50 \%. Single transverse variables allow to distinguish different approaches to FSI, but due to a large non-QE contribution the comparison to T2K data does not give an unambiguous view of FSI. We discuss electron scattering and argue that with a cut in missing energy FSI can be studied with minimal confounding factors in e.g. $e4\nu$. The agreement of the ROP and NEUT for T2K conditions lends confidence to these models as a tool in oscillation analyses for sufficiently large nucleon kinetic energies. These results urge for caution when a cascade model is applied for small nucleon energies. The assessment of model assumptions relevant to this region are strongly encouraged. This paper provides novel constraints on cascade models from proton-nucleus scattering that can be easily applied to other neutrino event generators.

Extended atomic structure calculations for energy levels and radiative data of Xe XLIII

We report an extensive and elaborate theoretical study of atomic data for Xe XLIII. We have calculated energies for the lowest 141 fin. structure levels by using Multi-Configuration Dirac Fock (MCDF) method. We have also considered Quantum Electrodynamics (QED) and Breit corrections in our calculations. We have presented the radiative data for electric dipole (E1) transitions among lowest 141 levels. We have made comparisons of our calculated excitation energies and EUV (Extreme Ultraviolet) transition wavelengths with the theoretically computed and experimentally observed energy levels and wavelengths at Electron Beam Ion Trap (EBIT) and a good agreement is achieved. 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 Xe XLIII which are not published elsewhere in the literature. We believe that our results may be beneficial in fusion plasma research and detection and investigation of EUV and Soft X-ray (SXR) spectral lines.

Atomic structure calculations, partition function, and thermodynamic parameters for W LXXII and Au LXXVII

In this work, we present a theoretical study of W LXXII (Li-like W71+) and Au LXXVII (Li-like Au76+) by employing a multi-configuration Dirac Fock method approach within the framework of the Dirac-Coulomb Hamiltonian including quantum electrodynamics and Breit corrections. We have presented energies of the lowest 42 fine structure energy levels and radiative data for electric dipole (E1) transitions within the lowest 42 levels. We have made comparisons with available energy levels compiled by NIST and achieved good agreement. We have also discussed discrepancies between our results and other theoretical results with possible reasons of discrepancy. Due to inadequate data in the literature for higher excited states, analogous relativistic distorted wave calculations have also been performed using the flexible atomic code to assess the reliability and accuracy of our results. Furthermore, we have calculated the partition function and thermodynamic properties by the fine structure approach. The variation of the partition function, internal energy, and specific heat with temperature is also discussed. We believe that our presented work and future comparisons with experimental observations will be beneficial in fusion plasma.

Spectroscopic study of EUV and SXR transitions of Cs XXV

We report an extensive and elaborate theoretical study of atomic data for Cs XXV by using multi-configuration Dirac–Fock method and calculated energy levels for the lowest 110 fine structure levels. 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 with theoretically calculated and experimentally observed energy levels. We have studied the effect of correlation by introducing more configurations in our calculations. We have also computed energy levels by performing similar relativistic distorted wave calculations using Flexible Atomic Code. Additionally, we have also provided new atomic data for Cs XXV and identified extreme ultraviolet and soft X-ray spectral lines with gA spectra for E1 and M2 transitions, which are not published elsewhere in the literature. We believe that our results may be beneficial in fusion plasma research and applications.

Electron-impact excitation of Xe+ and polarization of its subsequent emissions

Fully relativistic distorted wave calculations have been performed to study the electron impact excitation of singly ionized xenon from its ground 5p5 (J = 3/2) state to different fine structure excited states of the 5p46s, 5p46p, 5p47s, 5p47p, 5p45d and 5p46d configurations. The ground and excited bound states of Xe+ion have been represented through the relativistic multi-configuration Dirac-Fock wave functions while projectile electron distorted continuum wave functions are obtained by solving the Dirac equations. Results are reported for the excitation cross sections and the corresponding rate-coefficients of the considered different transitions. For each transition, analytic fitting to the calculated cross sections are also provided for plasma modeling purposes. In addition, using the density matrix theory and the calculated different magnetic sub-level excitation cross sections the linear polarization of the radiation emitted by the different optically allowed transitions are obtained and presented.

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.

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.

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.

Dielectronic recombination of berylliumlike Xe50+ ions: Measurement and theoretical calculations

Absolute rate coefficients for dielectronic recombination (DR) of Be-like 136Xe50+ have been measured at the heavy-ion storage ring ESR. The experimental results are compared with relativistic distorted-wave calculations employing the multiconfiguration Dirac-Fock method. Based on the DR measurements, multiple intra-L-shell excitation energies were determined.

Dielectronic recombination of lithiumlike Xe51+ ions: Storage ring experiment and theoretical calculations

Absolute rate coefficients for dielectronic recombination (DR) of Li-like 136Xe51+ have been measured at the heavy-ion storage ring ESR. The experimental results are compared with relativistic distorted-wave calculations employing the multiconfiguration Dirac-Fock method. Based on the DR measurements the 2s-2p1/2 and 2s-2p3/2 excitation energies in Li-like Xe51+ were determined with a relative accuracy of ~400 ppm.

Major role of multielectronicK-Lintershell resonant recombination processes in Li- to O-like ions of Ar, Fe, and Kr

Dielectronic and higher-order resonant electron recombination processes including a K-shell excitation were systematically measured at high resolution in electron beam ion traps. Storing highly charged Ar, Fe, and Kr ions, the dependence on atomic number Z of the contribution of these processes to the total recombination cross section was studied and compared with theoretical calculations. Large higher-order resonant recombination contributions are found, especially for systems with 10<Z<36. In some cases, they even surpass the strength of the dielectronic channel, which was hitherto presumed to be always the dominant one. These findings have consequences for the modeling of high-temperatur plasmas. Features attributed to inter-shell quadruelectronic recombination were also observed. The experimental data obtained for the He-like to O-like isoelectronic sequences compare well with the results of advanced relativistic distorted-wave calculations employing multiconfiguration Dirac-Fock bound state wave functions that include threefold and fourfold excitations.

Excitation of silver by electron impact

Differential cross sections for electron impact excitation of the 5p state of silver have been measured in conjunction with relativistic distorted-wave calculations.

Electron-impact excitation of zinc and ytterbium atoms

Relativistic distorted wave calculations have been carried out to study the electron-impact excitation of Zn and Yb atoms from their ground ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$ state which have outer shell configurations 3${d}^{10}$4${s}^{2}$ and 4${f}^{14}$6${s}^{2}$, respectively. Excitations to the lowest and next-lowest singlet $P$ states viz. (4$s$4$p$, 4$s$5$p$) ${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ in Zn and (6$s$6$p$, 6$s$7$p$) ${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ in Yb along with the (6$s$5$d$) ${}^{1}\phantom{\rule{-0.16em}{0ex}}{D}_{2}$ state in Yb have been considered. Differential and integrated cross section results have been obtained and compared with recent experimental results and theoretical convergent close coupling calculations. In general, good agreement between the theoretical calculations and experimental measurements has been observed.

Super-elastic electron scattering from the laser-excited 41P1 state of calcium at low incident energy

Atomic collision parameters have been measured for electron impact excitation of calcium using the superelastic scattering method, at incident electron energies equivalent to ∼10 eV and ∼12 eV. The parameters Plin, L⊥ and γ were derived for the 41P1 state, and the related Stokes parameters determined. The results are compared to previously published calculations from four different theories: a relativistic distorted wave calculation, an R-matrix calculation, an R-matrix theory using B-splines and a convergent close coupling theory.