Relativistic Distorted-wave Approximation Research Articles

Fine structure resolved excitation cross sections of singly ionized Ga for the modeling and diagnostics of Ga plasmas

Calculation of electron impact excitation cross sections for singly charged Ga ions plays a crucial role in plasma modeling, facilitating the comprehension of plasma behavior, characteristics, and dynamics in diverse domains, such as astrophysics, fusion research, the semiconductor industry, etc. In the available literature, there is a notable scarcity of, or even a complete absence of, these cross sections. Hence, in the present work, electron impact excitation cross sections are calculated for the transitions from the fine structure resolved energy levels of the configurations 4s2 and 4s4p to the fine structure resolved energy levels of the configurations 4s4p , 4s5s , 4p2 and 4s4d of the singly charged Ga ion (Ga+) using the relativistic distorted wave approximation theory with the target states represented by multi configurational Dirac Fock wavefunctions. The cross sections are calculated for projectile electron energy varying from threshold to 500 eV. Furthermore, the electron impact excitation rate coefficients for all the transitions under investigation are also calculated for electron temperatures ranging from 0.5 to 5 eV. In addition, analytic fitting of the rate coefficients is also performed, providing a practical resource for directly utilizing in plasma modeling applications.

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.

Relativistic calculation of electron impact excitation of tin: cross sections of importance in plasma modeling

The present work includes the calculation of electron impact excitation cross sections for the fine structure resolved transitions in Sn I and Sn II, using the relativistic distorted wave approximation with the aid of Dirac-Fock multiconfigurational wavefunctions. For Sn I, the cross sections are calculated for the excitations from the fine structure resolved energy levels of the manifolds, , , , and including the ground state, to the fine structure resolved levels of , , , , and manifolds for a wide range of projectile electron energy from 0 to 500 eV. Further, the cross sections are also calculated for the excitations of Sn II from the fine structure resolved energy levels of the manifolds, , , , and including the ground state, to the fine structure resolved levels of , , , , and manifolds. All the cross sections for Sn I except for the excitation from the ground state to the fine-structure resolved excited states of , and manifolds and all the cross sections for Sn II are reported for the first time. In order to ensure the consistency of the present calculations, a comparison of the oscillator strengths and transition probabilities is carried out with the available calculations and measurements. The present cross sections are also compared with previous calculations and observed to be in reasonable agreement. The calculated cross sections are of great interest in the modeling and diagnostic of various plasmas such as laser induced plasma, fusion plasma, etc. Further, to ease the use of calculated cross sections, the analytic fitting of the cross sections is also provided.

Flux-integrated semiexclusive cross sections for charged-current quasielastic and neutral-current elastic neutrino scattering off Ar40 and a sterile neutrino oscillation study

Flux-integrated semiexclusive differential cross sections for charged-current quasielastic and neutral-current elastic neutrino scattering on argon are analyzed. The cross sections are calculated using the relativistic distorted-wave impulse approximation with values of the nucleon axial mass ${M}_{A}=1\text{ }\text{ }\mathrm{GeV}$ and 1.2 GeV. The elastic scattering cross sections are also computed for different strange quark contributions to the neutral-current axial form factor. The flux-integrated differential cross sections as functions of reconstructed neutrino energy are evaluated for the far detector of the SBN experiment. The effects of the short baseline neutrino oscillations are taken into account in a $3+1$ framework. We found that cross sections depend on oscillation parameters and the ratio of the measured and predicted cross sections can be used in a sterile neutrino oscillation study.

On the development of relativistic distorted wave approximation for the energies and collision dynamics of atoms or ions subjected to the outside plasma

In this manuscript, we present the development of a relativistic distorted wave method for determining the energies and collision dynamics of plasma-immersed atoms or ions. The methodology is based on the Dirac–Coulomb Hamiltonian, in which contributions from relativity and higher order effects, such as quantum electrodynamics and Breit interaction, are incorporated. The key element in this method is that a modified Debye–Hückel approximation is employed to represent the effect of plasma screening. In order to correctly describe the (bound and continuous state) wave functions, a self-consistent field calculation incorporating the shielding potential is performed within the fully relativistic framework. The particle interaction within the scattering matrix element of the excitation process is described by the shielded Coulomb interaction. The present technique is illustrated by calculations of energy, line shift, transition probability, electron-impact excitation/ionization cross section, and photoionization cross section of a few-electron system confined in plasma environments. The present model is tested and validated against a number of known cases (simulations are made for the He-like Al11+ ion) in the literatures. Numerical results demonstrate that the modifications to the Coulomb potential proposed in the spatial and temporal criteria of the Debye–Hückel approximation allow us to improve the theoretical description of the plasma shielding and thus the dynamical processes in dense plasmas. Comparisons of our computational predictions and the recent experimental measurements are performed. The current work not only has far-reaching implications for our understanding of the dense plasma screening, but also has potential applications in fusion, laboratory astrophysics, and related disciplines.

Electron impact excitation cross section calculations of the fine structure transitions of Mo and their applications in the diagnostics of the laser induced Mo plasma

The current work reports a detailed calculation of electron impact excitation cross sections for the fine structure transitions of Mo from the manifolds 4d 55s, 4d 45s 2, 4d 6 and 4d 55p to the manifolds 4d 55s, 4d 45s 2, 4d 6, 4d 55p, 4d 45s5p, 4d 55d, 4d 56s, 4d 45s6s, and 4d 57s, using the relativistic distorted wave approximation for the applications in plasma modelling. Multi-configurational Dirac–Fock wave functions are used in the calculations. The oscillator strength and cross section results are compared with the previous calculations and measurements. A comprehensive collisional radiative (CR) model is developed and used to characterize laser induced molybdenum plasma to ensure that the calculated cross sections can be used for various plasma modelling applications. The current CR model has taken into account the electron impact excitation and de-excitation processes using the calculated consistent cross sections. The electron induced processes are dominant kinetic processes in the laser induced plasma. Furthermore, the diagnostics of the laser induced Mo plasma is done by coupling the current CR model with the experimental laser induced breakdown spectroscopic measurements of Mal et al (2021 Appl. Phys. B 127 52). The plasma parameter, i.e., electron temperature has been calculated using nine measured intensities of the emission lines of Mo, with wavelengths 406.9, 423.3, 438.2, 453.7, 476.0, 550.7, 553.3, 557.0 and 592.9 nm. The results are also compared with the values reported in the Boltzmann plot at various delay times ranging from 0.5 to 5.0 μs.

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.

Analysis of flux-integrated semiexclusive cross sections for charged-current quasielastic neutrino scattering off Ar40 at energies available at the MicroBooNE experiment

Flux-integrated semiexclusive differential and integral cross sections for quasielastic neutrino charged-current scattering on argon are analyzed. The cross sections are calculated using the relativistic distorted-wave impulse approximation and compare with recent MicroBooNE data. I found that the measured cross sections can be described well within the experimental uncertainties with value of the nucleon axial mass $1&lt;{M}_{A}&lt;1.2\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$. The contribution of the exclusive channel $({\mathbf{\ensuremath{\nu}}}_{\mathbf{\ensuremath{\mu}}},\mathbf{\ensuremath{\mu}}p)$ to the flux-integrated inclusive cross sections is about 50%.

RELATIVISTIC ENERGY APPROACH AND MANY-BODY PERTURBATION THEORY TO COMPUTING ELECTRON-COLLISION CROSS-SECTIONS OF COMPLEX MULTIELECTRON IONS

An advanced relativistic energy approach combined with a relativistic many-body perturbation theory with ab initio zeroth approximation is used to calculate the electron-collision excitation cross-sections for complex multielectron systems. The relativistic many-body perturbation theory is used alongside the gauge-invariant scheme to generate an optimal Dirac-Kohn-Sham- Debye-Hückel one-electron representation. The results of relativistic calculation (taking into account the exchange and correlation corrections) of the electron collision cross-sections of excitation for the neon-like ion of the krypton are presented and compared with alternative results calculation on the basis of the R-matrix method in the Breit-Pauli approximation, in the relativistic distorted wave approximation and R- matrix method in combination with Dirac-Fock approximation

Electron-impact excitation cross sections for Ar and Ar[formula omitted] by unitarized distorted-wave approximation

Unitarization for a relativistic distorted-wave approximation has been made by using two types of scattering matrix for reactance matrix and the electron-impact excitation cross sections for Ar and Ar+ are calculated by the unitarized relativistic distorted-wave method. The unitarization by using the scattering matrix obtained from diagonalization of the reactance matrix significantly reduces the cross sections rather than by using the scattering matrix given from inversion of matrix related to the reactance matrix which brings out better agreement with other more sophisticated R-matrix prediction and experiments at intermediate electron energies for Ar. The cross sections for Ar+ by the effective unitarization are smaller than those by available other prediction using perturbative relativistic distorted-wave approach.

Comparison of recoil polarization in the [formula omitted] process for protons extracted from s and p shells

We present the first measurements of the double ratio of the polarization-transfer components (Px′/Pz′)p/(Px′/Pz′)s for knock-out protons from the s and p shells in C12 measured by the C12(e→,e′p→) reaction in quasi-elastic kinematics. The data are compared to theoretical predictions in the relativistic distorted-wave impulse approximation. Our results show that the differences between s- and p-shell protons, observed when compared at the same initial momentum (missing momentum), largely disappear when the comparison is done at the same proton virtuality. We observe no difference in medium modifications between protons from the s and p shells with the same virtuality in spite of the large differences in the respective nuclear densities.

Analysis of circular polarization of the emitted photon in plasmas

In this paper, a new relativistic distorted wave approximation for cross section describing longitudinally-polarized electron impact excitation of ions in the presence of a strongly coupled plasma is proposed and implemented based on the flexible atomic code. The uniform electron gas model is used to incorporate the plasma effects, which includes the effect of static plasma screening on nuclear charge and the effect of confinement due to the neighbouring ions. For the bound and continuum wavefunctions, the Dirac equation with the ion-sphere potential is solved to account for relativistic effects. In order to check the consistency of the modifications, a self consistent theoretical attempt using the multiconfiguration Dirac-Fock method is also carried out to get the energy levels accounting for the plasma environment within the ion-sphere model. For the collision dynamics, as examples of applications, we investigate the total cross sections, the magnetic sublevels cross sections, and the degrees of circular polarizations of fluorescence radiation after 1s2s01→1s2ss03 and 1s2s01→1s2pp13,1 excitations of Helium-like Fe XXV ion by longitudinally-polarized electron impact with the ion-sphere potential. It is shown that the behavior of the cross sections for a pure Coulomb potential changes rapidly due to the plasma screening effects described by the ion-sphere potential in the process of calculating scattering matrix elements. A detailed, quantitative, comparison between the present results and other available theoretical values is presented for the plasma-free cases, showing good agreement. Our results contribute to a better understanding of the fundamentals of fluorescence polarization in strongly coupled plasmas. Results obtained in this work are beneficial for the diagnostic determination of laboratory plasmas.

Local time dependence of the magnetic sublevel population and polarization of fluorescence radiation

We investigate the time-dependence magnetic sublevel population and polarization of x-ray photoemission for the 1s2p 3P2,1 → 1s2 1S0 lines of an exemplary ion Fe24+ due to impact excitation by a longitudinally polarized electron beam. The analysis is performed based on the fully relativistic distorted-wave approximation and the magnetic sublevel-to-magnetic sublevel collisional-radiative model. The radiative cascade process and Breit interaction are considered to make the results more precise. The time evolution of the magnetic sublevel populations and circular polarization properties are discussed. Our results reveal for the first time that the variations of the magnetic sublevel populations demonstrate a pattern when the time is shorter than 103 ps; some of the populations increase rapidly, while the others remain relatively constant. These dramatic influences also bring about notable changes in the polarization properties of fluorescence emission. We compare our results with other theoretical predictions and find good consistency. This work provides new insight into the fundamentals of x-ray radiation and further prompts the application of fluorescence polarization in plasma diagnostics.

Energy levels, oscillator strengths, radiative transition probabilities, level lifetimes and electron-impact excitation rate coefficients for Ne-like Mo XXXIII

The energy levels, oscillator strengths, radiative decay rates, lifetimes, collision strengths, direct and resonance electron-impact excitation rate coefficients have been computed for the 257 fine-structure levels arising from 1s22s22p5nl and 1s22s2p6n′l′ configurations belonging to the Mo32+ ion with n≤7, l≤4 and n′≤5, l′≤4. The model-potential approach is used for the target ion structure calculations. Additionally, we employ the multiconfiguration Dirac–Hartree–Fock method to further assess the energy levels and transition probabilities. The collision strengths for the electron-impact direct excitation are computed within the relativistic distorted-wave approximation at 34, 135, 680, 1700, 5436, and 12,740 eV scattered electron energy values. We also perform collision calculations at 85, 175, and 450 keV electron energies using the plane-wave approximation and interpolate the reduced cross section within Fano plots, thus accounting for relativistic effects at asymptotic energies. This assures the convergence of Maxwellian integration for effective collision strengths calculation at electron temperatures up to 80 keV. The resonance contribution to the excitation rates is accounted for within the independent process isolated resonance approximation by including Na-like Mo31+ doubly excited autoionization states arising from the 1s227nln′l′ configurations with n≤7,l≤4,n′≤20,l′≤8. Contributions from high n′≥21 Rydberg states to the excitation rate coefficients are included by employing the n′−3 extrapolation law for radiative and autoionization decay rates. Radiative decay of resonances to lower autoionization states followed by autoionization cascade as well as radiative damping via core transitions are included in our model. The highest rate coefficients corresponding to ground state excitations are the 2p–3d allowed and 2p–3p electric monopole transitions, respectively. Intercombination and generally higher-order electric multipole transitions amount to lower excitation rate coefficients but are not to be neglected. Magnetic transitions are only relevant for low electron temperatures since both their direct and resonance contributions to excitation significantly decrease with increasing electron energy. Present results compare well with existing data from literature. The resonance contributions play an important role in the accuracy of rate coefficients, especially for weak forbidden transitions at low electron temperatures. These results may be useful in fusion related plasmas, astrophysics and fundamental physics.

Cross sections by electron impact excitation and ionization of tungsten ions, W39+

Excitation cross sections by electron impact of tungsten ions, W39+, have been calculated using R-matrix method for a configuration state list consists of [Ar]3d104s24p5, [Ar]3d104s24p44l, (l = d, f), and [Ar]3d104s24p45l′, l′ = s, p. A set of configuration state functions (CSFs) with 2-electron excitations up to 5l orbitals have been included within the MCDF-calculations of the used radial integrals of collisional excitations. R-matrix calculations of collision strength and cross section have been executed for the intercombination transitions between 4p5, 4p44d, and 4p44f at different angular momenta using DARC code. Resonance cross section have been observed at low energy of incident electron in the range of ∼5=-40 Ryd, however, the strong lines limited between 5 and 25 Ryd. The relativistic distorted-wave (DW) approximation, Coulomb–Born-Exchange (CBE) approximation, and the Binary-Encounter-Dipole (BED) theory have been used to calculate the electron impact ionization (EII) of the present ion. The accuracies of the present results are estimated by comparing R-matrix calculations with the available literature.

Testing of quasi-elastic neutrino charged-current and two-body meson exchange current models with the MiniBooNE neutrino data and analysis of these processes at energies available at the NOvA experiment

The charged-current quasi-elastic (CCQE) scattering of muon neutrinos on a carbon target is analyzed using the relativistic distorted-wave impulse approximation (RDWIA) taking into account the contribution of the two-particle and two-hole meson exchange current ($2p-2h$ MEC) to the weak response functions. A fit the RDWIA+MEC model to the MiniBooNE neutrino data is performed and the best fit value of nucleon axial mass $M_A=1.2 \pm 0.06$ GeV is obtained. We also extract the values of the axial form factor $F_A(Q^2)$ as a function of the squared momentum transfer $Q^2$ from the measured $d\sigma/dQ^2$ cross section. The flux-integrated CCQE-like differential cross sections for neutrino scattering at energies of the NOvA experiment are estimated within the RDWIA+MEC approach.

Linear polarization of the dielectronic recombination Kα satellite lines in Li-like [formula omitted

The degree of linear polarization of the dielectronic recombination Kα satellite lines in Li-like Au76+ is obtained within the density matrix formalism based on the relativistic atomic data computed via relativistic distorted wave approximation. In the absence of accurate laboratory wavelength measurements for the K-shell resonance lines in gold ions, the atomic data for the He-like Au77+ target ion were computed in a systematic approach and compared with existing semi-relativistic Breit-Pauli calculations [S. Nahar, A.K. Pradhan, C. Sur, JQSRT 2008;109:1951]. The computation for the recombined Au76+ ion comprises 915 fine-structure levels arising from 1s2nl, 1s2snl, 1s2pnl, and 1s3l3l′ configurations, with n ≤ 9 and l ≤ 4, l′ ≤ 2, which yield 731 Kα transitions of type 1s2pnl−1s2nl within 0.17486 to 0.18776 Åspectral range. The degree of linear polarization for the overall Kα satellites as well as for each individual line is computed. Present results show how radiation from neighboring resonances gives peaks of local minima or maxima in the polarization when plotted against the kinetic energy of the incoming electron. Interference effects occurring for bright lines emitted from spatially close resonances result in depolarization of the radiation and displacement of the polarization peaks. Present quantitative results are useful for gold plasma diagnostics and fundamental physics .

Angular distribution and polarization of X-ray radiation in highly charged He-like ions: hyperfine-induced transition

The angular distribution and polarization properties of the X-rays produced by the hyperfine-induced transition are investigated within a fully relativistic distorted-wave approximation. The calculations are performed for the 1s2p3∕2 3P2F i = 3/2 → 1s2 1S0F f = 1/2 component of the Kα1 decay for highly charged He-like 119Sn48+ and 207Tl79+ ions with nuclear spin I = 1/2 following impact excitations by an un-polarized and a completely longitudinally-polarized electron beam, respectively. The Breit interaction and mutipole mixing between the leading M2 decay and the hyperfine-induced E1 decay corrections to both linear and circular polarizations of the emitted X-ray radiations are evaluated. All these effects are found to be significant and may potentially explain the disagreement between the theories and experiments related to the polarization properties of the X-ray radiation.

Quasielastic neutrino charged-current scattering off C12 : Effects of the meson exchange currents and large nucleon axial mass

The quasi-elastic scattering of muon neutrino and electrons on a carbon target are analyzed using the relativistic distorted-wave impulse approximation (RDWIA). We also evaluate the contribution of the two-particle and two-hole meson exchange current ($2p-2h$ MEC) to electroweak response functions. The nuclear model dependence of the (anti)neutrino cross sections is studied within the RDWIA+MEC approach and RDWIA model with the large nucleon axial mass. It is shown that the results for the squared momentum transfer distribution $d\sigma/dQ^2$ and for invariant mass of the final hadronic system distribution $d\sigma/dW$ obtained within these models are substantially different.