Distorted-wave Model Research Articles

Fast computation approach of electron-impact ionization and excitation cross-sections for atoms and ions with medium- and high-<i>Z</i> elements

The atomic data of medium- and high-<i>Z</i> elements, such as electron-impact ionization and excitation cross-sections, possess extensive applications in fields such as fusion science and X-ray interactions with matter. There are atoms and ions in high energy density plasma, with different charge states and energy states ranging from ground states to highly excited states, and the cross-sections of each charge state and energy state need to be calculated. The bottlenecks limiting computational performance are the inevitable relativistic effects of medium- and high-<i>Z</i> elements and the extremely complex electronic configurations. Taking tantalum (Ta) for example, by using the relativistic Dirac-Fock theory and distorted wave model, we compute the electron-impact ionization and excitation cross-sections of Ta from the ground state atom up to Ta<sup>72+</sup> with the incident electron energy range of 1–150 keV. The detailed configuration accounting (DCA) reaction channel cross-sections are derived by summing and weighting the original detailed level accounting (DLA) cross-sections. After examining the data, two regularities are found. In terms of DLA, the pre-averaging DCA cross-sections have varying initial DLA energy levels but are typically close to each other. There is not a straightforward function that can explain the discrepancies between them. In terms of DCA, inner subshells typically contribute very little to the total cross-section as their ionization and excitation cross-sections are orders of magnitude smaller than those of outer subshells. We provide two techniques to reduce the computational costs based on the regularities. To minimize the total number of DLA reaction channels used in the computation, the initial DLA energy levels can be randomly sampled. Through a Monte Carlo numerical experiment, we determine the appropriate number of sampling points that can reduce the total number of DLA channels by an order of magnitude while maintaining a 5% error margin. In terms of impact ionization, since small cross-section DCA channels are insignificant, only a tiny portion of the DCA channels are required to preserve a 95% accuracy of the entire cross-section. It is possible to use the analytical Binary Encounter Bethe (BEB) formula to determine which DCA channels should be neglected before the computation to reduce computational costs. In terms of electron-impact excitation, just the cross-sections of the same excited subshells as the preserved ionized subshells, which are determined in the previous electron-impact ionization (EII) calculations, are needed. Finally, we compare our EII results with theoretical and experimental results. In the low incident electron energy range of below 2 keV, our results accord with the theoretical result of the 6s EII cross-section of the Ta atom and the experimental result of the total EII cross-section of the Ta<sup>1+</sup> ion. In the high energy range of below 150 keV, our results are also consistent with the theoretical result of the 1s EII cross-section of the Ta atom and the experimental result of the 1s EII cross-section of the Cu atom. Our results reasonably match the previous experimental and theoretical results in low-energy range and high-energy range, inner subshell and outer subshell, indicating the accuracy of our calculation. The proposed optimizing strategy can be applied to various medium- to high-<i>Z</i> elements and is compatible to most computation codes.

Application of the semiclassical distorted wave model to the inclusive (d, d′x) reaction

We apply the semiclassical distorted wave model to the deuteroninduced inclusive (d, d′x) reaction. The calculated double differential cross sections (DDXs) as a function of the deuteron emission energy and the scattering angle are compared with experimental data. The calculated DDXs reasonably reproduce experimental data in the small energy-transfer region and at the forward angles. It is found that the refraction, which is the changes in the kinematics of the deuteron inside a nucleus, is necessary to reasonably reproduce the experimental data. We show that the refraction causes the increase/decrease in the differential cross section of the elementary process, hence the DDX.

Interface of equation of state, atomic data, and opacities in the solar problem

ABSTRACT The dependence of the Rosseland Mean Opacity (RMO) on the equation of state and the number of included atomic levels of iron ions prevalent at the solar radiative/convection boundary is investigated. The ‘chemical picture’ Mihalas–Hummer–Däppen (MHD) equation-of-state (EOS), and its variant QMHD–EOS, are studied at two representative temperature–density sets at the base of the convection zone and the Sandia Z experiment: (2 × 106 K, 1023/cc) and (2.11 × 106 K, 3.16 × 1022/cc), respectively. It is found that whereas the new atomic data sets from accurate R-matrix calculations for opacities (RMOP) are vastly overcomplete, involving hundreds to over a thousand levels of each of the three Fe ions considered – Fe xvii, Fe xviii, Fe xix – the EOS constrains contributions to RMOs by relatively fewer levels. The RMOP iron opacity spectrum is quite different from the Opacity Project distorted wave model and shows considerably more plasma broadening effects. This work points to possible improvements needed in the EOS for opacities in high-energy–density plasma sources.

High-energy two-electron transfer in ion-atom collisions

Two-electron transfer by fast heavy nuclei from heliumlike targets is studied. A detailed sequence of comprehensive computations is carried out in a large keV–MeV range of the projectile energies. This set is illustrated with total cross sections for double capture by alpha particles from helium atoms using several frequently applied four-body quantum-mechanical distorted wave models with the correct boundary conditions. The sensitivity of the obtained total cross sections is examined for different choices of the bound and continuum states. Especially at high energies, the influence of the compactness of the bound states is investigated by reference to the mechanism of the velocity matching kinematic double electron capture. Also considered is the dependence of these cross sections on the electronic screening of the projectile and the target nuclear charges in the bound and continuum states. The impact of this electronic shielding on total cross sections is assessed by reference to the corresponding bare nuclear charges in the bound and continuum states. Relative to all the available experimental data (100–6000 keV), the found striking model-dependence implies that two-electron transfer is sharply different from the associated one-electron transfer involving the same colliding particles.

Spatial–Temporal Distribution of the Euphausiid Euphausia pacifica and Fish Schools in the Coastal Southwestern East Sea

The spatial and temporal distribution of euphausiid krill Euphausia pacifica (Crustacea: Malacostraca) and of fish schools were observed along acoustic transects at the southwestern East Sea coastline of Korea. Two-frequency (38- and 120-kHz) acoustic backscatter data were examined from April to July 2010. A decibel identification window (SV 120–38) and school detection algorithm identified Euphausia pacifica and fish schools in the acoustic backscatter, respectively. The E. pacifica was regularly observed in middle of southern waters, where phytoplankton was abundant during spring, and irregularly during summer, when phytoplankton was homogeneously distributed. Using the distorted-wave Born approximation model, the acoustic density we calculated of E. pacifica was higher in spring (April: 75.9 mg m−2, May: 85.3 mg m−2) than in summer (June: 71.4 mg m−2, July: 54.1 mg m−2). The fish schools observed by the acoustic data tended to significantly increase from spring to summer. Although major fish species, such as anchovies and herring, fed on copepods and euphausiids in the survey area, the temporal and spatial distribution of E. pacifica was weakly correlated with the distribution of the fish schools. These findings aid in our understanding of the temporal and spatial distribution dynamics of euphausiids and fish schools in the food web of the coastal southwestern East Sea.

Fully differential analysis of the electron impact ionization of hydrogen in Debye plasmas

In this work, electron impact ionizing collisions on atomic hydrogen embedded in weakly coupled plasmas are studied at impact energies of 80 and 150 eV. Fully differential cross sections calculated by means of a distorted wave model which explicitly considers the screening effect among the three interacting particles in the final state are presented and analyzed. Compared to the unscreened case, clear differences in shape and magnitude are found for the dominant structures, the binary and recoil peaks, suggesting that the role played in the collision by the different particles varies with the Debye screening length. A scaling law for the fully differential cross section in terms of the nuclear charge Z, first proposed by Kornberg and Miraglia in the photo-double ionization context, is shown to also hold for the electron impact ionization of hydrogenic ions in the present screened context.

Absolute triple differential cross sections for low-energy electron impact ionization of biochemically relevant systems: Water, tetrahydrofuran, and hydrated tetrahydrofuran

An experimental procedure is reported, which provides the absolute triple differential cross sections (ATDCSs) for electron-impact ionization of large (bio)molecules. This type of measurements represents the most stringent tests for new or existing theoretical models. We will use this procedure to test the accuracy of the best currently available theoretical models for the problems of electron-impact (65 eV) ionization of the molecules water $({\mathrm{H}}_{2}\mathrm{O})$, tetrahydrofuran $({\mathrm{C}}_{4}{\mathrm{H}}_{8}\mathrm{O})$, and their hydrogen-bonded dimer ${\mathrm{H}}_{2}\mathrm{O}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{C}}_{4}{\mathrm{H}}_{8}\mathrm{O}$. The cross sections were calculated using the molecular three-body distorted-wave (M3DW) model, the multicenter three-distorted-wave (MCTDW) approach, and the multicenter three-distorted-wave using the Ward-Macek approximation (MCTDW-WM). When compared to the new experimental ATDCS results which cover almost the full solid angle of the ejected electron and a broad range of ejected electron energies and projectile scattering angles, it is found that the data for water are generally well reproduced by the M3DW model, while strong deviations in the absolute magnitude of the cross sections are found for the MCTDW. The MCTDW-WM model provides improved agreement over the MCTDW. These theoretical models, however, become less adequate for the ATDCS of ${\mathrm{C}}_{4}{\mathrm{H}}_{8}\mathrm{O}$, in particular concerning the absolute magnitude. Furthermore, we find that a water environment can play a noticeable role for the ionization dynamics in the case of hydrated molecules.

Quantitative comparison of opacities calculated using the R-matrix and distorted-wave methods: Fe xvii

ABSTRACT We present here a detailed calculation of opacities for Fe xvii at the physical conditions corresponding to the base of the Solar convection zone. Many ingredients are involved in the calculation of opacities. We review the impact of each ingredient on the final monochromatic and mean opacities (Rosseland and Planck). The necessary atomic data were calculated with the R-matrix and the distorted-wave (DW) methods. We study the effect of broadening, of resolution, of the extent of configuration sets and of configuration interaction to understand the differences between several theoretical predictions as well as the existing large disagreement with measurements. New Dirac R-matrix calculations including all configurations up to the n = 4, 5, and 6 complexes have been performed as well as corresponding Breit–Pauli DW calculations. The DW calculations have been extended to include autoionizing initial levels. A quantitative contrast is made between comparable DW and R-matrix models. We have reached self-convergence with n = 6 R-matrix and DW calculations. Populations in autoionizing initial levels contribute significantly to the opacities and should not be neglected. The R-matrix and DW results are consistent under the similar treatment of resonance broadening. The comparison with the experiment shows a persistent difference in the continuum while the filling of the windows shows some improvement. This study defines our path to the next generation of opacities and opacity tables for stellar modelling.

Improved theoretical calculations for electron-impact ionization of DNA analogue molecules.

Ionizing interactions between charged particles and molecules of biological relevance have attracted considerable interest in the last decade due to its importance in medical radiation therapy. We have previously calculated triply differential cross sections for five biomolecules in collaboration with experimental groups. We used the molecular 3-body distorted wave approximation for these calculations. For ionization of biomolecules, experimentalists are unable to determine the orientation of the molecule at the time of ionization, which means that the calculated cross sections need to be averaged over all molecular orientations. At the time the calculations were performed, it was not numerically feasible for us to perform proper averaging over orientations, so we introduced the orientation averaged molecular orbital approximation to make the calculations possible. We now have the computational capability to properly perform this average, so, here, we present new results with a proper average over orientations and compare with the previous calculations and experiment. Since the original calculations, results from two different distorted-wave models have also been published and the new results will also be compared with those calculations. Overall, the new results are in better agreement with the experiment.

Distorted wave model for sub-shell electron capture cross sections of noble gases by bare ion impact

SynopsisElectron capture from noble gases (He, Ne and Ar) are investigated in the framework of the quantum-mechanical distorted wave model. In this model, we use an independent electron model taking particular care of the representation of the bound and continuum target states. The results for partial and total capture cross sections are compared with other theoretical calculations and experimental data. The present results are found to be in very good agreement with the available experimental findings.

Cross section scaling for the ionization of H2O by highly charged ions

SynopsisA classical trajectory Monte Carlo model that explicitly considers the ten electrons of the H2O molecule is used to study electron production in collisions involving bare ions. Present results are contrasted to the reported experimental data and to other theoretical results obtained by means of distorted wave models. Focus is made on the energy range 100 (keV/amu)/ZP-1000 (keV/amu)/ZP along which a simple scaling for the net cross section is introduced.

Electron emission in collisions between dressed ions and multielectronic targets: the role of the projectile distortion

SynopsisA further improvement of the CDW and CDW-EIS distorted wave models for ionization by dressed ion impact is made by taking into account the projectile form factor into the projectile distortions.

Ionization of phenol by single electron impact: triple differential cross sections

Triple differential cross sections (TDCS) for the ionization by single electron impact of the highest and next-highest occupied molecular orbitals of phenol are provided in this work. A first Born approach is used, describing the ejected electron by a distorted wave. The molecular wave functions are developed in a single-center form using the computational chemistry program Gaussian. The TDCSs are calculated for an unknown molecular orientation with the proper average (PA) approach and using four different models. In the distorted wave model (DW) the atoms positions do not intervene in the interaction potential between the incoming electron and the molecular target, while in the distorted wave multi-center model (DW-MC) they are taken into account. In the DW-Gamow and the DW-MC-Gamow models, the repulsion between the outgoing electrons is described by adding the Gamow factor to the DW and DW-MC models. In general, all results are in good agreement with the experimental data. A small difference is observed between the DW and DW-MC results in the recoil region. Adding the Gamow factor improves the angular position and the relative amplitude of the two peaks observed in the binary region. When the TDCSs are compared to other theoretical results relying on the orientation averaged molecular orbital (OAMO) approximation, the improved agreement with the experimental data reinforces the importance of the PA approach.

Electron impact ionization of helium, neon and argon at intermediate energies

With a relatively simple distorted-wave model, in which the ejected and the scattered electrons see different residual systems depending on their energies, in this paper we show the calculation of the CPE cross sections for electron impact ionization of He, Ne and Ar. Combined with the ‘maximum interference’ exchange approximation, this model gives results which for Ne and Ar are in better agreement with the experiment than the other existing theoretical models.

Acoustic characteristics of three bladderless fishes

The acoustic characteristics of bladderless fishes were examined by measuring the target strength (TS) of three species, pointhead flounder (flat-shaped), Arabesque greenling (spindle-shaped) and sandeel (cylinder-shaped). TS measurements were collected in a seawater tank (10 × 6 × 5 m) using the EK80 echo sounder (Simrad, Norway) and ES70-7C transducer (Simrad) over a frequency range of 45–90 kHz with a tether method. After TS measurement of the whole fish, we separated the flesh from the body (for pointhead flounder and arabesque greenling) and measured the TS of the head and bones. Pitch angle characteristics were measured from a head-down orientation (−30 deg) to a head-up orientation (30 deg), and TS was processed using Echoview 9 software (Echoview, Australia). TS patterns were examined with respect to orientation using the distorted-wave Born approximation model. The standard length, width, and height of fish were inputted into the model. The three bladderless fishes tested have different body shapes, meaning different areas are exposed to sound waves at the same body length. Therefore, the relationship between TS and the cross-section of the dorsal aspect of bladderless fish is discussed. [Work supported by the Sasakawa Scientific Research Grant from The Japan Science Society.]

Multicenter distorted-wave approach for electron-impact ionization of molecules

We have previously used the molecular three-body distorted-wave model to examine electron-impact single ionization of molecules. One of the possible weaknesses of this approach lies in the fact that the continuum electron wave functions do not depend on the orientation of the molecule. Here we introduce a model called the multicenter molecular three-body distorted-wave (MCM3DW) approach, for which the continuum electron wave functions depend on the orientation of the molecule at the time of ionization. The MCM3DW results are compared with experimental data taken from work by Dorn and colleagues [Ren et al., Phys. Rev. A 91, 032707 (2015); Phys. Rev. A 93, 062704 (2016); Phys. Rev. A 95, 022701 (2017); Phys. Rev. Lett. 109, 123202 (2012); Gong et al., Phys. Rev. A 98, 042710 (2018)] in which they measured triple differential cross sections for single ionization of molecular hydrogen while simultaneously determining the orientation of the ${{\mathrm{H}}_{2}}^{+}$ ion at the time of ionization. Comparisons are also made with previous theoretical calculations. It is found that orientation effects are important for low incident energy electrons. Very nice agreement with experiment and the time-dependent close coupling results is found for an incident electron energy of 26 eV. Orientation effects become relatively unimportant by the time the incident electron energy is 54 eV.

Polarization potential and its effects on (e, 2e) reactions at intermediate energy

In this paper, we propose a new polarization potential model based on second-order quantum perturbation theory to describe polarization effects on (e, 2e) reactions at intermediate energy. Differently from previous models, nine singly excited states are accurately considered in the present model. Compared with other approximate polarization potential models, the present model shows similar asymptotic behavior, but differs strongly in the close-core region. Using all of the polarization potentials in previous third-order distorted-wave Born approximation calculations, good agreement with experiments is only observed for the present potential model, which indicates that the present polarization model may describe the polarization interaction better in the close-core region. Furthermore, we also compare present absolute TDCS with other R-matrix calculations. The improved distorted-wave model shows better predictions for the (e, 2e) reactions at intermediate energy.

Classical and semiclassical simulations of differential single charge exchange in fast alpha-helium collisions

Within the framework of an independent particle model, the differential single charge transfer process in the collision of fast helium ions with neutral helium targets is theoretically studied by means of the classical trajectory Monte Carlo (CTMC) method. Also, the specified reactions are investigated using two semiclassical continuum distorted wave models with eikonal initial and final states. These theories are usually identified as CDW-EIS and CDW-EFS. Using the CTMC theory, both the electron capture and the excitation probabilities are estimated and discussed as functions of the collision impact parameter. Also, the distribution of the final projectile (n, l) states and the impact parameter dependence of the electron transfer to the final n levels are investigated. Using the theories, the projectile angular distribution of the fully differential cross-sections are calculated for several impact energies in the range of 60–630 keV/u for which the experimental data are available. The obtained results are compared to each other and to their corresponding experimental values. In most of the considered cases, comparisons show that the applied treatments are in qualitative agreement with the experimental data.

Triple differential cross sections for the ionization of tetrahydrofuran by electron impact

We provide triple differential cross sections (TDCS) for the ionization of tetrahydrofuran (THF) by single electron impact in coplanar asymmetric kinematics in the intermediate energy regime. For the Cs and C2 THF isomers, the analysis is carried out using (i) the highest occupied molecular orbitals energies available from ab initio calculations, and (ii) the TDCSs computed from a Coulomb wave (CW) and a distorted wave (DW) to describe the ejected electron. The calculated TDCSs using both the CW and DW models are in better agreement with experimental data than those obtained using the molecular three-body distorted wave model. Hence, we show that the developed framework can be applied to a relatively complex molecule and that the proposed models successfully describe the ionization of both THF isomers.

Experimental study on Ti K shell ionization cross sections induced by 8-9.5 keV positrons

Due to lack of experimental data of the inner shell ionization cross sections induced by low-energy positron, advanced theoretical models developed in recent years cannot be correctly evaluated, and the application of slow positron beam technique is greatly limited. Here we present the method of obtaining reliable experiment data of atomic inner-shell ionization cross section by positron impact. In this work, the slow positron beam device is used to generate 8-9.5 keV positron beams impacting on a pure thick Ti target, and the silicon drift detector (SDD) is adopted to collect the X-ray spectra produced by positrons impacting on thick Ti target, and the incident positron numbers are obtained by applying an HPGe detector to on-line collect annihilation photons. Then the experimental characteristic X-ray yields of Ti K shell impacted by 8-9.5 keV positron could be acquired. Meantime, the simulated characteristic X-ray yields are acquired by the PENELOPE program simulating the experiments. In the comparison between the experimental yields and the simulated yields based on two sets of different inner shell ionization cross section database in the PENELOPE code, i.e. the optical data model (ODM) and the distorted-wave Born approximation model (DWBA), there is a large difference between the simulated data from the ODM theoretical model and the experimental values, while the simulated yields from the DWBA theoretical model are in good agreement with the experimental results. Accordingly, a correction factor is introduced to modify the DWBA theoretical model database which is used in the PENELOPE, and then the experimental process is re-simulated. When the simulated yields and the experimental yields are in the highest consistence, the reliable Ti K shell ionization cross sections impacted by 8-9.5 keV positron could be obtained. The biggest advantage of using this method to obtain atomic inner-shell ionization cross section impacted by positron is that the effects of the multiple scattering of incident positrons in the thick target, from the bremsstrahlung and annihilation photons, and other secondary particles on the experimental characteristic X-rays do not need calculating (the calculation method that has been developed previously cannot give the more correct result about the contribution of the multiple scattering of incident positrons, from the bremsstrahlung and annihilation photons, and other secondary particles to characteristic X-rays).