Cross Sections For Ionization Of Atoms Research Articles

DeepCSNet: a deep learning method for predicting electron-impact doubly differential ionization cross sections

Abstract Electron-impact ionization cross sections of atoms and molecules are essential for plasma modelling. However, experimentally determining the absolute cross sections is not easy, and ab initio calculations become computationally prohibitive as molecular complexity increases. Existing AI-based prediction methods suffer from limited data availability and poor generalization. To address these issues, we propose DeepCSNet, a deep learning approach designed to predict electron-impact ionization cross sections using limited training data. We present two configurations of DeepCSNet: one tailored for specific molecules and another for various molecules. Both configurations can typically achieve a relative L2 error less than 5%. The present numerical results, focusing on electron-impact doubly differential ionization cross sections, demonstrate DeepCSNet's generalization ability, predicting cross sections across a wide range of energies and incident angles. Additionally, DeepCSNet shows promising results in predicting cross sections for molecules not included in the training set, even large molecules with more than 10 constituent atoms, highlighting its potential for practical applications.

Inner-shell ionization cross sections of atoms by positron impact

The relativistic binary-encounter-Bethe model with Wannier-type threshold law is employed to obtain the inner-shell ionization cross sections of multi-electron atoms (Ni, Cu, Y, Ag, Au, Yb, Ta, and Pb) for positron impact energies from the thresholds up to 105 keV. There is good agreement between the present calculations and the experimental data. The constant in the acceleration term derived from the Wannier law is determined to be 0.2 and 0.5 for the K- and L-shells, respectively.

Rapid Access to Empirical Impact Ionization Cross Sections for Atoms and Ions across the Periodic Table

Electron-impact ionization (EII) processes are essential for modelling high-temperature plasma in quite different research areas, from astrophysics to material science to plasma and fusion research and in several places elsewhere. In most, if not all, of these fields, partial and total EII cross sections are required, and often for a good range of electron energies, in order to determine, for instance, the level population of ions and spectral line intensities in plasma under both local and non-local thermodynamic equilibrium conditions. To obey these needs, various kinds of semi-empirical EII cross sections have been applied in practice, often simply because of the large computational demands in dealing explicitly with two free electrons within the continuum. Here, we expand Jac, the Jena Atomic Calculator, to provide such empirical EII cross sections for (most) atoms and ions across the periodic table. Five empirical models from the recent literature have been implemented to support a simple and rapid access to the partial EII cross sections for electrons from a (partly filled) shell (nℓ)q as well as the total ionization cross sections. We here restrict ourselves to the direct part of the EII cross section, whereas the impact excitation of electrons with subsequent autoionization and the resonant electron capture with double autoionization have been left aside in this first implementation. Rapid access to the (direct) EII cross sections will help already to better understand the role of electron-impact processes in the diagnostics of fusion plasma or the interpretation of astrophysical spectra.

Electron impact ionization in the icy Galilean satellites’ atmospheres

Electron impact ionization is critical in producing the ionospheres on many planetary bodies and, as discussed here, is critical for interpreting spacecraft and telescopic observations of the tenuous atmospheres of the icy Galilean satellites of Jupiter (Europa, Ganymede, and Callisto), which form an interesting planetary system. Fortunately, laboratory measurements, extrapolated by theoretical models, were developed and published over a number of years by K. Becker and colleagues (see Deutsch et al. in Adv At Mol Opt Phys 57:87–155, 2009) to provide accurate electron impact ionization cross sections for atoms and molecules, which are crucial to correctly interpret these measurements. Because of their relevance for the Jovian icy satellites, we provide useful fits to the complex, semiempirical Deutsch–Märk formula for energy-dependent electron impact ionization cross sections of gas-phase water products (i.e., H $$_2$$ O, H $$_2$$ , O $$_2$$ , H, O). These are then used with measurements of the thermal plasma in the Jovian magnetosphere to produce ionization rates for comparison with solar photo-ionization rates at the icy Galilean satellites.

A model potential for computing total ionization cross sections of atoms and molecules by electron impact

A model potential for computing total ionization cross sections of atoms and molecules by electron impact

Constraints from a many-body method on spin-independent dark matter scattering off electrons using data from germanium and xenon detectors

Scattering of light dark matter (LDM) particles with atomic electrons is studied in the context of effective field theory. Contact and long-range interactions between dark matter and an electron are both considered. A state-of-the-art many-body method is used to evaluate the spin-independent atomic ionization cross sections of LDM-electron scattering, with an estimated error about 20%. New upper limits are derived on parameter space spanned by LDM mass and effective coupling strengths using data from the CDMSlite, XENON10, XENON100, and XENON1T experiments. Comparison with existing calculations shows the importance of atomic structure. Two aspects particularly important are relativistic effect for inner-shell ionization and final-state free electron wave function which sensitively depends on the underlying atomic approaches.

X-ray K and L terms estimation in free many-electron atoms and ions

Information about x-ray terms is necessary to calculate an ionization cross section of atoms or ions by intense energy beam of other particles, also for spectroscopic research method, astrophysical applications. In the paper the simple method is offered to estimate x-ray terms of many-electron atoms and ions. It is based on the atomic number and ionization degree scaling of electron orbital energies. The Dirac–Fock data of some ions of three elements (V, Pd, U) are used to construct the required dependence. One can calculate K and L x-ray terms of ions of the same and other elements using the appropriate polynomial approximations. The inaccuracy does not exceed 8%.

Experimental and theoretical cross sections for K -shell ionization of 52Te , 73Ta , and 83Bi by electrons with energies up to 100 keV

In this work we present a combined experimental and theoretical study of $K$-shell ionization by electrons with energies close to the threshold. The ionization cross sections of the $K$ shells of Te, Ta, and Bi atoms have been measured up to 100 keV with uncertainties ranging from 4% to 8%. In turn, calculations have been done using the subconfiguration average distorted-wave (SCADW) method, which includes the full two-body retarded electromagnetic interaction between the projectile and target electrons. The predictions of the SCADW method are in good agreement with the experimental data. In contrast, theoretical cross sections based on first-order perturbation theory where the transverse interaction is computed with plane waves instead of distorted waves underestimate the SCADW values as well as the experimental data. The difference between the two investigated ab initio formalisms grows with atomic number, being 3% for Te, 15% for Ta, and 25% for Bi. An additional comparison of both theoretical approaches with recent measurements for Au $K$ supports the conclusion that the SCADW method reproduces well the experimental $K$-shell ionization cross section of atoms with intermediate to large $Z$ near the threshold.

K-shell ionization cross sections of atoms by muons and pions

The K-shell ionization cross sections of copper and silver atoms by muons and pions with negative and positive charge have been calculated with the classical trajectory Monte Carlo method and the plane-wave Born approximation with corrections for the Coulomb-deflection and binding-energy effects. Both results are in good agreement with each other. The obtained cross sections for muons on copper are also compared with the coupled-channels calculations. The dependence of the K-shell ionization cross sections on the sign of the projectile as well as on the projectile mass is discussed.Graphical abstract

Constraints on millicharged particles with low-threshold germanium detectors at Kuo-Sheng Reactor Neutrino Laboratory

Relativistic millicharged particles ($\chi_q$) have been proposed in various extensions to the Standard Model of particle physics. We consider the scenarios where they are produced at nuclear reactor core and via interactions of cosmic-rays with the earth's atmosphere. Millicharged particles could also be candidates for dark matter, and become relativistic through acceleration by supernova explosion shock waves. The atomic ionization cross section of $\chi_q$ with matter are derived with the equivalent photon approximation. Smoking-gun signatures with significant enhancement in the differential cross section are identified. New limits on the mass and charge of $\chi_q$ are derived, using data taken with a point-contact germanium detector with 500g mass functioning at an energy threshold of 300~eV at the Kuo-Sheng Reactor Neutrino Laboratory.

Abstract ID: 165 Assessment of RBED electron-impact ionization cross sections for Monte Carlo electron transport

Electron-impact ionization cross sections for atoms and molecules are essential for the modelling of radiation effects in a wide range of applications. Current state-of-the-art theoretical calculations are based on the distorted-wave Born approximation (DWBA), which provides an improvement in accuracy and validity range over the plane-wave Born approximation (PWBA) by accounting consistently for exchange effects as well as the distortion of the projectile wave functions by the field of the target atom. However, numerical DWBA calculations are elaborate and slow, and tabulated data only exist for integrated cross sections, whereas differential cross sections are also needed in Monte Carlo simulations. The relativistic binary-encounter-dipole (RBED) model combines classical binary-encounter theory with Bethe’s PWBA-based dipole model without the need for any empirical adjustable parameters [1] . The analytical RBED model provides integrated as well as differential cross sections and is much simpler than the DWBA [2] , requiring as input only the binding energy, average kinetic energy, and optical oscillator strength (OOS) for each atomic subshell. Due to the difficulty of obtaining accurate OOSs, simplified models (known as RBEB and RBEQ) which assume a simple functional form for the OOS have also been proposed, and have been employed almost exclusively in studies since then. Here we calculate electron-impact ionization cross sections for a set of atoms spanning the periodic table using the more accurate RBED model, relying on OOSs obtained numerically with self-consistent potentials as described in [3] . Compared to RBEB, we find that the RBED results show better agreement with DWBA data for the K-shell of all atoms and over the entire energy range. The improvement is more pronounced for lower-Z elements, where the agreement between RBED and DWBA is near perfect. For higher shells, there is also better agreement at high energies for all elements, but near the threshold the improvement is less consistent and depends on the specific atomic shells. The disagreements between the RBED and DWBA cross sections near the threshold are due to the interplay between Coulomb and exchange effects, and highlight the limitations of using semi-empirical scaling factors. In the near future we will compile tables of RBED data for biologically-relevant elements, and ultimately implement them in Monte Carlo track-structure codes.

Electron impact L and M-subshell ionization cross sections for atoms (14 ≤ Z ≤ 92) including the relativistic effects

SynopsisElectron impact inner-subshell (L and M) ionization cross sections for various atoms (14≤Z≤92) are calculated and compared with experimental and other theoretical results.

Calculation of electron-impact ionization cross sections: Bottom-up inductive vs. top-down deductive approaches

This paper attempts to elucidate the relationship between bottom-up inductive and top-down deductive approaches to the calculation of electron-impact ionization cross sections for atoms. Specifically, the ionization cross sections for atomic hydrogen and helium derived from the various approaches are compared in detail.

Projectile and target scaling of the total ionization cross sections of atoms and molecules

A scaling for the total ionization cross sections of atomic and molecular targets by neutral to highly charged projectiles with energies ranging from a few keV/u to many MeV/u is presented, with few free parameters, all velocity independent, and whose values do not vary appreciably for the projectiles and atomic and molecular targets considered here. Another important feature of the proposed scaling is that it has been built considering the characteristics of the collision systems, taking into account the various physical processes that lead to target ionization and the velocity regions where each of them dominates, and performing a smooth transition between them. This scaling describes quite well the existent experimental data covering a broad range of collision systems as diverse as H${}^{+}$ on H, Xe${}^{30+}$ on He, or O${}^{6+}$ on uracil.

Electron impact total ionization cross sections for atoms with Z = 49–54

Spherical complex optical potential formalism and complex scattering potential–ionization contribution are used to generate electron impact total inelastic and total ionization cross section, respectively, for the atoms In, Sn, Sb, Te, I and Xe. Roothaan–Hartree–Fock calculations are used to approximate the atomic orbital wavefunction and hence to model the target charge densities and static potentials for these atoms. The results for the above targets are presented for energies ranging from ionization threshold to 2000 eV. Graphs are plotted with other theories and measurements wherever available. We have obtained a systematic and uniform result with an overall agreement with other data for all the elements presented here.

Calculated cross sections for the single ionization of atoms (N, Cu, As, Se, Sn, Sb, Te, I, Pb) by electron impact

By correcting some primary parameters in the semi-classical Deutsch–Märk (DM) formula, this paper calculates the absolute single electron-impact ionization cross sections of atoms N, Cu, As, Se, Sn, Sb, Te, I and Pb from threshold to 10000 eV. The calculated cross sections are compared with available experimental data and other theoretical results. An excellent agreement was achieved between the calculated and measured cross sections for these atoms over a wide range of impact energies.

Electron-impact ionization of atoms in high-temperature dense plasmas

Electron-impact ionization cross sections for atoms in high-temperature dense plasmas are calculated in a configuration-average distorted-wave method. For those conditions in which the Coulomb coupling parameter is small, we use the Debye-H\"uckel potential to screen the projectile electron from the nucleus and target electrons. Ionization cross sections are calculated for both ${\text{Ne}}^{4+}$ and ${\text{Au}}^{47+}$ at high temperatures and various electron densities up to $1.0\ifmmode\times\else\texttimes\fi{}{10}^{25}\text{ }{\text{cm}}^{\ensuremath{-}3}$. In general we find that as the density increases, the ionization cross section decreases at all incident energies. We also find that as the charge on the atomic ion becomes larger, the relative density effect becomes smaller.

Empirical model for electron impact ionization cross sections of neutral atoms

A simple empirical formula is proposed for the rapid calculation of electron impact total ionization cross sections both for the open- and closed-shell neutral atoms considered in the range 1≤ Z≤92 and the incident electron energies from threshold to about 104 eV. The results of the present analysis are compared with the available experimental and theoretical data. The proposed model provides a fast method for calculating fairly accurate electron impact total ionization cross sections of atoms. This model may be a prudent choice, for the practitioners in the field of applied sciences e.g. in plasma modeling, due to its simple inherent structure.

Geometrical model approximation for ionization cross sections of atoms and ions in ion-atom collisions

The applicability of the geometrical model (GM) proposed in [14, 15] to calculate the ionization probability and cross section of atoms and ions during collisions with ions, including structural ions, was studied at high velocities of partners. The GM represents a version of the classical impulse approximation. It was shown that the GM in all cases under consideration allows estimation of the ionization probability and total corss section of an atom or an ion during collisions with ions with deviations of no more than 50% from the results of the classical Monte Carlo method. GM calculations are rather simple in computation respect and limit the ionization probability by unity at arbitrary impact parameters.

Binary encounter approximation for the electron-impact double ionization cross section of atoms and ions

An binary encounter approximation is formulated for the direct (without any excitation of autoionization levels) double ionization of atoms and ions by electron impacts. Analytical expressions are derived for the cross section, which qualitatively represent the main dependences on the incident electron energy and atomic parameters.