“Atoms” Special Issue (Electron Scattering from Atoms, Ions and Molecules)

Electron collision physics covers a broad range of processes in atoms and molecules. Understanding these processes can be achieved via experimental and theoretical investigations that support and challenge each other. The last few decades have seen tremendous progress in both the computational and experimental techniques applied to study and model electron-driven processes. Access to modern supercomputer facilities has allowed for the computational modelling of collision processes involving complex atoms and molecules [1,2,3,4,5,6] and this in turn allows for sophisticated modelling and diagnostic assessment of various plasmas [1,7,8]. Applications of electron collision physics range from fusion [3,7], precision measurement and attoclocks [9] to radiation damage and biomedical research [10,11]. This volume collates diverse applications of collision physics, highlighting the importance and power of theoretical and computational techniques while also presenting new experiments which disclose the exciting new developments in collision processes.

Pulsed mater injection in plasma devices is an actively growing research direction with many important applications including fusion, material processing, plasma–surface interactions, plasma thrusters, etc. Sadek et al. in [7] report on experiments with a magneton RF plasma which operated in argon. Pulsed argon gas injection is analyzed by optical emission spectroscopy of argon 2p-1s transitions. The measured line intensities in the 700–900 nm wavelength range are compared with those computed from a collisional–radiative (CR) model in order to determine time-resolved electron temperature in the pulsed injection conditions. In the CR modelling, the population mechanisms under consideration are direct and stepwise electron impact excitation (including cascades from high-energy levels), the while depopulation mechanisms considered are radiative transitions (mitigated by radiation trapping) and quenching reactions induced by collisions with neutral argon atoms. It was demonstrated that the full CR model better describes the optical spectrum than the coronal model, thereby revealing the importance of considering mechanisms involving Ar 1s levels and especially radiation trapping.

Plasma diagnosis via the utilization of optical emission spectroscopy (OES) is a powerful technique used to study plasma kinetics and gain knowledge of the production rate of different species present in the plasma. Information on key plasma parameters, such as electron temperature and electron density, can be obtained by comparing the OES measurements with the results of plasma modelling. To assess plasmas that significantly deviate from the equilibrium conditions, appropriate collisional–radiative (CR) models must be developed. Shukla et al. in [1] report on the development of a such model for Ar and Ar⁺ plasma. Their CR model uses a comprehensive set of cross sections to describe electron impact excitations between different fine-structure resolved levels of Ar and Ar⁺. The cross sections are obtained using relativistic distorted wave theory and are generally in good agreement with more accurate but more restrictive R-matrix calculations. In addition, the electron impact ionization, radiation trapping, diffusion, and three-body recombination processes are considered. Argon plasmas are of particular interest due to a considerable discrepancy between the electron temperature values obtained from the Langmuir probe and the line-ratio estimates in argon helicon plasma. The CR model was applied to an argon helicon plasma reported by Soltani and Habibi [12] for both ICP and helicon modes at various powers.

The interaction of high-energy radiation with condensed matter leads to the production of a large number low-energy electrons and ions via a cascade of ionization processes. In biological matter, these secondary electrons can interact resonantly or directly with biomolecules, causing damage to the DNA and the RNA in terms of either single or double-strand breaks. The complete set of absolute cross sections resulting from low- to intermediate-energy electron collisions with DNA molecules is required for radiation damage modelling, e.g., in Monte Carlo particle track simulation. Such cross sections include the total ionization and dissociative ionization cross sections. However, the cross sections for dissociative ionization, also known as partial cross sections, are very scarce. Rehman and Krishnakumar in [10] have used a crossed beam electron–molecular experiment along with the relative flow technique to measure absolute total and partial ionization cross sections of adenine molecules. The most abundant fragment cations from adenine include C_nH_nN_n⁺ (n = 5, 4, 3, 2, 1) at m/z of 135 (C₅N₅H₅+), 108 (C₄N₄H₄⁺), 81 (C₃N₃H₃⁺), 54 (C₂N₂H₂⁺), 27 (CNH⁺), and HCNH⁺. Good agreement was found with binary-encounter dipole calculations of Huo et al. [13]. The dominance of C_nH_nN_n⁺ (n = 1 to 5), confirmed by the cross section measurements, suggests that the most favored pathway for adenine dissociation via electron ionization is effective due to the loss of HCN molecules in succession.

Dissociative electron attachment (DEA) is the dominant pathway for the interaction of low-energy electrons with molecules. DEA is a resonant process whereby the electron energy is translated to the nuclear motion via the dynamics of the negative ion resonance state (NIRA). A fascinating feature of DEA is site selectivity, which directly correlates with the functional group present at the site and originates from the nature of NIRS as core excited resonances. Tadsare et al. in [11] studied DEA processes in aromatic molecules aniline and benzylamine. These are present in many biological molecules, including DNA bases. It was found that H⁻ and CN⁻ are two dominant channels in the measurements of DEA to aniline and benzylamine, with H⁻ being the most dominant for both molecules. The absolute cross sections, as a function of electron energy for these channels, have been produced from both molecules. The DEA dynamics of the H⁻ channel has been investigated using the velocity slice imaging technique. The kinetic energy and angular distribution of hydride anions, formed in DEA to aniline and benzylamine, have been determined. The results of the investigation show that the functional group-dependent site-selective fragmentation, observed in aliphatic compounds, can also be seen in aromatic compounds.

In most of the electron–atom elastic scattering studies, a model potential approach is used consisting of static, exchange, polarization and absorption potentials [14]. The model potential is then used in the Schrodinger or Dirac equations depending upon whether the calculation is non-relativistic or relativistic. The equations can be solved through partial wave phase shift analysis and scattering phase shifts are obtained. The cross sections are eventually calculated using the phase shifts. In order to calculate model potential, charge density of the atom is required to obtain the static and exchange potentials and polarizability of the atom for calculating the polarization potential. Thus, accurate atomic structure calculations must be performed to establish the charge density and polarizability in addition to solving the scattering problem. Sahoo [2], using relativistic coupled-cluster (RCC) theory [15], via his calculations provided the electron density functions for obtaining the static and exchange potentials of the atoms. He presented the accurate electron densities and electric polarizabilities of Be, Mg, Ne and Ar atoms using two variants of the RCC method. Using these quantities, model potentials for the electron scattering of these atoms can be constructed. He also evaluated the second- and third-order electric dipole and quadrupole polarizabilities using a linear response approach.

Electron scattering cross sections of neutral tin are important for fusion research. Indeed, they have applications as fusion reactors, e.g., ITER. Accurate and comprehensive collision data for electron scattering on both neutral and all ion stages of tin will enable the modelling of plasma containing tin and the identification of tin spectral signatures across the different regions of the fusion plasma [16]. The collision data available for electron scattering on atomic tin are limited to several theoretical works and one experimental study. In view of this, Umer et al. [3] carried out electron scattering cross sections calculations from atomic tin using the relativistic convergent close-coupling method [17]. They presented integrated and momentum transfer cross sections for elastic scattering from the ground and the first four excited states of tin. Various integrated and selected differential cross sections are presented for excitation of the 5p², 5p6s, 5p5d and 5p6p manifolds from the ground state. The total ionization cross sections are calculated from the ground and the first four excited states, accounting for the direct ionization of the 5p valence shell and the closed 5s shell and the indirect contributions from excitation–autoionization.

In the scattering calculations from a projectile on a target, the results are reported in terms of different cross sections. However, the scattering time delay has garnered recent attention because it allows for the characterization of the projectile–target interaction in the temporal domain. In general, it is assumed that scattering interactions constitute instantaneous responses to the incident projectile. In reality, attoseconds (as) of delay in the time scale are needed to determine the specific interaction. This means that, compared to the projectile that does not feel the scattering centre, the scattered particles experience a time lag or time advancement. This phenomenon can be represented through a parameter known as Eisenbud–Wigner–Smith (EWS) time delay [18]. Aiswarya and Jose [4] presented a study on the angular time delay of e-C₆₀ elastic scattering in their paper. They employed the annular square well (ASW) potential to simulate the C₆₀ environment. In fact, the time delay in electron scattering depends on both the scattering angle θ and scattered electron energy E. The contribution from different partial waves to the total angular time delay profile was examined in detail.

There are various ions which are considered for carrying out high-precision measurements such as testing Lorentz symmetry violations, parity nonconservation effects, non-linear isotope shift effects and quantum information, including for the optical atomic clock experiments. In fact, optical lattices, when blended with unique features of optical transitions in the ionic system, lead to the revolution in the clock frequency states. Singly charged alkaline-earth ions are the most eligible candidates for consideration for use high-precision measurements due to several advantages they possess. Since the confinement of Mg⁺ ions in a monochromatic optical dipole trap has become feasible experimentally for several ms, the pathways to implement these ions and thus realize optical lattice clocks have been opened up due to the fact that ions provide more accurate atomic clocks. This is due to the fact that various systematics in the ions can be controlled easily. Jyoti et al. [9] reported the magic wavelengths (λ_magics) [19] and tune-out wavelengths (λ_Ts) of many S_1/2 and D_3/2,5/2 states, as well as transitions among these states of the Mg⁺, Ca⁺, Sr⁺ and Ba⁺ ions that are independent of M values. In many earlier studies, values of the electric dipole (E1) matrix elements were inferred precisely by combining measurements and calculations of λmagic. Similarly, the λ_T values of an atomic state can be used to infer the E1 matrix element [20].

Arretche et al. [5] studied the low-energy scattering of electron–Zn/Cd by applying model exchange and semiempirical polarization potentials. Their study was motivated by the fact that the total cross section measurements for electron scattering by Zn and Cd performed previously and the existence of p-wave shape resonances below 1 eV are well established in the literature. It was suggested that a second d-wave shape resonance could exist in both systems at an energy slightly higher than the one recorded for the p-wave but still below the inelastic threshold. In view of this, they reported the elastic scattering calculations for electron collisions with Zn and Cd atoms below 4 eV using a semiempirical approach [21], as well the scattering length for both targets. Their results show that the d-wave shape resonance can be found in Zn but is absent in Cd.

Campbell et al. [8] reported an interesting study on the inclusion of electron interactions by rate equations in chemical models [22]. The concept of treating subranges of the electron energy spectrum as species in chemical models was investigated. This is intended to facilitate the simple modification of chemical models by incorporating the electron interactions as additional rate equations. It is anticipated that this embedding of the fine details of the energy dependence of the electron interactions into rate equations will yield an improvement in computational efficiency compared to other methods. In their study, the authors proposed and tested a method to simulate nonequilibrium interactions of electrons with gas molecules. In this method, the energy range of the electrons is split into subranges that are then treated in a time-step calculation in the same way as chemical species. As such, the electron interactions can be incorporated easily into existing simulations without new coding being required. The authors found that, in excitation of gas molecules with one vibrationally excited level, the initial energy of the electrons was transferred to the gas molecules until an equilibrium was reached that, with sufficiently small subranges, was very close to the predicted equilibrium values. This equilibrium was then maintained over a long time (10⁶ s), validating the method of calculating the rates for the electron interactions. It was observed that the simulated electron spectrum was also very close to the predicted Maxwellian distribution. Thus, they concluded that their proposed method is capable of producing accurate results. However, the minimum number of subranges, and thus computational efficiency, will need to be assessed for the requirements and circumstances of particular applications.

In recent years, the electron impact ionization of atoms, molecules and ions which are the most fundamental atomic processes has been studied using different theoretical and experimental techniques. Electron impact ionization, also referred to as (e, 2e), involves the collision of an incident electron with a target (either an atom or an ion or a molecule), leading to the ionization of the target [23]. Upon determining the energies and the momenta of all the particles involved in the collision, complete understanding of the ionization process is established. Thus, (e, 2e) collisions have become an important tool for investigating the collision dynamics of targets. The triple differential cross section (TDCS) is the physical quantity that is of prime interest in these studies, providing information about collision processes, ionization mechanisms, and the dependence of the ionization process on the electron kinematics under which ionization is taking place. Pandey and Purohit [6] carried out calculations for the electron impact triple differential cross section (TDCS) and reported the results for nitrogen molecules. The TDCSs have been obtained using distorted wave Born formalism [24] by taking the orientation averaged molecular orbital (OAMO) approximation.

This current volume of the Special Issue presents a collection of interesting papers related to electron scattering from various atoms and molecules and explores the possible applications of these studies and their findings to plasma physics.