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We discuss an extension of the Single-Active-Electron (SAE) approximation in atoms by allowing the model potential to depend on the angular-momentum quantum number ℓ. We refer to this extension as the ℓ-SAE approximation. The main ideas behind ℓ-SAE are illustrated using the helium atom as a benchmark system. We show that introducing ℓ-dependent potentials improves the accuracy of key quantities in atomic structure computed from the Time-Independent Schrödinger Equation (TISE), including energies, oscillator strengths, and static and dynamic polarizabilities, compared to the standard SAE approach. Additionally, we demonstrate that the ℓ-SAE approximation is suitable for quantum simulations of light−atom interactions described by the Time-Dependent Schrödinger Equation (TDSE). As an illustration, we simulate High-order Harmonic Generation (HHG) and the three-sideband (3SB) version of the Reconstruction of Attosecond Beating by Interference of Two-photon Transitions (RABBITT) technique, achieving enhanced accuracy comparable to that obtained in all-electron calculations. One of the main advantages of the ℓ-SAE approach is that existing SAE codes can be easily adapted to handle ℓ-dependent potentials without any additional computational cost. 

We revisit the current status of high-precision calculations for electron-impact excitation of the (1s3s)3,1S states in helium in the low-energy near-threshold regime that is characterized by a large number of resonance features. Having noticed discrepancies between predictions from two previous large-scale calculations for this problem, we report new results and make recommendations regarding the absolute cross-sections that should be used in modeling applications. 

Abstract Introduction: We present an extensive theoretical investigation of the electron impact excitation of doubly-ionized titanium (Ti III) to meet the needs of spectral analysis and plasma modeling. OBJECTIVES: The main objective of this work is to extend the currently scarce database of both structure and collision data for Ti III. METHODS: The calculation was performed in the close-coupling approximation using theB-splineR-matrix method. The multi-configuration Hartree–Fock method in combination withB-spline configuration interaction expansions and the non-orthogonal orbitals technique is employed for accurate descriptions of the target wave functions and adequate accounts of the various interactions between the target states. Relativistic effects are treated at the semi-relativistic Breit-Pauli approximation level. RESULTS: The present close-coupling expansion includes 138 fine-structure levels of Ti III belonging to the $3d^2$, $4s^2$, $4s4p$, $3d4l$( $l=0-3$), $3d5l$( $l=0-3$), $3d6s$, and $3d6p$configurations. Comprehensive sets of radiative and electron collisional data are reported for all of the possible transitions between the 138 fine-structure levels. Thermally averaged collision strengths are determined using a Maxwellian distribution for a wide range of temperatures from ${10}^2$K to ${10}^5$K. The accuracy of the calculated radiative parameters is validated by comparing with available values from the NIST database and previous literature. CONCLUSION: Given the lack of sufficient currently available experimental and theoretical data, the electron impact excitation cross sections of the Ti III fine-structure levels presented here are systematic, extensive, and internally consistent, thus making them suitable for many modeling applications. 

The Atomic, Molecular, and Optical Science (AMOS) Gateway is a comprehensive cyberinfrastructure for research and educational activities in computational AMO science. The B-Spline atomic R-Matrix (BSR) suite of programs is one of several computer programs currently available on the gateway. It is an excellent example of the gateway’s potential to increase the scientific productivity of AMOS users. While the suite is available to be used in batch mode, its complexity does not make it well-suited to the approach taken in the gateway’s default setup. The complexity originates from the need to execute many different computations and to construct generally complex workflows, requiring numerous input files that must be used in a specific sequence. The BSR graphical user interface described in this paper was developed to considerably simplify employing the BSR codes on the gateway, making BSR available to a large group of researchers and students interested in AMO science. 

We present an efficient numerical method to solve the time-dependent Schrödinger equation in the single-active electron picture for atoms interacting with intense optical laser fields. Our approach is based on a non-uniform radial grid with smoothly increasing steps for the electron distance from the residual ion. We study the accuracy and efficiency of the method, as well as its applicability to investigate strong-field ionization phenomena, the process of high-order harmonic generation, and the dynamics of highly excited Rydberg states. 

Abstract The active-particle number density is a key parameter for plasma material processing, space propulsion, and plasma-assisted combustion. The traditional actinometry method focuses on measuring the density of the atoms in the ground state, but there is a lack of an effective optical emission spectroscopy method to measure intra-shell excited-state densities. The latter atoms have chemical selectivity and higher energy, and they can easily change the material morphology as well as the ionization and combustion paths. In this work, we present a novel state-resolved actinometry (SRA) method, supported by a krypton line-ratio method for the electron temperature and density, to measure the number densities of nitrogen atoms in the ground and intra-shell excited states. The SRA method is based on a collisional-radiative model, considering the kinetics of atomic nitrogen and krypton including their excited states. The densities measured by our method are compared with those obtained from a dissociative model in a miniature electron cyclotron resonance (ECR) plasma source. Furthermore, the saturation effect, in which the electron density remains constant due to the microwave propagation in an ECR plasma once the power reaches a certain value, is used to verify the electron density measured by the line-ratio method. An ionization balance model is also presented to examine the measured electron temperature. All the values obtained with the different methods are in good agreement with each other, and hence a set of verified rate coefficient data used in our method can be provided. A novel concept, the ‘excited-state system’, is presented to quickly build an optical diagnostic method based on the analysis of quantum number propensity and selection rules. 

Abstract The circular dichroism (CD) of photoelectrons generated by near-infrared (NIR) laser pulses using multiphoton ionization of excited He⁺ions in the 3p(m= +1) state is investigated. The ions were prepared by circularly polarized extreme ultraviolet (XUV) pulses. For circularly polarized NIR pulses co- and counter-rotating relative to the polarization of the XUV pulse, a complex variation of the CD is observed as a result of intensity- and polarization-dependent Freeman resonances, with and without additional dichroic AC-Stark shifts. The experimental results are compared with numerical solutions of the time-dependent Schrödinger equation to identify and interpret the pronounced variation of the experimentally observed CD. 

Abstract The ionization fraction is a key figure of merit for optimizing the performance of plasma device. This work presents an optical emission spectroscopy (OES) method to determine the ionization fraction in low-temperature xenon plasma. The emission line-ratio of xenon ionic and atomic 6p–6stransitions is used in this method. A comprehensive collisional-radiative model developed in our previous work is employed to describe the relationship between the line-ratios and the plasma parameters. It is found that some special line-ratios have a sensitive relationship to the ionization fraction, e.g. the ratio of the 460.30 nm line and 828.01 nm lines. These line-ratios are selected for the diagnostic method. The method is demonstrated in a magnetized discharge chamber. The axially-resolved emission spectra of the ionization chamber are measured, and from those the ionization fraction along the chamber axis is determined via the OES method. The axially-resolved ionization fraction is found to be dependent on the magnetic field and agrees well with those obtained from a Langmuir probe. In the experiment, the probe is overheated under some conditions, possibly due to the bombardment by energetic particles. In this case, no results can be obtained from the probe, while the OES method can still obtain reasonable results. Combined with optical tomography and spectral imaging technology, the OES method can also provide the spatial distribution of the ionization fraction, which is needed for revealing the discharge mechanisms of plasma devices.