Search Results (1,050)

The critical binding of quantum states in Screened Coulomb Potentials such as Yukawa/Debye, Hulthén, and ECSC (Exponential Cosine Screened Coulomb) potentials is of perennial interest and relevance in many fields of science, ranging from nuclear and particle physics; plasma physics, astrophysics, cosmology, and nuclear fusion; physical chemistry, condensed matter, and materials physics; to synthetic nanostructures and nanophotonics. The purpose of this paper is to heuristically explore two related mysteries, one new, the other more than 50 years old. The solutions to these mysteries have implications for a much broader class of potentials, those addressed by Klaus and Simon. In our recent paper we presented numerical calculations using the Phase Method (PM), which is accurate to 60 digits and to screening lengths $\mathcal{D}\le {10}^3$ au and $l=0$–20 of the critical binding parameters for these potentials and, for Yukawa and ECSC, $l=0$–12 to $\mathcal{D}\le {10}^5$ au, at 30 digits. In doing so, we discovered an anomalous period-40 sawtooth structure in the critical parameters of the ECSC potential that is not observed for the Yukawa potential. In this second paper, we quantitatively explain the origin and periodicity of this newly discovered structure. To do so, we use two complementary approaches: a “neoclassical” (NC) variant of conventional semiclassical phase-space quantization and the PM for very precise fully quantum calculations. The observed period-40 sawtooth structure is quantitatively explained in terms of a novel “tick-tock” mechanism. The periodicity is calculated in terms of the ratio of phase-space integrals for the primary and secondary potential wells. A quartic double-well potential is used as a simple model to further illustrate the tick-tock mechanism. Using the NC method, an approximate expression is derived to predict the locations of tick-tock glitches from higher-order wells; it is confirmed by a PM calculation up to $\mathcal{D}\le {10}^6$ au. The second mystery is a strangely linear dependence of the total number of bound states vs. screening length for both the Yukawa and ECSC potentials. Using the PM, we confirm and extend these empirical relations. We show, using the PM, that an approximate trivariate linear relation between the square root of the critical screening length $\sqrt{D_c}$, state number n, and angular momentum l applies to these potentials. This, plus a geometrical state accumulation argument, solve the second mystery. We show these properties derive from the scaling relation between screening length and coupling constant and, as such, are predicted to be applicable to the whole class of potentials. These results are expected to be of both theoretical interest and experimental relevance when interpreting spectra or calculating thermal properties. The significance of these results, and the applicability of these methods and conclusions to a vast array of related potentials, is briefly discussed. Full article

We present an extensive set of theoretical results for differential, integrated, and momentum-transfer cross sections for the elastic scattering of electrons by zinc, cadmium, and mercury. Our approach is a self-consistent relativistic calculation, with a semi-empirically adjustable cutoff radius of the polarization potential. This study further extends the application of our method of calculations, previously employed for stable inert gases and alkaline-earth metals. Based on the satisfactory agreement of our previous investigations with experimental values and other precise theoretical results, we expect to provide a set of accurate data for Zn, Cd and Hg. Full article

We theoretically study the single ionization of liquid water by impact of fast electrons. A realistic description of the wavefunction for an isolated water molecule in the liquid phase is obtained by means of a Wannier orbital formalism. In this way, we consider ionization from the most external orbitals 1B₁, 2A₁, 1B₂ and 1A₁ of a single liquid water molecule. Triple, double, single differential and total cross sections are computed through a first order model with proper Coulomb conditions for the ionized electron. We compare our calculations with measurements and other theoretical results for liquid and gaseous phases. An analysis of the main features of the cross sections is performed. Previous theoretical works found almost no discrepancies between these observables in spite of the physical dissimilarities of both phases. In this work, we compare our results with other theories and with the available experiments for vapor. We report interesting differences between the differential and total cross sections of the mentioned phases. Full article

Ionization potentials and electron affinities provide the energetic basis for several conceptual density functional theory descriptors, but their use in donor–acceptor maps requires careful distinction between physically bound anions, weak or borderline electron-affinity cases, and formally computed diagnostic states. In this work, a periodic donor–acceptor descriptor map was constructed for main-group atoms from H to Kr using a $\Delta$SCF-DFT framework. Neutral atoms, monocations, and formally defined monoanionic states were evaluated to obtain ionization potentials, electron affinities, and global reactivity descriptors, including electronegativity, chemical hardness, chemical potential, electrophilicity, electrodonating power, and electroaccepting power. The production dataset was calculated at the $\omega$B97X-D4/def2-QZVPPD level and benchmarked against reference atomic data. This protocol reproduced ionization potentials with a mean absolute error of 0.134 eV and electron affinities with a mean absolute error of 0.116 eV for the reference EA set, including the weak calcium case. A functional and basis-set sensitivity analysis using $\omega$B97X-D4/def2-TZVPPD, PBE0/def2-QZVPPD, and PBE0/def2-TZVPPD showed that ionization potentials are comparatively robust, whereas electron affinities are strongly affected by the quality of the diffuse basis set. The normalized donor–acceptor map reproduces chemically intuitive periodic trends, with alkali metals occupying the strong-donor region and halogens defining the strong-acceptor region. The analysis explicitly separates core validation atoms from weak or borderline electron-affinity cases and diagnostic finite-basis anionic states, emphasizing that formally computed negative electron affinities for unbound anions should not be interpreted as physical bound states. The resulting nonrelativistic dataset provides a reproducible atomic descriptor reference for interpreting donor–acceptor behavior in atoms, clusters, superatoms, doped materials, and charge-transfer systems. Full article

We present a theoretical study focused on the photoelectron spectrum of near-infrared (NIR) laser-driven ionization of hydrogen atoms by attosecond pulse trains composed of several HHs of the former. We analyze the effects of increasing the intensity of the NIR probe laser to account for the interference of multiple quantum pathways arising from mainbands formed in ionization by the attosecond pulse train within the strong-field approximation (SFA) beyond the commonly used first-order perturbative (in the NIR laser intensity) reconstruction of attosecond beating by interference of two-photon transitions (RABBIT). The structure of the energy bands formed in the photoelectron spectrum is governed by quantum interferences of the photoelectron wave packet released within one optical cycle of the NIR probe laser field—intracycle interference—and by the number of active high harmonic components, leading to higher-order Fourier contributions as a function of the NIR–XUV relative phase delay. We show that Fourier terms can be interpreted in terms of well-defined semiclassical trajectories. Our results demonstrate a significant departure from the standard two-path quantum-interference RABBIT picture, showing that both the phase-dependent oscillations of mainbands and sidebands and the extracted phase delays depend strongly on the probing laser intensity. The predictions of the SFA reveal that the above-threshold ionization bands exhibit systematic splitting and oscillation patterns as a function of the NIR intensity. SFA predictions are compared with results obtained within ab initio solutions of the time-dependent Schrödinger equation (TDSE), showing an excellent agreement, which evidences the minor effect of the Coulomb potential of the remaining ion on the escaping photoelectron for high energy above-threshold ionization. The precise study of the SFA reference phases is essential for the determination of the effect of the Coulomb potential on the escaping photoelectron for what these findings provide new insights into attosecond chronoscopy in the strong-field regime. Full article

Electron configurations are known to provide valuable insights into the electronic structure and behavior of atoms. They specify which and how the electronic (sub-) shells are occupied, and are thus an essential ingredient for most atomic observables. When combined with the shell model and the successive filling of shells, these configurations help explain the Periodic Table and much of chemical binding. They also establish a qualitative framework for analyzing excitation, ionization and relaxation processes and may facilitate a wide range of astrophysical and plasma simulations. Here, we review the role of electron configurations for understanding atomic behavior in interactions with particles and radiation. In particular, we identify several central requirements for an efficient treatment of configuration lists and define a domain-specific language in order to generate, manipulate and analyze such lists as well as to extract physically relevant information. We also demonstrate the implementation of this language in Jac, the Jena Atomic Calculator. An efficient handling of configurations will refine the coupling of structure codes with the spectral synthesis of plasma radiation, the setup of ionic cascades or even non-LTE plasma simulations. This common framework for dealing with electron configurations therefore improves consistency, reproducibility and scalability of atomic modeling. Full article

Total, momentum-transfer, and differential cross sections, together with spin-polarization (Sherman) functions, are reported for elastic scattering of low-energy electrons from neutral strontium atoms over the energy range 0.001–15 eV. The calculations are performed within a fully relativistic Dirac framework for the continuum states. The target structure is described using multi-configuration Dirac–Hartree–Fock wavefunctions obtained with the GRASP2018 package, while continuum orbitals are generated using the recently developed GRASPC extension. Long-range target polarization effects are incorporated using a dipole model potential, and exchange interactions are treated explicitly for the large and small components of the continuum wavefunctions. Particular attention is given to the ultralow-energy regime, where reliable cross section data for Sr remain limited. The calculated total cross section exhibits a broad maximum near 1 eV, while the momentum-transfer cross section shows a shallow minimum near 0.05–0.06 eV. The differential cross sections are in good agreement with earlier static-exchange-plus-polarization calculations over much of the 1–5 eV range, whereas at lower energies, visible differences appear, especially at forward angles where the results are most sensitive to the polarization interaction. In the ultralow-energy region, the present differential cross sections remain smooth and show no indication of additional low-lying shape resonances within the adopted model. The calculated Sherman functions follow the general trends of earlier theoretical studies at higher energies and decrease rapidly in the sub-eV range. Overall, the present results provide a consistent relativistic dataset for elastic e–Sr scattering at low energies, with emphasis on the near-threshold region. Full article

We study exotic orbits in the photoassociation process by considering both the vibrational and rotational motions in a classical model. In the presence of rotational motion, the exotic orbits possess regular bound segments even when the total energy exceeds the threshold energy of the interaction potential. Such features of the exotic orbits are interpreted by introducing an effective potential. We employ Lagrangian descriptors and escape time to characterize the phase-space structure and show that exotic orbits are distributed around the stable region in the short-range phase space. We further calculate the photoassociation probability. Our work provides new insights into the dynamical mechanisms of photoassociation processes. Full article

In this work, state-selective electron-capture processes in collisions of Ar¹⁶⁺ with ground-state hydrogen are analyzed in classical terms by means of the classical trajectory Z-CTMC method. Oscillations in the n-state-selective charge-exchange cross-sections are observed in the impact-energy range 1–10 keV/u for n-values greater than the $n_{max}$ value at which charge exchange maximizes. The oscillations are ascribed to an electron-swap mechanism between centers previously identified in ion–Rydberg and ion–alkali charge-exchange collisions. A detailed analysis of the structures in the perpendicular momentum-transfer distributions and their association with the different numbers of swaps is developed. Their dynamics in terms of the collisional impact parameters are also presented. Full article

Electron emission from hydrogen atoms induced by antiproton impact at intermediate energies is investigated using the one-centre Basis Generator Method within a semi-classical impact-parameter framework. The formulation employs a single-centre expansion of the time-dependent Schrödinger equation with a pseudostate basis consisting of hydrogenic orbitals acted upon by powers of a Yukawa-regularized potential, providing a compact and effective representation of the electronic continuum. Ionization probabilities are obtained by projecting the time-evolved wavefunction onto Coulomb continuum states, from which energy-differential cross sections (EDCS) are extracted. Exponential piecewise functions are constructed to interpolate between the pseudostate eigenenergies, yielding smooth EDCS profiles for each partial wave. The total EDCS, reconstructed by summing over all partial-wave contributions, exhibits good agreement with results from other pseudostate-based approaches. Full article

A developed method, based on the stationary second-order Rayleigh–Schrödinger many-body perturbation theory in an irreducible tensorial form, allows us to determine the most important core–valence, core, core–core, and valence–valence correlations for any atom or ion with an arbitrary number of valence and core electrons. This paper presents the Feynman diagrams that describe these correlations. Additionally, it provides the rules for obtaining algebraic expressions in an irreducible tensorial form for any Feynman diagram coming from second-order many-body perturbation theory. Whereas some types of the valence–valence and core–valence correlations are described by the three-particle Feynman diagrams, additional developments to calculate the spin-angular parts of these diagrams have been made to the program library librang of the Grasp2018 As an example of the application of the developed method, the atomic calculations of the energy level structure and transition data for Ar II are presented. Full article

Laser-induced breakdown in water-rich biological media results from the interplay between primary photoionization processes and avalanche amplification of free electrons. Understanding this competition is essential for predicting ablation thresholds under ultrashort-pulse irradiation. In this work, we develop an analytical rate-equation model for the buildup of electron density in water-like biological tissues. It combines photoionization and chromophore ionization into a single seed-generation term, while avalanche ionization is described through a cascade gain factor. This formulation provides a framework for describing cascade electron-impact ionization processes in liquid-like media under strong-field excitation. Our approach gives an analytical expression for the temporal evolution of electron density driven by a Gaussian laser pulse and makes it possible to separate the contributions of direct ionization of water and ionization of chromophore centers. The analytical results are compared with numerical simulations that include carrier diffusion, bimolecular recombination and trapping. The comparison clarifies the roles of seed formation and cascade amplification in the growth of the electron population. The predicted dependence of threshold fluence on pulse duration agrees well with experimental data reported for water-like tissues such as the corneal tissues at a wavelength of 800 nm. The model provides a simple analytical picture of ultrafast plasma formation and electron-driven energy deposition in water-like biological media. Full article

Resonant transfer and excitation (RTE) is a correlated two-electron ion–atom collision process mediated by the two-center electron–electron interaction: a projectile electron is excited while a target electron is captured, forming doubly excited states. These states decay via X-ray (RTEX) or Auger (RTEA) emission. For sufficiently fast collisions with light targets, RTE becomes analogous to dielectronic capture (DC)—a key plasma process—and is successfully described by the impulse approximation (IA). Early (1983–1992) RTEX and more stringent, state-selective RTEA measurements provided essential indirect DC cross-section information before direct electron–ion measurements became available. A 1992 review by the first author, focusing on zero-degree Auger projectile spectroscopy (ZAPS) of state-selective KLL D states, validated the IA for low-$Z_p$ ($Z_p\le 9$) projectile ions, yet a puzzling systematic discrepancy remained: IA RTEA cross-sections were consistently larger than experimental, with the disagreement increasing as $Z_p$ decreased. The present article reviews RTEA progress since 1992, including new refinements to IA calculations, an exact analytic IA formulation, and instrumental ZAPS improvements. A methodical analysis demonstrates impressive agreement across measurements spanning both pre- and post-1992 eras, including new experimental results, effectively eliminating previous systematic discrepancies. IA validity is confirmed down to boron ions, with He⁺ and certain Li-like ions remaining the only notable exceptions. Recently, a rigorous quantum mechanical ion–atom collision treatment has emerged: nonperturbative close-coupling calculations of transfer excitation for He-like carbon ions colliding with He confirm the dominance of RTE via two-center electron–electron interactions at large impact parameters, yielding RTEA results in excellent agreement with experiments. Full article

We propose an analytical model and perform numerical simulations to study the time distribution of the characteristic muonic oxygen X-ray emission following muon transfer from muonic hydrogen to oxygen in a H₂ + O₂ gas mixture. The model accounts for all fundamental processes that alter the kinetic energy and spin distribution of muonic hydrogen atoms. The impact of the uncertainties in various experimental parameters on the precision of the computed results is studied in detail by means of the Monte Carlo method. Specifically, we observe the presence of a minimum in the time dependence of the relative standard deviation of X-ray emission for realistic parameter combinations, which can serve as a benchmark for comparing experiments and numerical simulations. Verification against available experimental data reveals the potential of this approach for both description and parameter optimization in the planning and analysis of muonic experiments Full article