Screened Coulomb Potentials Research Articles

Enabling attractive-repulsive potentials in binary-collision-approximation monte-carlo codes for ion-surface interactions

Binary Collision Approximation (BCA) codes for ion-material interactions, such as SRIM, Tridyn, F-TRIDYN, and SDtrimSP, have historically been limited to screened Coulomb potentials even at low energies due to the difficulty in numerically solving the Distance of Closest Approach (DOCA) problem for attractive-repulsive potentials. Techniques such as direct n-body simulation or modifications to Newton’s method are either prohibitively costly or not guaranteed to work for all potentials. Advanced rootfinding techniques, such as companion matrix solvers, offer a solution. For many attractive-repulsive potentials, however, a companion matrix cannot be used directly, because there is no way to put the associated functions into a monomial basis form. A complementary technique is proxy rootfinding—by finding the best-fit polynomial approximant of a function, the zeros of the approximant can be guaranteed to be close to the zeros of the function. Using the Chebyshev basis and grid offers additional guarantees with regards to the quality of the approximation, the speed of convergence, and the avoidance of Runge’s phenomenon. By finding Chebyshev interpolants and using the Chebyshev-Frobenius companion matrix, the zeros of any real function on a bounded domain can be found. Here we show that using an Adaptive Chebyshev Proxy Rootfinder with Automatic Subdivision (ACPRAS) with appropriate scaling functions, numerical issues presented by attractive-repulsive potentials, including those of scale, can be handled. Using these techniques, we show that it is possible to include any physically reasonable interatomic potential in a BCA code, and to guarantee correctness of the resulting scattering angle calculations.

Critical screening parameters of one-electron systems with screened Coulomb potentials: circular Rydberg states

The critical screening parameters (λ c ) of one-electron systems in circular states under short-range screened Coulomb potentials (SCPs) are investigated using the generalized pseudospectral method. High-precision values of λ c are obtained for bound states with the principal quantum number n up to a thousand. The polynomial fittings based on the numerical values indicate that the high-Rydberg limits of the n 2-scaled critical screening parameters, i.e. , are equal to , , and , respectively, for the Debye–Hückel, Hulthén, and exponential cosine SCPs. It is surprisingly found that these high-Rydberg limits can be well-reproduced from Bohr’s correspondence principle together with the semi-classical model of the hydrogen atom. We further show that both the present numerical calculations and the semi-classical analysis can be extended to other short-range potentials such as the generalized exponential, Lennard–Jones, modified Pöschl–Teller, shifted Morse, Woods–Saxon, and Manning–Rosen potentials that attract wide interest in atomic, molecular, and nuclear physics.

Formation of Antihydrogen Ion in Positronium-Antihydrogen Collision with Screened Coulomb Potential

Formation of Antihydrogen Ion in Positronium-Antihydrogen Collision with Screened Coulomb Potential

Hyperpolarizabilities of hydrogenlike atoms in Debye and dense quantum plasmas.

The hyperpolarizabilities of the hydrogenlike atoms in Debye and dense quantum plasmas are calculated using the sum-over-states formalism based on the generalized pseudospectral method. The Debye-Hückel and exponential-cosine screened Coulomb potentials are employed to model the screening effects in, respectively, Debye and dense quantum plasmas. Our numerical calculation demonstrates that the present method shows exponential convergence in calculating the hyperpolarizabilities of one-electron systems and the obtained results significantly improve previous predictions in the strong screening environment. The asymptotic behavior of hyperpolarizability near the system bound-continuum limit is investigated and the results for some low-lying excited states are reported. By comparing the fourth-order corrected energies in terms of hyperpolarizability with the resonance energies using the complex-scaling method, we empirically conclude that the applicability of hyperpolarizability in perturbatively estimating the system energy in Debye plasmas lies in the range of [0,F_{max}/2], where F_{max} refers to the maximum electric field strength at which the fourth-order energy correction is equal to the second-order term.

О применимости универсальной функции Линдхарда для описания сечений рассеяния атомных частиц

It is shown that the application of the universal Lindhard function for calculating the scattering cross section of atomic particles is, as a rule, limited to the region of scattering angles less than 20. The results obtained for various popular interaction potentials are compared with the available experimental data. It is shown that the presence of inelastic channels in scattering leads to the appearance of additional maxima in the scattering cross section. Recommendations are given on the use of the universal Lindhard function to describe quasi-elastic scattering in the region =·sin(/2)>0.01,  is the reduced impact energy,  is the scattering angle. At high energies, the scattering is well described by screened Coulomb potentials, and the application of the Lindhard function provides an accuracy of 10% for calculating the scattering cross sections.

Critical screening parameters of one-electron systems with screened Coulomb potentials: high Rydberg limit

We develop an efficient numerical method to directly calculate the critical screening parameters for one-electron systems with Hulthén and Debye–Hückel screened Coulomb potentials (SCPs). Compared to indirect methods, which locate the critical screening parameters via searching the potential parameters with near-zero energy, the method developed in this work directly calculates the critical screening parameters as eigenvalues of a generalized eigenvalue problem. This feature allows us to simultaneously determine the critical parameters for bound states from low-lying excitation to high-lying Rydberg limit with high accuracy. The method is applied to SCPs to investigate the asymptotic behavior of critical screening parameters as the principal quantum number n approaches infinity. It has been shown that the critical screening parameters in Hulthén and Debye–Hückel potentials follow the 2n −2 and 4n −2/π asymptotic laws, respectively, and that the orbital angular momentum affects the higher-order coefficients linearly.

Double quantum ionization cross-sections for more general exponential cosine screened coulomb potential

Double-quantum ionization cross-sections for hydrogen atom have been calculated for the more general exponential cosine screened coulomb (MGECSC) potential. The ionization cross-sections are calculated as a function of the wavelength of the incident photons, as well as the potential parameters, using linearly and circularly polarized radiation. The transition matrix elements are calculated using the efficient pseudostate summation technique which has proved to be very accurate in these calculations. Numerical data is also presented for the double-quantum ionization cross-sections for hydrogen atom under the effect of MGECSC potential.

A method to predict texture effect on ion beam channeling analysis of polycrystals and the application to study the mosaic spreading effect in highly oriented pyrolytic graphite

We propose a method to convert the channeling Rutherford backscattering spectrum yield map of a single crystal to a polycrystal through a matrix rotation technique. The rotation matrix is determined by the deviation of the crystal axial direction from the original z axis. The final yield map is created after averaging the rotated yields using the texture function as the weight factor. For highly oriented pyrolytic graphite (HOPG) exhibiting mosaic spread, the method leads to a Gaussian kernel averaging of the map obtained from a single crystal. The yield map of a single crystal is obtained by a simulation of ion trajectories in a potential field described by Moliere screened Coulomb potentials. Yield maps are calculated under variousσ values (standard deviations of mosaic spread). The simulated results are compared with experimental results obtained using 1.2 MeV alpha particle. σ is extracted through the best fitting, demonstrating that the method can be used to obtain texture details. The effects of mosaic spread on minimum yield χmin and the half-width at half maximum of angular scans ψ1/2 are systematically modeled and compared with previous theoretical equations. The study also shows that previous theoretical equations are valid only at small σ values. The proposed method can be applied to any type of polycrystal and is not limited to HOPG. It provides near-surface mosaic spread and crystallography information with a longitudinal depth resolution of tens of nanometers and is not influenced by grain shapes.

ECCPA: Calculation of classical and quantum cross sections for elastic collisions of charged particles with atoms

ECCPA: Calculation of classical and quantum cross sections for elastic collisions of charged particles with atoms

Kinetic Energy Density Functionals Based on a Generalized Screened Coulomb Potential: Linear Response and Future Perspectives

We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals.

Plasma Confined Ground and Excited State Helium Atom: A Comparison Theorem Study Using Variational Monte Carlo and Lagrange Mesh Method

The energy eigenvalues of the ground state helium atom and lowest two excited states corresponding to the configurations 1s2s embedded in the plasma environment using Hulthén, Debye–Hückel and exponential cosine screened Coulomb model potentials are investigated within the variational Monte Carlo method, starting with the ultracompact trial wave functions in the form of generalized Hylleraas–Kinoshita functions and Guevara–Harris–Turbiner functions. The Lagrange mesh method calculations of energy are reported for the He atom in the ground and excited 1S and 3S states, which are in excellent agreement with the variational Monte Carlo results. Interesting relative ordering of eigenvalues are reported corresponding to the different screened Coulomb potentials in the He ground and excited electronic states, which are rationalized in terms of the comparison theorem of quantum mechanics.

Critical screening parameters and critical behaviors of one-electron systems with screened Coulomb potentials

The critical screening parameters for one-electron systems screened by Hulthén, Debye–Hückel, and exponential cosine screened Coulomb potentials are calculated with an accuracy close to the precision of numerical arithmetic. The results for a H atom with an infinitely heavy nucleus are reported from the ground to high-lying excited states, and those for arbitrary two-body charged systems are derived from the Zm-scaling law. A thorough comparison of the critical screening parameters for the ground and the first p-wave excited states with previous predictions is made to demonstrate the accuracy of our calculations. The critical behaviors of system-bound and pseudo-continuum eigenenergies for s- and non-s-wave states are shown to follow the quadratic and linear laws, respectively. The variation of the corresponding wave functions is analyzed in detail. For systems with non-zero orbital angular momenta, the bound states convert into shape-type resonances when the screening parameter exceeds the critical value. The resonance energy shares the same linear law as the pseudo-continuum state, while the resonance width varies by an l-dependent power law. It is further shown that the different asymptotic behaviors of the resonance energy and width are consistent with the complex analog of the Hellmann–Feynman theorem.

Nanoparticle Tracing during Laser Powder Bed Fusion of Oxide Dispersion Strengthened Steels.

The control of nanoparticle agglomeration during the fabrication of oxide dispersion strengthened steels is a key factor in maximizing their mechanical and high temperature reinforcement properties. However, the characterization of the nanoparticle evolution during processing represents a challenge due to the lack of experimental methodologies that allow in situ evaluation during laser powder bed fusion (LPBF) of nanoparticle-additivated steel powders. To address this problem, a simulation scheme is proposed to trace the drift and the interactions of the nanoparticles in the melt pool by joint heat-melt-microstructure–coupled phase-field simulation with nanoparticle kinematics. Van der Waals attraction and electrostatic repulsion with screened-Coulomb potential are explicitly employed to model the interactions with assumptions made based on reported experimental evidence. Numerical simulations have been conducted for LPBF of oxide nanoparticle-additivated PM2000 powder considering various factors, including the nanoparticle composition and size distribution. The obtained results provide a statistical and graphical demonstration of the temporal and spatial variations of the traced nanoparticles, showing ∼55% of the nanoparticles within the generated grains, and a smaller fraction of ∼30% in the pores, ∼13% on the surface, and ∼2% on the grain boundaries. To prove the methodology and compare it with experimental observations, the simulations are performed for LPBF of a 0.005 wt % yttrium oxide nanoparticle-additivated PM2000 powder and the final degree of nanoparticle agglomeration and distribution are analyzed with respect to a series of geometric and material parameters.

Diatomic Molecules and Mass Spectrum of Heavy Quarkonium System with Kratzer- Screened Coulomb Potential (KSCP) through the Solutions of the Schrödinger Equation

In this work, we obtain solutions of the Schrödinger equation with Kratzer-screened Coulomb potential (KSCP) model using the series expansion method. Explicitly, we compute the bound state energy eigenvalues for selected diatomic molecules of N2, CO, NO, and CH, respectively, for the various vibrational and rotational quantum states and the numerical energy eigenvalues agree with the existing literature. Three special cases were considered. The energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium system such as charmonium and bottomonium. The results agree with the experimental data and other recent theoretical studies.

Multipole polarizabilities for hydrogen-like atoms in Hulthén potential with and without spherical confinement

The multipole polarizabilities for hydrogen-like atoms with Hulthen potential are calculated with the sum-over-states formalism where the system bound and pseudocontinuum states are produced by employing the generalized pseudospectral method. Energies for nonzero angular momentum states, transition oscillator strengths, and dipole polarizabilities for the ground state of H atom with HP are calculated with high accuracy and compared with previous calculations. Quadrupole, octupole, and hexadecapole polarizabilities for both the ground and excited states are reported for the first time. The combined effect of Hulthen potential and impenetrable sphere on the polarizabilities is investigated, and the relation of such system with the confined H atom and particle in a box is discussed. Further comparison among Hulthen, screened Coulomb, and exponential cosine screened Coulomb potentials reveals that although the ground state energies follow the comparison theorem very well, their first-order energy corrections show complicated variations.

High‐precision calculation of relativistic corrections for hydrogen‐like atoms with screened Coulomb potentials

AbstractThe first‐order relativistic corrections to the non‐relativistic energies of hydrogen‐like atom embedded in plasma screening environments are calculated in the framework of direct perturbation theory by using the generalized pseudospectral method. The standard Debye–Hückel potential, exponential cosine screened Coulomb potential, and Hulthén potential are employed to model different screening conditions and their effects on the eigenenergies of hydrogen‐like atoms are investigated. The relativistic corrections which include the relativistic mass correction, Darwin term, and the spin‐orbit coupling term for both the ground and excited states are reported as functions of screening parameters. Comparison with previous theoretical predictions shows that both the relativistic mass correction and spin‐orbit coupling obtained in this work are in good agreement with previous estimations, while significant discrepancy and even opposite trend is found for the Darwin term. The overall relativistic‐corrected system energies predicted in this work, however, are in good agreement with the fully relativistic calculations available in the literature. We finally present the scaling law of the first‐order relativistic corrections and discuss the validity of the direct perturbation theory with respect to both the nuclear charge and the screening parameter.

Structural properties of Li atom under quantum and classical plasmas: A composite variational framework

AbstractStructural properties of 1s2nl (2L) [n = 2–5, l = 0–4; where, n and l are the principal quantum number and orbital angular momentum quantum number, respectively] states of Li atom embedded in classical weakly coupled plasma (WCP) and dense quantum plasma (DQP) have been discussed. The Debye‐Hckel potential or the screened‐Coulomb potential (SCP) and exponential‐cosine‐screened Coulomb potential (ECSCP) have been used to mimic the WCP and DQP, respectively. Li atom has been treated as a composite system with a frozen core Li+ ion and a chemically active valence electron. The Rayleigh‐Ritz variational method with Hylleraas‐type basis set has been used to estimate the energy eigenvalue of 1s2 (1S) state of Li+ ion core and a pure exponential basis has been considered to compute the energy of nl (2L) states of the valence electron of Li atom. The influence of ECSCP and SCP on the radial probability distribution of the valence electron of the Li atom has also been studied.

Tsallis entropy: A comparative study for the 1s2-state of helium atom

The Tsallis entropies are reported, as a function of the Tsallis index q and the screening parameter μ, in position space, for the ground state of the helium atom. Three different potentials, namely Coulomb, Yukawa, and exponential cosine screened Coulomb potentials and their combinations are used in the calculations. The simple Hylleraas correlated wave function, with a three-parameter, is applied to focus on getting the most characteristic physical features of the electron-electron repulsion results. The values are calculated in one- and two-electron charge densities. Moreover, for a comparative study, the Hartree-Fock approximation, which implements a numerical grid method, is employed. Additionally, the modified Tsallis index, Qq, is proposed and calculated to predict the best value of q in the combined potentials, and it was found that 0.5≤q<1.0.

The information theory of the helium atom in screened Coulomb potentials

AbstractIn this work, we show Hartree–Fock (HF) results for the Shannon entropy, Rényi entropy, Tsallis entropy, Onicescu information energy, and ground‐state properties of the helium atom in screened Coulomb potentials. We solve the HF equations through a numerical grid method where the screened functions model two plasma environments: the Debye–Hückel screening (DHS) and the exponential‐cosine‐screened‐Coulomb (ECSC) model potentials. For plasma conditions near to the energy ionization, for the Shannon entropy, we report an increase of the ∼80% and ∼60% for the DHS and ECSC potentials concerning the unscreened case. A similar situation is found for the Rényi and Tsallis entropies where an increase of ∼86% and ∼57% is reported in the presence of the DHS and ECSC potential functions. Our results allow us to obtain knowledge of the information theory parameters in the description of the electron localization for the helium atom screened by the DHS and ECSC potentials. Finally, our information theory findings in the absence of the screening functions are in excellent agreement with the available results found in the literature.

An equation of state for expanded metals

We present a model equation of states for expanded metals, which contains a pressure term due to a screened-Coulomb potential with a screening parameter reflecting the Mott–Anderson metal-to-nonmetal transition. As anticipated almost 80 years ago by Zel’dovich and Landau, this term gives rise to a second coexistence line in the phase diagram, indicating a phase separation between a metallic and a nonmetallic liquid.