Screened Coulomb Potentials Research Articles

Numerical study of cluster formation in binary charged colloids.

Cluster formation of oppositely charged colloidal particles is studied numerically. A simple Brownian dynamics method with a screened-Coulomb (Yukawa) potential is employed for numerical simulations. An equilibrium phase which consists of clusters and unassociated particles is obtained. It is shown that the equilibrium association number of clusters and their shapes are determined by charge numbers and charge ratio of the binary particles. The phase diagram of cluster formation for various charge numbers and their ratios is obtained. A simple relation between the association number and the charge ratio is found. It is demonstrated that in the case of high charge ratio the cluster takes a multilayer structure which is highly symmetric. It is also pointed out that the cluster-particle interaction changes dynamically in the cluster formation process, which is involved in the selection of final cluster structure.

High-lying doubly excited resonances in Ps− interacting with screened Coulomb potentials

The effect of screened Coulomb potentials on the high-lying doubly-excited resonance states of the positronium negative ion has been investigated using the method of complex-scaling together with employing highly correlated Hylleraas-type wave functions. Resonance parameters (resonance energy positions and widths) below the N = 4, 5, and 6 Ps thresholds for various screening parameters are determined.

Dynamic polarizability and electric multipolar transitions in two electron atoms under exponential cosine screened coulomb potential

Detailed investigations on the frequency dependent polarizabilities, transition energies, oscillator strengths, and transition probabilities of two electron systems He, Be2+, C4+, and O6+ under electric dipolar (E1) and quadrupolar (E2) excitations have been performed using exponential cosine screened coulomb potential with a view to understand the structural behaviour of such systems due to external confinement produced by plasma environment. Time dependent coupled Hartree–Fock theory within a variational framework has been adopted for studying the first three low lying excited states 1s2:1Se→1snp:1Po (n = 2, 3, 4) and 1snd:1De (n = 3, 4, 5) under such excitations. Quantitatively, the effect of confinement produced by the external plasma has been taken care of by considering the change in atomic potential through plasma screening, directly related to the coupling strength of the plasma with the atomic charge cloud. With increased plasma screening, a gradual destabilisation of the energy levels with subsequent reduction of the ionization potential and number of excited states has been observed. Behavioral pattern of the frequency dependent polarizabilities, excitation energies, oscillator strengths, and transition probabilities under systematic increase of the screening has been investigated. Results have been compared thoroughly with those available for free systems and under confinement by exponential cosine screened and screened Coulomb potential.

Generalization of the model of Debye-Hückel according to a matrix approach. Application to the calculation of the potential of mean force in the case of electrolytes, polyelectrolytes and colloids

In this paper we have generalized on the basis of the superposition principle, the Debye-Hückel model in the case of a spatial distribution of “n” fixed ions surrounded by an ionic atmosphere. According to this approach, the mean electrostatic potential at a position M is written as a sum of individual screened Coulomb potentials: ∑ni=1(Zie/ε)Aiexp(−χri)/ri. The electro-neutrality condition allows the obtaining of the exact expression of the superposition coefficients {Ai} in terms of the elements {Dij} of an explicit n–n matrix [D] which depend on the effective radii Ri of the ions and on their distances of separation dij. As applications: a) we have improved the expression of the PMF's approximation of Debye; b) we have simplified and resolved in the limits of this model, the BBGKY hierarchy, in order to obtain the PMF potential Wij(dij) and hence the screen parameter χ from the second Stillinger–Lovett restriction; c) we have also proposed an explicit expression for the electrostatic part of the DLVO potential; and finally, d) we have justified and improved the potentials of interaction of Yukawa between chain groups in the case of polyelectrolyte solutions.

Natural and Unnatural Parity Resonance States in the Positron-Hydrogen System with Screened Coulomb Interactions

In the present work, we report calculations of resonances in the positron-hydrogen system interacting with screened Coulomb potentials using the method of complex scaling together with employing correlated Hylleraas wave functions. Resonances with natural and unnatural parities are investigated. For the natural parity case, resonance parameters (energy and width) for D-wave resonance states with even parity lying below various positronium and hydrogen thresholds up to the H(N = 4) level are determined. For the unnatural parity case, results for P-even and D-odd resonance states with various screened Coulomb interaction strengths are located below different lower-lying Ps and H thresholds.

Hyperpolarizability of two electron atoms under exponential cosine screened coulomb potential

Hyperpolarizability of two electron atoms He, Li+, Be2+, B3+, and C4+ embedded under quantum plasma environment has been calculated for the first time using exponential cosine screened coulomb potential (ECSCP) arising out of the interaction of atomic charge cloud with such an environment. Coupled Hartree-Fock theory within variational scheme has been utilised to estimate such nonlinear optical property for systematic variation of the screening parameter arising out of the coupling strength of the plasma with atomic charge cloud. Hyperpolarizability of the ions increases systematically with increase of the screening parameter. Results have been compared with respect to those obtained from the interaction of atomic systems with a Debye plasma environment giving rise to SCP. Interesting feature is observed for the polarizability and hyperpolarizability values under increasing screening parameters of ECSCP and SCP. Hyperpolarizability values for zero screening compare well with those available for the free ions.

Deflections of photoelectron classical trajectories in screened Coulomb potentials of H2+**Project supported by the National Natural Science Foundation of China (Grant Nos. 11104180, 11175120, 11121504, and 11322438) and the Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (Grant No. 131010).

The photoelectron momentum distribution of in circularly polarized laser fields is studied based on classical trajectory calculations. We screen Coulomb potentials at different radii, and trace trajectories of an ensemble of electrons in such screened Coulomb potentials and circularly polarized laser fields. Simulations show that electron trajectories are bent by Coulomb fields, resulting in the laser-intensity-dependent drift of photoelectron momentum distributions in the laser polarization plane. This study intuitively explains how Coulomb potentials modify photoelectron momenta.

Discrete Charge Effects on the Potential Distribution in and around Soft Particles

The potential distribution in and around a soft particle, i.e., a porous polyelectrolyte particle, in an electrolyte solution is usually derived via a continuum model in which fixed charges inside the soft particle are distributed with a continuous charge density. In this paper, on the basis of a previous result for a plate like soft particle consisting of a cubic lattice of fixed point charges, we derive expressions for the electric potential distribution for the case of a soft sphere and a soft cylinder. These expressions are given in terms of a sum of the screened Coulomb potentials produced by the point charges within the soft particle. We show how the discrete charge model approaches the continuous charge model as the lattice spacing becomes very small.

Influence of dense quantum plasmas on fine-structure splitting of Lyman doublets of hydrogenic systems

Relativistic calculations are performed to study the effects of oscillatory quantum plasma screening on the fine-structure splitting between the components of Lyman-α and β line doublets of atomic hydrogen and hydrgen-like argon ion within dense quantum plasmas, where the effective two-body (electron–nucleus) interaction is modeled by the Shukla–Eliasson oscillatory exponential cosine screened-Coulomb potential. The numerical solutions of the radial Dirac equation for the quantum plasma-embedded atomic systems reveal that the oscillatory quantum screening effect suppresses the doublet (energy) splitting substantially and the suppression becomes more prominent at large quantum wave number kq. In the absence of the oscillatory cosine screening term, much larger amount of suppression is noticed at larger values of kq, and the corresponding results represent the screening effect of an exponential screened-Coulomb two-body interaction. The Z4 scaling of the Lyman doublet splitting in low-Z hydrogen isoelectron...

Simulation of ion beam scattering in a gas stripper

Ion beam scattering in the gas stripper of an accelerator mass spectrometer (AMS) enlarges the beam phase space and broadens its energy distribution. As the size of the injected beam depends on the acceleration voltage through phase space compression, the stripper becomes a limiting factor of the overall system transmission especially for low energy AMS system in the sub MV region. The spatial beam broadening and collisions with the accelerator tube walls are a possible source for machine background and energy loss fluctuations influence the mass resolution and thus isotope separation. To investigate the physical processes responsible for these effects, a computer simulation approach was chosen. Monte Carlo simulation methods are applied to simulate elastic two body scattering processes in screened Coulomb potentials in a (gas) stripper and formulas are derived to correctly determine random collision parameters and free path lengths for arbitrary (and non-homogeneous) gas densities. A simple parametric form for the underlying scattering cross sections is discussed which features important scaling behaviors. An implementation of the simulation was able to correctly model the data gained with the TANDY AMS system at ETH Zurich. The experiment covered transmission measurements of uranium ions in helium and beam profile measurements after the ion beam passed through the He-stripper. Beam profiles measured up to very high stripper densities could be understood in full system simulations including the relevant ion optics. The presented model therefore simulates the fundamental physics of the interaction between an ion beam and a gas stripper reliably. It provides a powerful and flexible tool for optimizing existing AMS stripper geometries and for designing new, state of the art low energy AMS systems.

Dynamic numerical simulations of magnetically interacting suspensions in creeping flow

The equations governing the motion of N magnetic particles suspended in a viscous fluid at low Reynolds and finite Stokes numbers are solved by direct numerical simulations for different Péclet numbers. The Langevin dynamics simulations include all dipole–dipole magnetic interactions for force and torque. An external applied magnetic field and near field interactions represented by contact and repulsion forces are also considered. Repulsive forces are modeled using a variation of the screened-Coulomb type potential. The initial particle distribution is an ergodic ensemble in which each member consists of N mutually impenetrable spheres whose centers are randomly distributed in a prismatic cell of volume V with wall boundaries. The stability of the proposed numerical method and its convergence in calculating some relevant macroscopic properties of the magnetic suspension are carefully examined. The simulations are used to investigate structure transition from an isotropic random distribution of particles to other structures in the presence of an external magnetic field and magnetic particle–particle interactions. The simulations show dimmers and short chain formation in the suspension space at low volume fraction. When the volume fraction is increased long chains and thin anisotropic structures may be observed along the magnetic field direction. The numerical method is also used to calculate the steady state equilibrium magnetization, and accurate results are obtained for different particle volume fractions ϕ in agreement with Oϕ3 asymptotic theories. The method presented is able to consider up to 3000 particles with accuracy and computational efficiency. Typical configurations and particle trajectories are also shown and discussed from a physical point of view.

Long term simulation of point defect cluster size distributions from atomic displacement cascades in Fe70Cr20Ni10

We have used an Object Kinetic Monte Carlo (OKMC) model to simulate the long term evolution of the primary damage in Fe70Cr20Ni10 alloys. The mean number of Frenkel pairs created by different Primary Knocked on Atoms (PKA) was estimated by Molecular Dynamics using a ternary EAM potential developed in the framework of the PERFORM-60 European project. This number was then used to obtain the vacancy–interstitial recombination distance required in the calculation of displacement cascades in the Binary Collision Approximation (BCA) with code MARLOWE (Robinson, 1989). The BCA cascades have been generated in the 10–100keV range with the MARLOWE code and two different screened Coulomb potentials, namely, the Molière approximation to the Thomas–Fermi potential and the so-called “Universal” potential by Ziegler, Biersack and Littmark (ZBL). These cascades have been used as input to the OKMC code LAKIMOCA (Domain et al., 2004), with a set of parameters for describing the mobility of point defect clusters based on ab initio calculations and experimental data. The cluster size distributions have been estimated for irradiation doses of 0.1 and 1dpa, and a dose rate of 10−7dpa/s at 600K. We demonstrate that, like in the case of BCC iron, cluster size distributions in the long term are independent of the cascade energy and that the recursive cascade model suggested for BCC iron in Souidi et al. (2011) also applies to FCC Fe70Cr20Ni10. The results also show that the influence of the BCA potential is sizeable but the qualitative correspondence in the predicted long term evolution is excellent.

Screened Electrostatic Interactions in Molecular Mechanics.

In a typical application of molecular mechanics (MM), the electrostatic interactions are calculated from parametrized partial atomic charges treated as point charges interacting by radial Coulomb potentials. This does not usually yield accurate electrostatic interactions at van der Waals distances, but this is compensated by additional parametrized terms, for example Lennard-Jones potentials. In the present work, we present a scheme involving radial screened Coulomb potentials that reproduces the accurate electrostatics much more accurately. The screening accounts for charge penetration of one subsystem's charge cloud into that of another subsystem, and it is incorporated into the interaction potential in a way similar to what we proposed in a previous article (J. Chem. Theory Comput. 2010, 6, 3330) for combined quantum mechanical and molecular mechanical (QM/MM) simulations, but the screening parameters are reoptimized for MM. The optimization is carried out with electrostatic-potential-fitted partial atomic charges, but the optimized parameters should be useful with any realistic charge model. In the model we employ, the charge density of an atom is approximated as the sum of a point charge representing the nucleus and inner electrons and a smeared charge representing the outermost electrons; in particular, for all atoms except hydrogens, the smeared charge represents the two outermost electrons in the present model. We find that the charge penetration effect can cause very significant deviations from the popular point-charge model, and by comparison to electrostatic interactions calculated by symmetry-adapted perturbation theory, we find that the present results are considerably more accurate than point-charge electrostatic interactions. The mean unsigned error in electrostatics for a large and diverse data set (192 interaction energies) decreases from 9.2 to 3.3 kcal/mol, and the error in the electrostatics for 10 water dimers decreases from 1.7 to 0.5 kcal/mol. We could have decreased the average errors further, but at the cost of sometimes significantly overestimating the screening; instead we chose a more conservative (safer) parametrization that systematically underestimates the screening (which by definition means it improves over point charges) and only occasionally overestimates it. Despite this conservative choice, we find that the screened MM method is even more accurate for the electrostatics than unscreened QM/MM calculations. This new method is easy to implement in any MM program, and it can be used to develop more physical force fields for molecular simulations.

Dynamical polarization in ABC-stacked multilayer graphene in a magnetic field

In the continuum low energy model, we calculate the one-loop dynamical polarization functions in ABC-stacked (rhombohedral) $n$-layer graphene in a magnetic field. Neglecting the trigonal warping effects, they are derived as functions of wavevector and frequency at finite chemical potential, temperature, band gap, and the width of Landau levels. The analytic results are given in terms of digamma functions and generalized Laguerre polynomials and have the form of double sums over Landau levels. Various particular limits for polarization functions (static, clean, etc.) are discussed. The intralayer and interlayer screened Coulomb potentials are numerically calculated as functions of momentum and frequency.

Gas-liquid phase coexistence and crossover behavior of binary ionic fluids with screened Coulomb interactions.

We study the effects of an interaction range on the gas-liquid phase diagram and the crossover behavior of a simple model of ionic fluids: an equimolar binary mixture of equisized hard spheres interacting through screened Coulomb potentials which are repulsive between particles of the same species and attractive between particles of different species. Using the collective variables theory, we find explicit expressions for the relevant coefficients of the effective φ{4} Ginzburg-Landau Hamiltonian in a one-loop approximation. Within the framework of this approximation, we calculate the critical parameters and gas-liquid phase diagrams for varying inverse screening length z. Both the critical temperature scaled by the Yukawa potential contact value and the critical density rapidly decrease with an increase of the interaction range (a decrease of z) and then for z<0.05 they slowly approach the values found for a restricted primitive model (RPM). We find that gas-liquid coexistence region reduces with an increase of z and completely vanishes at z≃2.78. Our results clearly show that an increase in the interaction range leads to a decrease of the crossover temperature. For z≃0.01, the crossover temperature is the same as for the RPM.

Correlated n1,3S states for two-electron atoms in screened potentials

Two-electron atoms in screened and exponential cosine screened Coulomb potentials are studied. We have calculated within a Configuration Interaction approach, the ground and first excited states energies, and other mean values, for H−, He and Li+. We analyze their evolution with the screening parameters, and provide practical fits which allow for a practical and rapid evaluation for plasma applications.

Doubly-excited 2p23Pe state of the hydrogen negative ion in Debye plasmas

The screening effects of Debye plasmas on the 2p23Pe state of H− ion and on its radiative transition to the H−(3Po) states are investigated. The plasma conditions are modeled by screened Coulomb potentials characterized by the Debye length. It is shown that the metastable bound 2p23Pe state in the absence of plasma screenings would transform to a shape resonance lying above the H(2p) threshold when the Debye length decreases to a critical value. The complex-scaling method together with the configuration interaction-type wave functions is used to extract the resonance energy and width. The transition wavelengths of the 2p23Pe state to the 2s2p3Po resonant state and the 1skp3Po continuum are calculated in a wide range of Debye lengths. It is shown that wavelengths are prolonged significantly by increasing the screening effects.

Strong plasma screening in thermonuclear reactions: Electron drop model

We analyze enhancement of thermonuclear fusion reactions due to strong plasma screening in dense matter using a simple electron drop model. The model assumes fusion in a potential that is screened by an effective electron cloud around colliding nuclei (extended Salpeter ion-sphere model). We calculate the mean field screened Coulomb potentials for atomic nuclei with equal and nonequal charges, appropriate astrophysical S factors, and enhancement factors of reaction rates. As a byproduct, we study analytic behavior of the screening potential at small separations between the reactants. In this model, astrophysical S factors depend not only on nuclear physics but on plasma screening as well. The enhancement factors are in good agreement with calculations by other methods. This allows us to formulate the combined, pure analytic model of strong plasma screening in thermonuclear reactions. The results can be useful for simulating nuclear burning in white dwarfs and neutron stars.

Generalized Onsager theory for strongly anisometric patchy colloids

The implications of soft "patchy" interactions on the orientational disorder-order transition of strongly elongated colloidal rods and flat disks is studied within a simple Onsager-van der Waals density functional theory. The theory provides a generic framework for studying the liquid crystal phase behaviour of highly anisometric cylindrical colloids which carry a distinct geometrical pattern of repulsive or attractive soft interactions localized on the particle surface. In this paper, we apply our theory to the case of charged rods and disks for which the local electrostatic interactions can be described by a screened-Coulomb potential. We consider infinitely thin rod like cylinders with a uniform line charge and infinitely thin discotic cylinders with several distinctly different surface charge patterns. Irrespective of the backbone shape the isotropic-nematic phase diagrams of charged colloids feature a generic destabilization of nematic order at low ionic strength, a dramatic narrowing of the biphasic density region, and a reentrant phenomenon upon reducing the electrostatic screening. The low screening regime is characterized by a complete suppression of nematic order in favor of positionally ordered liquid crystal phases.

On Recent Analytical Results for Solution of the Scattering Problem for the Sharply Screened Coulomb Potential

Exact representations for the wave function and for the Green function of the Hamiltonian with the sharply screened Coulomb potential are given. The representations are obtained by summing up the partial wave series. The final form of the wave function and the Green function in the region of the coordinate space where the potential is not zero are given in terms of the Coulomb wave function and the Coulomb Green function, respectively. The exact representation has been obtained for the transition operator in the configuration space.