Point Charges and Conducting Planes for Yukawa’s Potential and Coulomb’s Potential

In this work, we modeled and simulated the electric potential generated by point charges in the region of grounded conductor planes for Yukawa potential (e−μ/r) and Coulomb potential (1/r). We show the symbolic expression for the electric potential and some graphs for it and for the electric field with different values of μ. We observe that the electric potential decreases as the value of μ increases and that does not allow all the charge to be distributed on the surface of the conductor.

The Yukawa potential in semirelativistic formulation via supersymmetry quantum mechanics

We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. Useful figures and tables are also included.

Dirac equation for the Hulthén potential within the Yukawa-type tensor interaction

Using the Nikiforov-Uvarov （NU） method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthen potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number K. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.

Spinless particles in the field of unequal scalar vector Yukawa potentials

We present analytical bound state solutions of the spin-zero Klein–Gordon （KG） particles in the field of unequal mix-ture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of the Nikiforov–Uvarov （NU） method. Further, we solve the KG–Yukawa problem for its exact numerical energy eigenvalues via the amplitude phase （AP） method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst the energy states of the KG–Yukawa problem. The dependence of the energy on the dimension D is numerically discussed for spatial dimensions D = 2–6.

Approximate solution of the spin-one Duffin-Kemmer-Petiau(DKP) equation under a non-minimal vector Yukawa potential in(1+1)-dimensions

We solve the Duffin-Kemmer-Petiau （DKP） equation with a non-minimal vector Yukawa potential in （1＋1）- dimensional spa^e-time for spin-1 particles. The Nikiforov Uvarov method is used in the calculations, and the eigen- functions as well as the energy eigenvalues are obtained in a proper Pekeris-type approximation.

Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

A bound state solution is a quantum state solution of a particle subjected to a potential such that the particle＇s energy is less than the potential at both negative and positive infinity. The particle＇s energy may also be negative as the potential approaches zero at infinity. It is characterized by the discretized eigenvalues and eigenfunctions, which contain all the necessary information regarding the quantum systems under consideration. The bound state problems need to be extended using a more precise method and approximation scheme. This study focuses on the non-relativistic bound state solutions to the generalized inverse quadratic Yukawa potential. The expression for the non-relativistic energy eigenvalues and radial eigenfunctions are derived using proper quantization rule and formula method, respectively. The results reveal that both the ground and first excited energy eigenvalues depend largely on the angular momentum numbers, screening parameters, reduced mass, and the potential depth. The energy eigenvalues, angular momentum numbers, screening parameters, reduced mass, and the potential depth or potential coupling strength determine the nature of bound state of quantum particles. The explored model is also suitable for explaining both the bound and continuum states of quantum systems.

Point Charge between Two Grounded and Conducting Planes Forming a 60°Angle and for Yukawa’s Potential and Coulomb’s Potential

For a point charge between two grounded conductor planes forming a 60° angle, the potential and electric field generated by point charge for Yukawa’s potential (e-μr/r) and Coulomb’s potential (1/r) are modeled and simulated. The expression for the potential that generalizes the cases discussed in López-Mariño, M. and Trujillo Caballero, J. (2017) Point Charges and Conducting Planes for Yukawa’s Potential and Coulomb’s Potential. Journal of Electromagnetic Analysis and Applications, 9, 135-146. https://doi.org/10.4236/jemaa.2017.910012 is presented. Graphs for the potential and electric field for both cases are showed using Maple, that of Coulomb and that of Yukawa for different values of μ . The purpose of this work is to offer students a practical guide for problem analysis of electrostatics using Maple’s capabilities as a computational tool.

Momentum Eigensolutions of Feinberg-Horodecki Equation with Time-Dependent Screened Kratzer-Hellmann Potential

We obtain an approximate value of the quantized momentum eigenvalues, Pn, together with the space-like coherent eigenvectors for the space-like counterpart of the Schrödinger equation, the Feinberg-Horodecki equation, with a screened Kratzer-Hellmann potential which is constructed by the temporal counterpart of the spatial form of this potential. In addition, we got exact eigenvalues of the momentum and the eigenstates by solving Feinberg-Horodecki equation with Kratzer potential. The present work is illustrated with three special cases of the screened Kratzer-Hellman potential: the time-dependent screened Kratzer potential, time-dependent Hellmann potential and, the time-dependent screened Coulomb potential.

Approximate Bound State Solutions for Certain Molecular Potentials

We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number l and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.

Bound states and critical behavior of the Yukawa potential

We investigate the bound states of the Yukawa potential V(r)=-λexp(-αr)/r, using different algorithms: solving the Schrodinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = αC, above which no bound state exists. We study the relation between αC and A for various angular momentum quantum number l. and find in atomic units, αC(l) = λ[A1 exp(-l/B1) + A2exp(-l/B2)], with A1 = 1.020(18), B1 = 0.443(14), A2 = 0.170(17), and B2 = 2.490(180).

Effect of Particle＇s Size on the Structural and Dynamical Properties in 2D Dusty Plasma

In a two-dimensional （219） dusty plasma system, the size of particles is considered under two different interparticle potentials （Yukawa potential and Dressed potential）. The structural and dynamical characters are investigated by molecular dynamics simulation respectively. The results show that the 2D systems via Yukawa and Dressed potentials have a different critical coupling constant F corresponding to the systems beginning to coagulate and exhibit different crystal configurations. Also we find that the size of particles has little influence on the 2D system＇s structure characters.

Spin and Pseudospin Symmetries of Dirac Equation and the Yukawa Potential as the Tensor Interaction

Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov-Uvarov methodology. The solutions are discussed in detail.

Alpha Decay Half-Lives of Some Nuclei from Ground State to Ground State with Yukawa Proximity Potential

We study the half-lives of some nuclei via the alpha-decay process from ground state to ground state. To go through the problem, we have considered a potential model with Yukawa proximity potential and have thereby calculated the half-lives. The comparison with the existing data is motivating.

Calculating Binding Energy for Odd Isotopes of Beryllium （7 ≤ A ≤ 13）

In this article, we present exact solution of the Schr6dinger equation （for an N-identical body-force） for odd-A isotopes of Beryllium in the presence of Yukawa potential by Nikiforov-Uvarov （NU） method. The NU method can be used to solve second order differential equation. By this method, we find the wave equation and binding energy. Numerical results of binding energy are presented and show that these results are in good agreement with experimental values.

Molecular Structure of Atomic Nucleus

In this work, we extend our work on the Heisenberg model of the neutron formulated as a dwarf hydrogen-like atom under the influence of the More General Exponential Screened Coulomb Potential (MGESCP) to show that an atomic nucleus may possess a molecular structure made up of atoms bonding together by a potential used to describe the strong force associated with a generalised Yukawa MGESCP potential. We show that the neutrons and protons are arranged into narrow lattices therefore they may fold to form three-dimensional shells by bonding similar to hydrogen bonding. In particular, the nucleons may form stable structures such as that of fullerenes in which the vertices are occupied by the nucleons which are simply just protons. For example, a nucleus with a total number of 60 nucleons may arrange itself into the topological structure of a buckminsterfullerene. We also apply Schrödinger wave equation with central field approximation to describe the quantum dynamics of nuclei of atomic atoms that now possess the physical structure of a dwarf molecular ion.

Investigation of deformed nuclei with a new potential combination

We investigate the alpha-decay half-lives of non-spherical nuclei with the Yukawa potential as the prox- imity potential and an angle-dependent term that accounts for the deformation effects and apply the results to Ho, Tb, Lu, Tin, Ta, Hf, Yb, Re, Ir, Pt, Au, Po, etc. as examples. The comparison with the existing data is encouraging.

Borromean Windows for Three-Particle Systems under Screened Coulomb Interactions

We have carried out calculations to search Borromean windows(BWs) for 11 different three-body systems interacting with screened Coulomb(Yukawa-type) potentials using Hylleraas-type wave functions within the framework of a variational approach. The critical values of the screening parameters for the ground states of the systems under consideration are reported for which the three-body systems are stable, while all the possible fragments are unbound;that is, it shows windows for Borromean binding.

New Equation of State for Osmotic Pressures in Aqueous Saline Solutions of Lysozyme

A new equation of state is proposed to correlate the osmotic pressure data for aqueous lysozyme solutions with (NH 4) 2SO 4, (NH 4) 2C 2O 4 and (NH 4) 2HPO 4 at ionic strengths of 13.5 mol/kg and pH 4, 7 or 8 with only one adjustable parameter instead of the classical Derjaguin Landau Verwey Overbeek (DLVO) theory. The Carnahan Starling equation represents the contribution of the hard sphere repulsion to the osmotic pressure. The attractive dispersion interaction is represented by the Lennard Jones potential expressed by the equation of Cotterman et al. based on perturbation theory. The double layer repulsion interaction is represented by Yukawa potential expressed by the equation of state of Duh and Mier Y Teran based on mean spherical approximation. The total average relative deviation of the correlation of the osmotic pressure data is 1.68%.

A study on the distribution of adsorbed nanoparticles

We use Monte Carlo simulation to calculate the distributions of particles under adsorption force near planar and cylindrical surfaces, respectively. Both hard sphere interaction and repulsive Yukawa （screened coulomb） interaction are employed in our simulations. We study the influence of the inter-particle potentials. The difference between the MC simulation results and the analytical results of ideal gas model shows that the interaction between particles plays an important role in the density distribution under external fields. Moreover, the 2-dimensional constructions of particles close to the surface are studied and show relations of the interaction between particles. These results may indicate us how to improve the methods of building nanoparticle coatings and nano-scale patterns.

Revision of DASHMM:Dynamic Adaptive System for Hierarchical Multipole Methods

We present version 1.2.0 of DASHMM,a general library implementing hierarchical multipole methods using the asynchronous multi-tasking HPX-5 runtime system.Compared with the previous release[10],this new version:(1)enables execution in both shared and distributed memory architectures;(2)extends DASHMM’s infrastructure to support advanced multipole methods[18];and(3)provides built-in implementations of both the Yukawa[15]potential and Helmholtz[16]potential in the low frequency regime.These additions have not impacted the user interface,which remains simple and extensible.