Coulomb-like Interaction Research Articles

Relativistic symmetries of Schioberg and general Manning-Rosen potentials and the effects of tensor coupling

Abstract In this paper we solve the Dirac equation with Schioberg and general Manning- Rosen potentials including the Coulomb-like tensor interaction. The approximate analytical bound state solutions of the Dirac equation with the Schioberg and Manning-Rosen potential, energy equations and the corresponding unnormalized wave functions are obtained in a closed form using SUSYQM. We have also reported the numerical results to show the effect of the tensor interaction.

Use of generalized hyperspherical Sturmian functions for a three-body break-up model problem

A hyperspherical Sturmian approach recently developed for three-body break-up processes is tested through an analytically solvable S-wave model. The scattering process is represented by a non-homogeneous Schrödinger equation in which the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wavefunction and a bound state in the particles' coordinates. The model contains most of the difficulties encountered in a real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behaviour, and thus provides an interesting benchmark for numerical methods. Since the Sturmian basis functions are constructed so as to include the correct asymptotic behaviour, a very fast convergence of the scattering wavefunction is observed. Excellent agreement is found with the analytical results for the associated transition amplitude. This holds true down to very low energies, a domain which is usually challenging as it involves huge spatial extensions. Within our method, such calculations can be performed without increasing significantly the computational requirements.

Classical rotons in cold atomic traps

We predict the emergence of a roton minimum in the dispersion relation of elementary excitations in cold atomic gases in the presence of diffusive light. In large magneto-optical traps, multiple scattering of light is responsible for the collective behavior of the system, which is associated to an effective Coulomb-like interaction between the atoms. In optically thick clouds, the rescattered light undergoes diffusive propagation, which is responsible for a stochastic short-range force acting on the atoms. We show that the dynamical competition between these two forces is by the appearance of a roton minimum in the dispersion relation. Making use of the fluctuation-dissipation theorem, we show that the roton minimum is related to classical long-range order in the system.

Relativistic Symmetries in the Hulthén-like Potential and Tensor Interaction

In the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation for Hulthen-like potential including a Coulomb-like tensor interaction are obtained with any arbitrary spin–orbit coupling number κ using the Pekeris approximation. The generalized parametric Nikiforov–Uvarov (NU) method is used to obtain the energy eigenvalues and the corresponding wave functions in their closed forms. We show that tensor interaction removes degeneracies between spin and p-spin doublets. Some numerical results are also given.

An analytically solvable three-body break-up model problem in hyperspherical coordinates

An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrodinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real three-body scattering problem, e.g., non-separability in the electrons’ spherical coordinates and Coulombic asymptotic behavior. Since the coordinates’ coupling is completely different, the model provides an alternative test to that given by the Temkin-Poet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for three-body collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude.

Confined Doping on a Metallic Atomic Chain Structure

On Si(111)-(5×2)-Au it is shown that metallic sections of quantum wires between two doping adatoms establish a local electronic structure which is primarily defined by the section length. Such confined doping is a direct consequence of reduced dimensionality and is not observed in higher dimensions. Within a chain segment, the effect of a spatially independent charge-carrier concentration is superimposed by a Coulomb-like interaction due to the positively charged dopants. This offers a natural explanation for the relatively broad photoemission features and the complex appearance in scanning tunneling microscopy and spectroscopy images.

Relativistic New Yukawa-Like Potential and Tensor Coupling

We approximately solve the Dirac equation for a new suggested generalized inversely quadratic Yukawa (GIQY) potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions, in closed form, by using the parametric Nikiforov-Uvarov (NU) method. The numerical results show that the Coulomb-like tensor interaction, removes degeneracies between spin and p-spin state doublets. The Dirac solutions in the presence of exact spin symmetry are reduced to Schr\"odinger solutions for Yukawa and inversely quadratic Yukawa potentials.

Effect of tensor interaction in the Dirac-attractive radial problem under pseudospin symmetry limit

We approximately investigated pseudospin symmetric solutions of the Dirac equation for attractive radial potential, including a Coulomb-like tensor interaction under pseudospin symmetry limit for any spin-orbit quantum number κ. By using the parametric generalization of the Nikiforov-Uvarov method, the energy eigenvalues equation and the corresponding wave functions have been obtained in closed forms. Some numerical results are also given. We presented tensor interaction removes degeneracy between two states in pseudospin doublets.

Relativistic study of the energy-dependent Coulomb potential including Coulomb-like tensor interaction

The exact Dirac equation for the energy-dependent Coulomb (EDC) potential including a Coulomb-like tensor (CLT) potential has been studied in the presence of spin and pseudospin symmetries with arbitrary spin–orbit quantum number, κ. The energy eigenvalues and corresponding eigenfunctions are obtained in the framework of the asymptotic iteration method. Some numerical results are obtained in the presence and absence of EDC and CLT potentials.

Approximate spin and pseudospin solutions to the Dirac equation for the inversely quadratic Yukawa potential and tensor interaction

We approximately solve the Dirac equation for the inversely quadratic Yukawa potential including a Coulomb-like tensor potential with arbitrary spin–orbit coupling quantum number κ. In the framework of the spin and pseudospin (pspin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions in closed form by using the Nikiforov–Uvarov method. The numerical results show that the Coulomb-like tensor interaction removes degeneracies between spin and pseudospin state doublets.

Spin Symmetry in Dirac-Attractive Radial Problem and Tensor Potential

In this paper, we solve the Dirac equation under spin symmetry limit for attractive radial potential including a Coulomb-like tensor interaction. By using the parametric generalization of the Nikiforov-Uvarov method, the energy eigenvalues equation and the corresponding wave functions have been obtained in closed forms. Some numerical results are given too.

Magnetization processes in rectangular versus rhombic planar superlattices of magnetic bars

Rectangular and rhombic patterned superlattices of magnetic bar elements have been experimentally studied and theoretically modeled in order to analyze the role of the array geometry in their magnetization reversal and coercivity. The results show that a dominating part of the coercive field ($\ensuremath{\approx}$250 Oe) is due to the reversal processes within a single bar element (independent of the array geometry) which is well described by the standard micromagnetic calculation. Otherwise, a smaller ($\ensuremath{\approx}$60 Oe) but significant difference between the magnetization loops in the two geometries is related to the magnetostatic coupling effects between the bars and it is reasonably accounted for with a simple model of Coulomb-like interaction between terminal magnetic charges. The possibility to use this geometry effect to control the performance of artificial magnetic media is discussed.

Solution of the Dirac Equation with Position-Dependent Mass for q-Parameter Modified Pöschl–Teller and Coulomb-like Tensor Potential

In this research, we have been obtained the Dirac equation for q-parameter modified Poschl–Teller potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number by choosing a position-dependent mass. The energy eigenvalues equation and the corresponding unnormalized wave functions have been obtained. The Nikiforov-Uvarov method has been used in the calculations.

Small Volume-Fraction Limit of the Diblock Copolymer Problem: II. Diffuse-Interface Functional

We present the first of two articles on the small volume fraction limit of a nonlocal Cahn–Hilliard functional introduced to model microphase separation of diblock copolymers. Here we focus attention on the sharp-interface version of the functional and consider a limit in which the volume fraction tends to zero but the number of minority phases (called particles) remains $O(1)$. Using the language of $\Gamma$-convergence, we focus on two levels of this convergence and derive first- and second-order effective energies, whose energy landscapes are simpler and more transparent. These limiting energies are only finite on weighted sums of delta functions, corresponding to the concentration of mass into “point particles.” At the highest level, the effective energy is entirely local and contains information about the structure of each particle but no information about their spatial distribution. At the next level we encounter a Coulomb-like interaction between the particles, which is responsible for the pattern ...

Pair production of color-octet scalars at the LHC

Heavy colored scalar particles, which exist in many models of new physics, can be pair produced at the LHC via gluon-gluon fusion and possibly form quarkoniumlike bound states. If the scalars are also charged under the electroweak gauge group, these bound states can then decay into electroweak bosons. This yields a resonant cross section for final states such as $\ensuremath{\gamma}\ensuremath{\gamma}$ that can exceed standard model backgrounds. This paper studies this process in the Manohar-Wise model of color-octet scalars (COS). Important threshold logarithms and final state Coulomb-like QCD interactions are resummed using effective field theory. We compute the resummed cross section for gluon-gluon fusion to COS pairs at the LHC as well as the resonant cross section for octetonium decaying to $\ensuremath{\gamma}\ensuremath{\gamma}$. The latter cross section exceeds the standard model diphoton cross section when the COS mass is less than 500 (350) GeV for $\sqrt{s}=14(7)\text{ }\text{ }\mathrm{TeV}$. Nonobservation of resonances below these energies can significantly improve existing bounds on COS masses.

Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method

In this Letter, the Dirac equation is exactly solved for spatially-dependent mass Coulomb potential including a Coulomb-like tensor potential under pseudospin symmetry limit by using asymptotic iteration method with arbitrary spin–orbit coupling number κ. The energy eigenvalues and corresponding eigenfunctions are obtained and some numerical results are given.

Possible Observation of Critical Phenomena in Fine Particle (Dusty, Complex) Plasmas

The possibility to observe critical phenomena in fine particles plasmas is discussed in terms of both characteristic dimensionless parameters of statistical mechanics and real conditions such as densities and temperatures in fine particle (dusty, complex) plasma experiments. In addition to the possibility originating from the divergence of the isothermal compressibility of strongly coupled one-component plasmas and Coulomb-like systems, it is shown that we have another possibility in the domain of intermediate coupling with feasible experimental conditions. In both cases, the Coulomb and Coulomb-like interactions between fine particles drive the system to thermodynamic instability and critical phenomena belong to the same universality class. The mechanisms, however, are completely different.

Stability of the pentaquark in a naive string model

The pentaquark is studied in a simple model of confinement in which the quarks and the antiquark are linked by flux tubes of minimal cumulated length and the Coulomb-like interaction, the spin-dependent terms, and the antisymmetrization constraints are neglected. The ground state is found to be stable against spontaneous dissociation into a meson and a baryon, both in the case of five equal-mass constituents and for a static quark or antiquark surrounded by four equal masses.

10.1007/s11450-008-2014-7

We carry out an investigation of the P-wave hyperons Λ Σ, and ξ employing the field correlator method in QCD. This method allows us to derive the effective Hamiltonian (EH) approach successfully applied to the meson and ground-state baryon spectra. The EH is written in the form of the nonrelativistic three-quark Hamiltonian with perturbative Coulomb-like and nonperturbative string interactions and the specific mass term. We solve the three-quark problem using the hyperspherical approach. With only two parameters, the string tension σ and the strong coupling constant α s , a unified quantitative description of the ground and excited hyperon states is achieved. In particular, we predict that all the hyperon states have the similar cost (in Δ) ∼460 MeV.

A one-dimensional dipole lattice model for water in narrow nanopores

We present a recently developed one-dimensional dipole lattice model that accurately captures the key properties of water in narrow nanopores. For this model, we derive three equivalent representations of the Hamiltonian that together yield a transparent physical picture of the energetics of the water chain and permit efficient computer simulations. In the charge representation, the Hamiltonian consists of nearest-neighbor interactions and Coulomb-like interactions of effective charges at the ends of dipole ordered segments. Approximations based on the charge picture shed light on the influence of the Coulomb-like interactions on the structure of nanopore water. We use Monte Carlo simulations to study the system behavior of the full Hamiltonian and its approximations as a function of chemical potential and system size and investigate the bimodal character of the density distribution occurring at small system sizes.