Coulomb-like Interaction Research Articles

Tensor coupling and relativistic spin and pseudospin symmetries of the Pöschl–Teller-like potential

In this research, we have been obtained the Dirac equation for second Pöschl–Teller-like potential including a Coulomb-like tensor interaction with arbitrary spin–orbit coupling quantum number κ. Under the condition of spin and pseudospin (p-spin) symmetries, we use the basic concept of the supersymmetric shape invariance formulism in quantum mechanics and the function analysis method to obtain energy eigenvalues and corresponding two-component spinors of the Dirac particle. We have also shown that tensor interaction removes degeneracies between spin and p-spin doublets. Some numerical results are also given.

Quantum multicriticality in bilayer graphene with a tunable energy gap

We develop a theory for quantum phases and quantum multicriticality in bilayer graphene in the presence of an explicit energy gap in the noninteracting spectrum by extending previous renormalization group (RG) analyses of electron-electron interactions in gapless bilayer graphene at finite temperature to include the effect of an electric field applied perpendicular to the sample, which produces an energy gap in the single-particle electron-hole dispersion. We determine the possible outcomes of the resulting RG equations, represented by ``fixed rays'' along which ratios of the coupling constants remain constant and map out the leading instabilities of the system for an interaction of the form of a Coulomb interaction that is screened by two parallel conducting plates placed equidistant from the electron. We find that some of the fixed rays on the ``target plane'' found in the zero-field case are no longer valid fixed rays, but that all four of the isolated rays are still valid. We also find five additional fixed rays that are not present in the zero-field case. We then construct maps of the leading instability (or instabilities) of the system for the screened Coulomb-like interaction as a function of the overall interaction strength and interaction range for four values of the applied electric field. We find that the pattern of leading instabilities is the same as that found in the zero-field case, namely, that the system is unstable to a layer antiferromagnetic state for short-ranged interactions, to a nematic state for long-ranged interactions, and to both for intermediate-ranged interactions. However, if the interaction becomes too long ranged or too weak, then the system will exhibit no instabilities. The ranges at which the nematic instability first appears, the antiferromagnetic instability disappears, and the nematic instability disappears all decrease with increasing applied electric field. Our main qualitative finding, that the applied electric field opposes the emergence of symmetry-broken phases in general, suppressing, however, the antiferromagnetc phase more strongly compared with the nematic phase, is directly testable experimentally.

Relativistic symmetries of Deng—Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interactions

Relativistic symmetries of the Dirac equation under spin and pseudo-spin symmetries are investigated and a combination of Deng—Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interaction terms are considered. The energy equation is obtained by using the Nikiforov—Uvarov method and the corresponding wave functions are expressed in terms of the hypergeometric functions. The effects of the Coulomb and Yukawa tensor interactions are numerically discussed as well.

Laplace Transformation Approach to the Spin Symmetry of the Mie-Type Potential with a Coulomb Tensor Interaction

The Dirac equation is solved exactly under the condition of spin symmetry for a spin 1=2 particle in the field of Mie-type potential and a Coulomb-like tensor interaction via the Laplace transform approach (LTA). The Dirac bound state energy equation and the corresponding normalized wave functions are obtained in closed forms with any spin-orbit coupling term k. The effects of the tensor interaction and the potential parameters on the bound states are also studied. It is noticed that the tensor interaction removes degeneracy between two states in spin doublets. Some numerical results are given and a few special cases of interest are presented. We have demonstrated that in the nonrelativistic limit, the solutions of the Dirac system converges to that of the Schrödinger system. The nonrelativistic limits of the present solutions are compared with the ones obtained by findings of other methods. Our results are sufficiently accurate for practical purpose.

Bound State Solutions of the Dirac Equation for the Eckart Potential with Coulomb-Like Yukawa-Like Tensor Interactions

In this paper, we present the approximate bound state solutions of the Dirac equation within the framework of spin and pseudospin symmetries for Eckart potential for arbitrary κ—state using Nikiforov–Uvarov method. The tensor interactions of Coulomb-like and Yukawa-like form are considered and the effects of these tensors and the degeneracy removing role are discussed in detail. Numerical results and figures to show the effect of the tensor interactions are also reported.

Gamma-ray evidence for dark matter clumps

We discuss the possibility of identification of point-like gamma-ray sources (PGS) with small scale dark matter (DM) clumps in our Galaxy. Gamma-rays are supposed to originate from annihilation of DM particles in the clumps, where annihilation rate is supposed to be enhanced, besides higher density, due to smaller relative velocities $v$ of DM particles. We parameterized the annihilation cross section $\sigma_\text{ann}(v)$ in the form of an arbitrary power law dependence on the relative velocity $v$ with/without factor of Sommerfeld-Gamow-Sakharov, implying existence of a new Coulomb-like interaction. Adopting different parameters of cross section and clump, satisfying condition $\Omega\lesssim 0.2$ on density of DM particles of question, they are constrained from comparison with Fermi/LAT data on unidentified PGS as well as on diffuse $\gamma$-radiation; results are applied to concrete DM candidates. Such analysis is found to be sensitive enough to existing uncertainty in the density profiles of DM in the clump what can provide a tool for their test. Also we discuss possibilities when gamma-radiating clump changes visibly its position on celestial sphere and it is seen as a spatially extended gamma-source (EGS), what can be probed in future experiments like Gamma-400.

Gamma-Ray Effects of Dark Forces in Dark Matter Clumps

Existence of new gauge U(1) symmetry possessed by dark matter (DM) particles implies the existence of a new Coulomb-like interaction, which leads to Sommerfeld-Gamow-Sakharov enhancement of dark matter annihilation at low relative velocities. We discuss a possibility to put constraints on such dark forces of dark matter from the observational data on the gamma radiation in our Galaxy. Gamma-rays are supposed to originate from annihilation of DM particles in the small scale clumps, in which annihilation rate is supposed to be enhanced, besides higher density, due to smaller relative velocitiesvof DM particles. For possible cross sections, mass of annihilating particles, masses of clumps, and the contribution of annihilating particles in the total DM density we constrain the strength of new dark long range forces from comparison of predicted gamma-ray signal with Fermi/LAT data on unidentified point-like gamma-ray sources (PGS) as well as on diffuseγ-radiation. Both data on diffuse radiation and data on PGS put lower constraints on annihilation cross section at any dark interaction constant, where diffuse radiation provides stronger constraint at smaller clump mass. Density of annihilating DM particles is conventionally supposed to be defined by the frozen annihilation processes in early Universe.

Pseudospin symmetry of the Dirac equation for a Möbius square plus Mie type potential with a Coulomb-like tensor interaction via SUSYQM

We investigate the approximate solution of the Dirac equation for a combination of Möbius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the bound-state energy equation and the corresponding spinor wave functions in an approximate analytical manner. We comment on the system via various useful figures and tables.

Relativistic symmetries in Yukawa-type interactions with Coulomb-like tensor

This study presents the solutions of the Dirac equation with a new suggested Yukawa-type potential for any spin–orbit quantum number κ interacting with a Coulomb-like tensor interaction. In the presence of spin and pseudospin (p-spin) symmetries, the approximate energy eigenvalues and wave functions are obtained by means of the parametric Nikiforov–Uvarov (pNU) method and the asymptotic iteration method (AIM). The numerical results show that the Coulomb-like tensor interaction removes degeneracies between spin and p-spin state doublets. The bound state solutions of the Schrödinger and Klein–Gordon equations for this new potential have also been presented. Our analytical results are in exact agreements with previous works.

Dirac equation for the generalized Deng-Fan potential with coulomb and Yukawa tensor interactions

In this paper, we investigate the bound-state solutions of the Dirac equation with the generalized Deng-Fan potential within the framework of spin and pseudospin symmetries and with Coulomblike and Yukawa-like tensor interactions by using a supersymmetric quantum-mechanics (SUSYQM) formulation. We obtain the energy eigenvalue equations and the corresponding upper and lower spinor wave functions for both the spin and the pseudospin cases. We also report some numerical results and figures to show the effect of the tensor interaction.

Eigen-spectra in the Dirac-attractive radial problem plus a tensor interaction under pseudospin and spin symmetry with the SUSY approach

We approximately solve the Dirac equation for attractive radial potential including a Coulomb-like tensor interaction under pseudospin and the spin symmetry limit for any arbitrary spin—orbit quantum number, by employing the supersymmetric (SUSY) quantum mechanics and supersymmetric shape invariance technique. We obtain the energy eigenvalue equation under the pseudospin and spin conditions. Some numerical results are compared with those obtained by the Nikiforove—Uvarov (NU) method.

Solutions of the Dirac equation with an improved expression of the Rosen–Morse potential energy model including Coulomb-like tensor interaction

In this study, we obtain the approximate analytical solutions of the Dirac equation for an improved expression of the Rosen–Morse potential energy model including the Coulomb-like tensor under the condition of spin and pseudospin symmetry. The analytical approach of parametric generalization of the Nikiforov–Uvarov method has been applied to the problem and the problem is discussed in a quite detailed manner.

An Integral Transform of Coulomb Green’s Function via Sturmian Representation and Off-Shell Scattering

By exploiting the term by term separability of the Sturmian function representation of the Coulomb Green’s function an integral transform of the corresponding outgoing wave Green’s function, that plays a crucial role in the studies of off-shell properties of the Coulomb and Coulomb-like interactions, is derived. Working in the representation space the off-shell Jost solutions and T-matrices for motion in Coulomb and Coulomb-modified nuclear potentials are expressed in terms of simple expressions involving hypergeometric functions. The effectiveness of our constructed expressions for the T-matrices is examined through a model calculation.

Approximate κ-state solutions to the Dirac Mobius square – Yukawa and Mobius square – quasi Yukawa problems under pseudospin and spin symmetry limits with Coulomb-like tensor interaction

In this paper, we present the Dirac equation for the Mobius square – Yukawa potentials including the tensor interaction term within the framework of pseudospin and spin symmetry limit with arbitrary spin–orbit quantum number, κ. We obtain the energy eigenvalues and the corresponding wave functions using the supersymmetry method. The limiting cases of the problem, which reduce to the Deng-Fan, Yukawa, and Coulomb potentials, are discussed.

Relativistic symmetries with the trigonometric Pöschl—Teller potential plus Coulomb-like tensor interaction

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Pöschl—Teller (tPT) potential including a Coulomb-like tensor interaction with arbitrary spin—orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ(κ ± 1)r−2. In view of spin and pseudo-spin (p-spin) symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method (AIM). We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ. The non-relativistic limit is also obtained.

Relativistic particle scattering states with tensor potential and spatially-dependent mass

We investigate the relativistic equation for particles with spin 1/2 in the q-parameter modified Pöschl-Teller potential, including Coulomb-like tensor interaction with spatially-dependent mass for the D-dimension. We present approximate solutions of the Dirac equation with these potentials for any spin-orbit quantum number κ under spin symmetry. The normalized wave functions are expressed in terms of the hyper-geometric series of the scattering states on the k/2π scale. We also give the formula for the phase shifts, and use the Nikiforov-Uvarov method to obtain the energy eigen-values equation.

Relativistic Spin and Pseudospin Symmetries of Inversely Quadratic Yukawa-like plus Mobius Square Potentials Including a Coulomb-like Tensor Interaction

The Dirac equation for the combined Mobius square and inversely quadratic Yukawa potentials including a Coulomb-like interaction term has been investigated in the presence of spin and pseudospin symmetries with arbitrary spin-orbit quantum number κ .We have obtained the explicit energy eigenvalues and the corresponding eigenfunctions by the framework of Nikiforov-Uvarov method.

Approximate relativistic bound states of a particle in Yukawa field with Coulomb tensor interaction

We obtain the approximate relativistic bound state of a spin- particle in the field of the Yukawa potential and a Coulomb-like tensor interaction with arbitrary spin–orbit coupling number κ under the spin and pseudospin (p-spin) symmetries. The asymptotic iteration method is used to obtain energy eigenvalues and the corresponding wave functions in their closed forms. Our numerical results show that the tensor interaction removes degeneracies between the spin and p-spin doublets and creates new degenerate doublets for various strengths of tensor coupling.

Fermionic particles with position-dependent mass in the presence of inversely quadratic Yukawa potential and tensor interaction

Approximate solutions of the Dirac equation with position-dependent mass are presented for the inversely quadratic Yukawa potential and Coulomb-like tensor interaction by using the asymptotic iteration method. The energy eigenvalues and the corresponding normalized eigenfunctions are obtained in the case of position-dependent mass and arbitrary spin-orbit quantum number k state and approximation on the spin-orbit coupling term.

Off-shell Jost solutions for Coulomb and Coulomb-like interactions in all partial waves

By exploiting the theory of ordinary differential equations, with judicious use of boundary conditions, interacting Green's functions and their integral transforms together with certain properties of higher transcendental functions, useful analytical expressions for the off-shell Jost solutions for motion in Coulomb and Coulomb-nuclear potentials are derived in maximal reduced form through different approaches to the problem in the representation space. The exact analytical expressions for the off-shell Jost solutions for Coulomb and Coulomb-like potentials are believed to be useful for the description of the charged particle scattering/reaction processes.