Bound state solutions of the Dirac equation with the Deng–Fan potential including a Coulomb tensor interaction

Approximate analytical solutions of the Dirac equation in the case of pseudospin and spin symmetry limits are inves- tigated under the Deng-Fan potential by applying the asymptotic iteration method for the arbitrary quantum numbers n and ~~. Some of the numerical results are also represented in both pseudospin symmetry and spin symmetry limits.

Relativistic symmetry of position-dependent mass particles in a Coulomb field including tensor interaction

The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials,including a tensor interaction under the spin and pseudospin symmetric limits.Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ.Some numerical results are also given,and the effect of tensor interaction on the bound states is presented.It is shown that tensor interaction removes the degeneracy between two states in the spin doublets.We also investigate the effects of the spatially-dependent mass on the bound states under spin symmetric limit conditions in the absence of tensor interaction.

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.

Relativistic symmetries with the trigonometric Pschl-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 Poeschl-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± i 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.

Tensor Interaction Effect in Dibaryon

The gluon and Goldstone boson induced tensor interaction effect on thedibaryon mass and the D-wave decay width has been studied in the quark delocalization, colorscreening model. The effective S-D wave transition interactions induced by gluon and Goldstone bosonexchanges decrease quickly as the increasing of the channel strangeness. The K and η meson tensorcontribution is negligible in this model. No six-quark state in the light Savor world can become abound one by the help of these tensor interactions except the deuteron. The partial D-wave decaywidth of I J~p = (1/2) 2~+ NΩ state to spin 0, 1 ΛΞ final state is 20.7 keV and 63.1 keVrespectively. It is a very narrow dibaryon resonance and might be detected in the relativistic heavyion reaction by the existing RHIC detectors through the reconstruction of the ΛΞ vertex mass andthe future COMPAS detector at CERN and FAIR project in Germany.

Dirac Equation with a New Tensor Interaction under Spin and Pseudospin Symmetries

The approximate analytical solutions of the Dirac equation under spin and pseudospin symmetries are examined using a suitable approximation scheme in the framework of parametric Nikiforov-Uvarov method.Because a tensor interaction in the Dirac equation removes the energy degeneracy in the spin and pseudospin doublets that leads to atomic stability,we study the Dirac equation with a Hellmann-like tensor potential newly proposed in this study.The newly proposed tensor potential removes the degeneracy from both the spin symmetry and pseudospin symmetry completely.The proposed tensor potential seems better than the Coulomb and Yukawa-like tensor potentials.

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.

Remove Degeneracy in Relativistic Symmetries for Manning–Rosen Plus Quasi-Hellman Potentials by Tensor Interaction

The relativistic Dirac equation under spin and pseudo-spin symmetries is investigated for Manning–Rosen plus quasi-Hellman potentials with tensor interaction. For the first time we consider the Hulthen plus Yukawa for tensor interaction. The Formula method is used to obtain the energy eigen-values and wave functions. We also discuss about the energy eigen-values and the Dirac spinors for the Manning–Rosen plus quasi-Hellman potentials for the spin and pseudo-spin symmetry with Formula method. To show the accuracy of the present model, some numerical results are shown in both pseudo-spin and spin symmetry limits.

Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation method

A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S（r） and a vector V（r） Mie-type potential in the radial coordinates, as well as a tensor potential U（r） in the form of Coulomb potential. In the pseudospin（p-spin） symmetry setting Σ = Cps and Δ = V（r）, an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin–orbit coupling number κ. Special attention is devoted to the caseΣ = 0 for which p-spin symmetry is exact. The Laplace transform approach（LTA） is used in our calculations. Some numerical results are obtained and compared with those of other methods.

Tensor force impact on shell evolution in neutron-rich Si and Ni isotopes

The influence of the tensor interaction of nucleons on the characteristics of neutron-rich silicon and nickel isotopes was studied in this work.Tensor forces are considered within the framework of the Hartree-Fock approach with the Skyrme interaction.The addition of a tensor component of interaction is shown to improve the description of the splittings between different single-particle states and decrease nucleon-nucleon pairing correlations in silicon and nickel nuclei.Special attention was directed toward the role of isovector tensor forces relevant to the interaction of like nucleons.

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 P5schl- 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 k 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.