Pseudospin Symmetry Research Articles

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.

Relativistic pseudospin and spin symmetries in physical systems – recent results

In this paper we revise the main features of pseudospin and spin symmetries of the Dirac equation with scalar and vector potentials and mention several of its applications to physical systems. These symmetries have been extensively researched in the last 15 years, especially pseudospin symmetry, mainly in its application in understanding certain nuclear structure features of heavy nuclei. The realization of both symmetries has also been studied using several mean-field scalar and vector potentials. For many classes of potentials, these symmetries allow to have analytical solutions of the Dirac equation which otherwise would not have been possible. We report here some recent results related to anti-fermions, Coulomb and confining potentials.

Approximate solutions to a spatially-dependent mass Dirac equation for modified Hylleraas plus Eckart potential with Yukawa potential as a tensor

In presence of spin (pseudo-spin) symmetry, approximate bounded fermionic (anti-fermionic) states of the effective mass Dirac equation for modified Hylleraas plus Eckart potential within Yukawa tensor interaction have been studied by means of the parametric Nikiforov–Uvarov method. We have obtained the analytical relativistic energy eigenvalues and their corresponding normalized two-spinor components of the wave functions in closed form by making an appropriate approximation to centrifugal (pseudo-centrifugal) term for any spin–orbit quantum number κ. Some special cases for various potential models have been investigated in relativistic and nonrelativistic limit. Further, numerical results for energy eigenvalues have been obtained within the exact spin and pseudo-spin symmetries.

Generalized tensor interaction and relativistic spin and pseudospin symmetries with the Manning-Rosen potential

We have investigated the Manning-Rosen potential under the framework of spin and pseudospin symmetries with generalized tensor interaction (GTI) using the parametric generalization of Nikiforov-Uvarovmethod. We have obtained the energy eigenvalues and the corresponding eigenfunction. We have also reported some numerical results and figures to show the effect of tensor interaction. The role of GTI is investigated in details. It is seen that the degenerate doublets in spin and pseudospin are changed due to the presence of GTI.

Solution of Dirac Equations for Cotangent Potential with Coulomb-type Tensor Interaction for Spin and Pseudospin Symmetries Using Romanovski Polynomials

Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 Abstract   The bound state solutions of Dirac equations for cotangent function potential with the Coulomb-type tensor potential under spin and pseudospin symmetric limits are obtained using finite Romanovski polynomials. The approximate relativistic energy spectra are obtained for spin and pseudospin symmetries exactly. The radial wave functions are obtained in terms of Romanovski polynomials in the limit of spin and pseudospin symmetric conditions. The Coulomb type tensor potential removes the doublet degeneracies for pseudospin and spin symmetric cases. The relativistic energy spectrum for the exact spin symmetric case reduces to the non-relativistic energy spectrum in the non-relativistic limit.     Abstrak   Solusi Persamaan Dirac untuk Potensial K otangen dengan Tensor Interaksi Tipe-Coulomb untuk Simetri Spin dan Pseudospin Menggunakan Polinomial Romanovski. Solusi keadaan terikat dari persamaan Dirac untuk potensial fungsi kotangen dengan potensial tensor tipe-Coulomb untuk simetri spin dan pseudospin diperoleh menggunakan polinomial Romanovski terbatas. Aproksimasi spektrum energi relativistik diperoleh secara eksak untuk simetri spin dan pseudospin. Fungsi gelombang radial diperoleh dalam bentuk polinomial Romanovski untuk keadaan simetri spin dan pseudospin. Potensial tensor tipe-Coulomb menghilangkan degenerasi doublet untuk kedua kasus simetri spin dan pseudospin. Pada batas non-relativistik, spektrum energi relativistik untuk kasus simetri spin eksak tereduksi menjadi spektrum energi non-relativistik.   Keywords: cotangent potential, Coulomb-type tensor, Dirac equation, pseudospin symmetry, Romanovski polynomials /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}

κ state solutions for the fermionic massive spin-½ particles interacting with double ring-shaped Kratzer and oscillator potentials

In recent years, an extensive survey on various wave equations of relativistic quantum mechanics with different types of potential interactions has been a line of great interest. In this regime, special attention has been given to the Dirac equation because the spin-½ fermions represent the most frequent building blocks of the molecules and atoms. Motivated by the considerable interest in this equation and its relativistic symmetries (spin and pseudospin), in the presence of solvable potential model, we attempt to obtain the relativistic bound states solution of the Dirac equation with double ring-shaped Kratzer and oscillator potentials under the condition of spin and pseudospin symmetries. The solutions are reported for arbitrary quantum number in a compact form. The analytic bound state energy eigenvalues and the associated upper- and lower-spinor components of two Dirac particles have been found. Several typical numerical results of the relativistic eigenenergies have also been presented. We found that the existence or absence of the ring shaped potential has strong effects on the eigenstates of the Kratzer and oscillator particles, with a wide band spectrum except for the pseudospin-oscillator particles, where there exist a narrow band gap.

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 investigated under the Deng—Fan potential by applying the asymptotic iteration method for the arbitrary quantum numbers n and κ. Some of the numerical results are also represented in both pseudospin symmetry and spin symmetry limits.

Solution of Dirac Equation for q-Deformed Eckart Potential with Yukawa-type Tensor Interaction for Spin and Pseudospin Symmetry Using Romanovski Polynomial

The motion of a nucleon in q-deformed Eckart potential field coupled with Yukawa-type tensor potential is described by using Dirac equation. The bound state solutions of Dirac equation for q-deformed Eckart potential with Yukawa-type tensor potential under exact spin- and pseudospin-symmetric limit are obtained using finite Romanovski polynomials. The approximate relativistic energy spectra are exactly obtained within the approximation scheme of centrifugal term. The relativistic energy is negative for pseudospin symmetry and positive for spin symmetry. The radial component of Dirac spinors are obtained in terms of Romanovski polynomials under exact spin- and pseudospin-symmetric conditions. The relativistic energy spectrum for the exact spin-symmetric case reduces to non-relativistic energy spectrum in the non-relativistic limit. Received: 23 October 2013; Revised: 02 November 2013 Accepted: 10 November 2013

What do the conditions of exact pseudospin symmetry in nuclear relativistic models mean in real nuclei?

We study the continuous evolution of the single-particle levels from a model satisfying exact spin symmetry (SS) to another one satisfying exact pseudospin symmetry (PSS), using a Dirac equation with potentials of scalar, vector and tensor type. All the standard pseudospin doublets (PSDs) appearing in the limit of the SS have their corre- sponding PSDs in the limit of the PSS but not vice versa. The PSS is strongly violated between the SS and PSS limits.

Relativistic symmetries of fermions in the background of the inversely quadratic Yukawa potential with Yukawa potential as a tensor

In the presence of spin and pseudo-spin symmetries, we obtain approximate analytical bound state solutions to the Dirac equation with scalar–vector inverse quadratic Yukawa potential including a Yukawa tensor interaction for any arbitrary spin–orbit quantum number, κ. The energy eigenvalues and their corresponding two-component spinor wave functions are obtained in closed form using the parametric Nikiforov–Uvarov method. It is noticed that the tensor interaction removes the degeneracy in the spin and p-spin doublets. Some numerical results are obtained for the lowest energy states within spin and pseudo-spin symmetries.

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.

Generalized Tensor Interaction and Relativistic Spin and Pseudospin Symmetries with the Manning–Rosen Potential

Generalized Tensor Interaction and Relativistic Spin and Pseudospin Symmetries with the Manning–Rosen Potential

Hyperbolic Manning-Rosen potential under spin and pseudospin symmetries of the Dirac equation with Coulomb-Hulthén-like tensor interactions

Hyperbolic Manning-Rosen potential under spin and pseudospin symmetries of the Dirac equation with Coulomb-Hulthén-like tensor interactions

Energy Levels of Spin-1/2 Particles with Yukawa Interaction

In this article, Yukawa interaction is used to study the relativistic spin-1/2 particles and obtain their energy levels. The role of Yukawa potential on the spin and pseudospin symmetry solution is investigated systematically by solving the Dirac equation with attractive scalar S(r) and repulsive vector V(r) potentials. Bound state spectrum and wave functions of Yukawa potential are obtained. It is found that the energy eigenvalues strongly depend on the potential parameters.

Dirac Equation under Scalar and Vector Generalized Isotonic Oscillators and Cornell Tensor Interaction

Spin and pseudospin symmetries of Dirac equation are solved under scalar and vector generalized isotonic oscillators and Cornell potential as a tensor interaction for arbitrary quantum number via the analytical ansatz approach. The spectrum of the system is numerically reported for typical values of the potential parameters.

Effective Field Theory for Two-Species Bosons in an Optical Lattice: Multiple Order, the Nambu–Goldstone Bosons, the Higgs Mode, and Vortex Lattice

In the previous papers, we studied the bosonic \(t\)–\(J\) mode and derived an effective field theory, which is a kind of quantum XY model. The bosonic \(t\)–\(J\) model is expected to be realized by experiments of two-component cold atoms in an optical lattice. In this paper, we consider a similar XY model that describes phase diagram of the \(t\)–\(J\) model with a mass difference. Phase diagram and critical behavior of the quantum XY model are clarified by means of the Monte-Carlo simulations. Effective field theory that describes the phase structure and low-energy excitations of the quantum XY model is derived. Nambu–Goldstone bosons and the Higgs mode are studied by using the effective field theory and interesting findings are obtained for the system with multiple order, i.e., Bose–Einstein condensations and pseudo-spin symmetry. We also investigate physical properties of the quantum XY model in an effective magnetic field that is realized by rotating the optical lattice, etc. We show that low-energy states of the system strongly depend on the strength of the “magnetic field”. For some specific strength of the magnetic field, vortex lattice forms and the correlation function of the bosons exhibits solid like behavior, which is a kind of Bose–Einstein condensation.

The Laplace transform approach for a Dirac isotonic oscillator with a tensor potential in D-dimensions

The exact bound-state energy and the corresponding eigenfunctions of a relativistic spin 1/2 harmonic oscillator with a centripetal barrier, known as an isotonic oscillator including the tensor interaction term are obtained in D-dimensions. In particular, we use the Laplace transform method in the pseudospin symmetry limit. It is shown that our analytical results are consistent with those obtained by Agboola (2012 J. Math. Phys. 53 052302) and Ikhdair and Sever (2011 J. Math. Phys. 52 122108) in the absence of the tensor interaction using different methods. Further, we give some numerical results on the energy levels for different values of related quantum numbers.

Pseudospin and spin symmetry of Dirac equation under Deng–Fan potential and Yukawa potential as a tensor interaction

In this paper, we have presented approximately analytical solution of Dirac equation under the pseudospin and spin symmetry for Deng–Fan potential. We have considered Yukawa potential as a tensor interaction. Some numerical results for energy eigenvalues and the corresponding wave functions of Dirac equation in both pseudospin and spin symmetry are reported. The effect of tensor interaction has been also investigated.

Spin and pseudospin symmetries of the Dirac equation with shifted Hulthén potential using supersymmetric quantum mechanics

In this paper, we obtain approximate analytical solutions of the Dirac equation for the shifted Hulthén potential within the framework of spin and pseudospin symmetry limits for arbitrary spin—orbit quantum number κ using the supersymmetry quantum mechanics. The energy eigenvalues and the corresponding Dirac wave functions are obtained in closed forms.

Mott-insulator to commensurate-solid transition in a4He layer onα-graphyne

Path-integral Monte Carlo calculations were performed to study the adsorption of ${}^{4}$He atoms on $\ensuremath{\alpha}$-graphyne. We find that one ${}^{4}$He atom can be embedded onto the in-plane center of each hexagon of the graphyne. In the first ${}^{4}$He layer above the ${}^{4}$He-embedded graphyne surface, a Mott-insulating state was observed at an areal density of 0.0706 \AA{}${}^{\ensuremath{-}2}$ with three ${}^{4}$He atoms occupying each hexagonal cell while the helium atoms form a commensurate triangular solid at a density of 0.0941 \AA{}${}^{\ensuremath{-}2}$. Here we show that the Ising pseudospin symmetry introduced for two degenerate configurations of three ${}^{4}$He atoms in a hexagonal cell can be broken by additional ${}^{4}$He atoms placed at the hexagon vertices, and the Mott-insulator to commensurate-solid transition is a transition from a nonmagnetic spin liquid of frustrated antiferromagnets to a spin-aligned ferromagnet under a particle-induced pseudomagnetic field.