Spin symmetry in the relativistic modified Rosen-Morse potential with the approximate centrifugal term

By applying a Pekeris-type approximation to the centrifugal term, we study the spin symmetry of a Dirac nucleon subjected to scalar and vector modified Rosen-Morse potentials. A complicated energy equation and associated two-component spinors with arbitrary spin-orbit coupling quantum number k are presented. The positive-energy bound states are checked numerically in the case of spin symmetry. The relativistic modified Rosen-Morse potential cannot trap a Dirac nucleon in the limiting case α→ 0.     

Pseudospin symmetry for modified Rosen-Morse potential including a Pekeris-type approximation to the pseudo-centrifugal term

By a novel algebraic method we study the approximate solution to the Dirac equation with scalar and vector second P?schl-Teller potential carrying spin symmetry. The transcendental energy equation and spinor wave functions with arbitrary spin-orbit coupling quantum number k are presented. It is found that there exist only positive-energy bound states in the case of spin symmetry. Also, the energy eigenvalue approaches a constant when the potential parameter a \alpha goes to zero. The equally scalar and vector case is studied briefly.     

Meson spectra with a power-law potential in the Dirac equation

A power law potential which is an equal admixture of scalar and vector parts with effective powerv ∞ 1/m _q , is proposed as a quark confining potential in the Dirac equation. The model is capable of predicting the meson spectroscopy encompassing both light and heavy quark-antiquark systems in a unified way.     

类Quesne环状球谐振子势场中的赝自旋对称性

提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质. 关键词： 类Quesne环状球谐振子势 Dirac方程 赝自旋对称性 束缚态     

一类相对论性非球谐振子系统的束缚态

给出了具有形式为12r²+A2r²的非球谐振子型标量势和矢量势 的相对论系 统在两种势相等的条件下三维Klein-Gordon方程，二维和三维Dirac方程的s波束缚态解. 关键词： 三维非球谐振子势 Klein-Gordon方程 Dirac方程 束缚态     

相对论性非球谐振子势场中的赝自旋对称性

求解了非球谐振子势场中1/2自旋粒子满足的Dirac方程,Dirac哈密顿量包含有标量非球谐振子势S(r)和矢量非球谐振子势V(r).在Σ(r)=S(r)+V(r)=0和Δ(r)=V(r)-S(r)=0的条件下,解析地得到了Dirac旋量波函数的束缚态解和能谱方程,结果表明非球谐振子势 关键词： 非球谐振子势 Dirac方程 赝自旋对称性 束缚态     

具有Hulthén的型势的Dirac方程的束缚态

本文给出,具有一维Hulthén型标量势和矢量势的Dirac方程的束缚态精确解。对于三维情况,在Hulthén型标量势和矢量势相等的条件下,给出Dirac方程的S波解。     

Solutions of Dirac equations with the Pöschl-Teller potential

By using the basic concepts of the supersymmetric quantum mechanics formalism and the function analysis method, we solve the Dirac equation with vector and scalar potentials and obtain the bound-state solutions for the nuclei in the relativistic P?schl-Teller potential. All of the analyses are prepared under the conditions of the exact spin symmetry and pseudospin symmetry. The exact energy equation and corresponding two-component spinor wave functions for s -wave bound states are obtained analytically.     

Can quarks always be confined by a linear potential?

It is demonstrated on the basis of the Dirac equation that quarks cannot be confined by a vector gluon potential of the form(r/r ₀)^a or[ln(r/r ₀]^a, a>0, if the quark-gluon interaction conserves parity. In order to confine quarks with the parity-conserving interaction, the effective gluon potential must be a pseudovector or a scalar. These are shown in a simple Yang-Mills field with theSU(2) group.     

Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry

In this Letter the approximately analytical bound state solutions of the Dirac equation with the Manning-Rosen potential for arbitrary spin-orbit coupling quantum number k are carried out by taking a properly approximate expansion for the spin-orbit coupling term. In the case of exact spin symmetry, the associated two-component spinor wave functions of the Dirac equation for arbitrary spin-orbit quantum number k are presented and the corresponding bound state energy equation is derived. We study briefly two special cases; the general s-wave problem and the equal scalar and vector Manning-Rosen potential.     

Generalized spin and pseudo-spin symmetry: Relativistic extension of supersymmetric quantum mechanics

We consider the Dirac equation in 1+1$1+1$ space–time dimension with vector, scalar and pseudo-scalar coupling. In the traditional spin (or pseudo-spin) symmetry, the difference between (or sum of) the scalar and vector potentials is a constant. Here, however, we introduce an alternative symmetry where the scalar or pseudo-scalar potential is proportional to the vector potential. This leads to a model with significant extensions to supersymmetric quantum mechanics. We present a formal solution of the problem but give explicit analytic results for specific examples.     

Klein–Gordon and Dirac Equations with Thermodynamic Quantities

We study the thermodynamic quantities such as the Helmholtz free energy, the mean energy and the specific heat for both the Klein–Gordon, and Dirac equations. Our analyze includes two main subsections: (1) statistical functions for the Klein–Gordon equation with a linear potential having Lorentz vector, and Lorentz scalar parts (2) thermodynamic functions for the Dirac equation with a Lorentz scalar, inverse-linear potential by assuming that the scalar potential field is strong (A ? 1). We restrict ourselves to the case where only the positive part of the spectrum gives a contribution to the sum in partition function. We give the analytical results for high temperatures.     

Exactly Solvable Combinations of Scalar and Vector Potentials for the Dirac Equation Interrelated by Riccati Equations

New classes of solvable scalar and vector potentials for the Dirac equation are obtained, together with the associated exact Dirac spinors. The method of derivation is based on an a priori constraint between the solutions, leading to an interrelation between the scalar and vector potential in the form ofa Riccati equation. The present note generalizes a series of former articles.     

Evidence for a real tensor potential in the inelastic scattering of 800 mev polarized protons from20ne using the dirac phenomenology

Coupled-channel calculations using the Dirac phenomenology have been performed to analyze cross-sections and analyzing powers data for inelastic scattering of 800 MeV, polarized protons from low-lying states in²⁰Ne. Good agreement with the data has been obtained by using a real tensor potential V _t ^r =27.02 MeV, in addition to real scalar potential and complex vector potential. Deformation parameters obtained at this energy of 800 MeV are very close to those obtained at an energy much lower (24.5 MeV). Once more, considerable improvements obtained by using Dirac equation, compared to Schrödinger calculations, are confirmed. The calculations are also consistent with V _s ⁱ =0.     

Massive Quasinormal Modes of a Schwarzschild-de Sitter Black Hole with a Global Monopole

Using the WKB approximation, we evaluate both the massless and massive scalar and Dirac fields quasinormal modes (QNMs) of a Schwarzschild-de Sitter black hole. The result shows that the field with higher masses and larger cosmological constant λ will decay more slowly. We also found that the global monopole is similar to a factor to modify the κ of Dirac field or l of scalar field, where κ is the angular momentum number of Dirac field, and l is the angular momentum number of scalar field.     

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 Hulthén potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number κ. 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.     

Pseudospin symmetry and a double ring-shaped spherical harmonic oscillator potential

A new double ring-shaped spherical harmonic oscillator potential is presented. The pseudospin symmetry in this system is investigated by solving the Dirac equation with equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy equation are obtained and some particular cases are discussed.      

Analytic Advantages of Spherically Symmetric Step-Function Potentials in the Dirac Equation with Scalar and Fourth Component of Vector Potential

The root mean square radii of the particle orbits are calculated (semi)analyticallyfor every bound state, using the Dirac equation with a scalar potentialU _s andfourth component of a vector potentialU _v in the case of a spherically symmetricstep-function shape with the same radiusR for these potentials. In addition, a(semi)analytic expression of the expectation value of the corresponding potentialenergy operator is derived. For the above quantities, expressions of the energyeigenvalues in terms of the potential parameters are needed and approximateformulas may be used in certain cases. This study emphasizes the analyticadvantages of the relativistic, spherically symmetric step-function potential model.Its applicability is discussed in connection with a problem of physical interest,namely that of the motion of a particle in hypernuclei.     

Excited states of mesons and the quark-antiquark interaction

The Dirac equation is used in an investigation of the properties of mesons according to the quark-antiquark model. The dependence of the meson mass on angular momentum excitation is considered for several models. The properties of the Dirac equation with a potential consisting of an equal mixture of scalar and vector potential are investigated.     

On particles tunneling from the Taub-NUT-AdS black hole

This paper discusses tunneling of scalar particles and Dirac particles from the Taub-NUT-AdS black hole by the Hamilton--Jacobi equation, initially used by Angheben et al, and the Dirac equation, recently proposed by Kerner and Mann. This is performed in the dragging coordinate frame so as to avoid the ergosphere dragging effect. A general form is obtained for the temperature of scalar and Dirac particles tunneling from the Taub-NUT-Ads black hole, which is commensurate with other methods as expected.