Dirac Equation under Scalar, Vector, and Tensor Cornell Interactions

Advances in High Energy Physics ◽

10.1155/2012/707041 ◽

2012 ◽

Vol 2012 ◽

pp. 1-17 ◽

Cited By ~ 4

Author(s):

H. Hassanabadi ◽

E. Maghsoodi ◽

S. Zarrinkamar ◽

H. Rahimov

Keyword(s):

Dirac Equation ◽

Quantum Number ◽

Ansatz Approach ◽

Potential Parameters ◽

Arbitrary Quantum

Spin and pseudospin symmetries of Dirac equation are solved under scalar, vector, and tensor interactions for arbitrary quantum number via the analytical ansatz approach. The spectrum of the system is numerically reported for typical values of the potential parameters.

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

Advances in High Energy Physics ◽

10.1155/2014/831938 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

H. Hassanabadi ◽

E. Maghsoodi ◽

Akpan N. Ikot ◽

S. Zarrinkamar

Keyword(s):

Dirac Equation ◽

Quantum Number ◽

Tensor Interaction ◽

Cornell Potential ◽

Ansatz Approach ◽

Potential Parameters ◽

Arbitrary Quantum

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.

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

Canadian Journal of Physics ◽

10.1139/p2012-061 ◽

2012 ◽

Vol 90 (7) ◽

pp. 655-660 ◽

Cited By ~ 5

Author(s):

M. Hamzavi ◽

S.M. Ikhdair

Keyword(s):

Dirac Equation ◽

Quantum Number ◽

Coulomb Potential ◽

Iteration Method ◽

Arbitrary Spin ◽

Tensor Interaction ◽

Asymptotic Iteration Method ◽

Spin Orbit ◽

Energy Eigenvalues ◽

Energy Dependent

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.

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Zur Theorie der Elementarteilchen

Zeitschrift für Naturforschung A ◽

10.1515/zna-1959-5-601 ◽

1959 ◽

Vol 14 (5-6) ◽

pp. 441-485 ◽

Cited By ~ 6

Author(s):

H.-P. Dürr ◽

W. Heisenberg ◽

H. Mitter ◽

S. Schlieder ◽

K. Yamazaki

Keyword(s):

Differential Equation ◽

Dirac Equation ◽

Linear Differential Equation ◽

Quantum Number ◽

Scale Transformation ◽

Discrete Groups ◽

Coupling Constant ◽

Symmetry Properties ◽

Linear Differential ◽

The Masses

The equation is analysed with respect to the following consequences. I the group theoretical structure of the equation is studied. The equation is invariant under a number of continous transformations: the inhomogeneous Lorentzgroup, the transformations of PAULI, GÜRSEY and TOUSCHEK, and the scale transformation [ϰ→η x or ψ → η⅔ψ(ϰη, l η)]. The PAULI-GÜRSEY group is used for the interpretation of the isospin; the γ5-transformation of TOUSCHEK establishes a quantum number IN, and the scale transformation leads to a quantum number IN, which both are connected with the baryonic and the leptonic number. The strangeness s=lN-lQ is suggested to be connected with the discrete groups of the equation and could then be defined and conserved only modulo 4. Of the discrete groups only the well known transformations P, C and T and the reversal of l (l→ - l) are briefly discussed. In II the vacuum expectation values of products of two field operators are studied. These values are considered to be only in a first approximation invariant under the Isospingroup. The deviations from the PAULI-GÜRSEY symmetry in higher approximations are supposed to be due to the replacement of the state “vacuum” by an idealised state “world”, which possesses an infinite isospin; the strange particles are consequently interpreted as states which “borrow” an isospin 1/2 or 1 from the ground state “world”. The concept of “One particle-wavefunctions” is discussed in III. The fermions of finite mass belong to wavefunctions obeying a KLEIN-Gordon-spinor equation instead of a DIRAC equation. The connection with the conventional formalism of the DIRAC equation is treated in detail. The process of ^-conjugation springing from these discussions is used for a variation of the methods of approximation needed later on for the determination of mass values and the pion-nucleon coupling constant. In IV the TAMM-DANCOFF method is applied in two different forms for an estimate of the masses of nucleons and π-mesons. The masses and the symmetry properties of the particles agree qualitatively with the experimental results. The scattering of π-mesons from nucleons is treated in V by a method related more closely to the BETHE-SALPETER theory than to the TAMM-DANCOFF method; the theory leads to a relativistic pseudovector-coupling as the main term and to a value of the coupling constant of the right order of magnitude. In VI the interaction for β-decay is analysed with respect to its symmetry properties. The theory leads to cs =cT= cp=0 and, in the lowest approximation, to cA= -cV, while in higher approximations the ratio cA/cv will be somewhat altered. In VII some mathematical questions are discussed that have been raised by PAULI at the Geneva conference 1958. For the renormalized operators of the Lee model an integro-differential equation is given, that contains only the arbitrarily small time interval Δt. It is further shown in detail why a linear differential equation leads to δ-functions on the light cone for the propagator, while a non linear differential equation can produce there a different kind of singularity.

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Relativistic Energy States of the A-Particle in Hypernuclei Using Gaussian Potentials

Zeitschrift für Naturforschung A ◽

10.1515/zna-1990-0104 ◽

1990 ◽

Vol 45 (1) ◽

pp. 14-16

Author(s):

C. G. Koutroulos

Keyword(s):

Dirac Equation ◽

Excited States ◽

Ground State ◽

Vector Potential ◽

Scalar Potential ◽

Binding Energies ◽

Relativistic Energy ◽

Gaussian Form ◽

Fourth Component ◽

Potential Parameters

Abstract The Dirac equation with scalar potential and fourth component of vector potential of the Gaussian form is solved numerically for potential parameters obtained by a least squares fitting of the ground state binding energies of the A in a number of hypernuclei. The binding energies in the ground and excited states for various hypernuclei are determined. The spacings between the various levels are also given

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APPROXIMATE BOUND DIRAC STATES FOR PSEUDOSCALAR HULTHÉN POTENTIAL

International Journal of Modern Physics E ◽

10.1142/s0218301313500353 ◽

2013 ◽

Vol 22 (06) ◽

pp. 1350035

Author(s):

M. HAMZAVI ◽

A. A. RAJABI ◽

F. KOOCHAKPOOR

Keyword(s):

Dirac Equation ◽

Energy Eigenvalue ◽

Spin Symmetry ◽

Bound State ◽

Hulthén Potential ◽

Energy Eigenvalues ◽

Hulthen Potential ◽

Approximate Analytical Solutions ◽

Potential Parameters ◽

Nu Method

In this paper, we present approximate analytical solutions of the Dirac equation with the pseudoscalar Hulthén potential under spin and pseudospin (p-spin) symmetry limits in (3+1) dimensions. The energy eigenvalues and corresponding eigenfunctions are given in their closed forms by using the Nikiforov–Uvarov (NU) method. Numerical results of the energy eigenvalue equations are presented to show the effects of the potential parameters on the bound-state energies.

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Relativistic Ground and Excited State Energies of a/1-Particle in Hypernuclei Using Woods-Saxon Potentials

Zeitschrift für Naturforschung A ◽

10.1515/zna-1989-1219 ◽

1989 ◽

Vol 44 (12) ◽

pp. 1234-1238 ◽

Cited By ~ 2

Author(s):

C. G. Koutroulos

Keyword(s):

Excited State ◽

Dirac Equation ◽

Excited States ◽

Ground State ◽

Scalar Potential ◽

Binding Energies ◽

Fitting Procedure ◽

Fourth Component ◽

Potential Parameters ◽

Good Agreement

Abstract The relativistic Dirac equation with a scalar potential and the fourth component of a vector potential of the Woods-Saxon shape is solved numerically for potential parameters obtained by a last squares fitting procedure of the ground state binding energies of the Λ in a number of hypernuclei and its binding energies in the ground and excited states (as well as the relevant spacings) for various hypcrnuclei are determined. The results are in very good agreement with the preliminary experimental ones given by Chrien on the basis of the (π+, K+) reaction on nuclei.

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