Interaction of dirac particle AMM with Coulomb field of a superheavy nucleus: Perturbative and nonperturbative aspects

The known systems of the radial equations describing the hydrogen atom on the basis of the Dirac equation in the Lobachevsky–Riemann spaces of constant curvature are investigated. In the both geometrical models, the differential equations of second order with six regular singular points are found, and their exact solutions of Frobenius type are constructed. To produce the quantization rule for energy values we use the known condition which separates the transcendental Frobenius solutions. This provides us with the energy spectra that are physically interpretable and are similar to those for the Klein–Fock–Gordon particle in these space models. These spectra are similar to those that previously have appeared in studying the same systems of the equations with the use of the semi-classical approximation.

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Dirac particle in Aharonov–Bohm–Coulomb field: Path integral treatment

Modern Physics Letters A ◽

10.1142/s0217732321502692 ◽

2022 ◽

Author(s):

A. Merdaci ◽

N. Boudiaf ◽

L. Chetouani

Keyword(s):

Green’S Function ◽

Green's Function ◽

Path Integral ◽

Spin Dynamics ◽

Coulomb Field ◽

Dirac Particle ◽

Coordinate Space ◽

Relativistic Limit ◽

Integral Treatment ◽

Aharonov Bohm

Exact Green’s function related to a Dirac particle submitted to the combination of Aharonov–Bohm and Coulomb potentials in [Formula: see text]) coordinate space is analytically calculated via path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger model. The energy spectrum as well as the corresponding normalized wave functions are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for Green’s function, it is shown that the non-relativistic limit of the Dirac particle is undertaken with much ease.

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Asymptotic behaviour of a Dirac particle in a Coulomb field

Il Nuovo Cimento A ◽

10.1007/bf02738369 ◽

1966 ◽

Vol 45 (4) ◽

pp. 801-812 ◽

Cited By ~ 21

Author(s):

J. Dollard ◽

G. Velo

Keyword(s):

Asymptotic Behaviour ◽

Coulomb Field ◽

Dirac Particle

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Dirac Particle in the Coulomb Field on the Background of Hyperbolic Lobachevsky Model

Nonlinear Phenomena in Complex Systems ◽

10.33581/1561-4085-2021-24-3-260-271 ◽

2021 ◽

Vol 24 (3) ◽

pp. 260-271

Author(s):

E. M. Ovsiyuk ◽

A. D. Koral’kov ◽

A. V. Chichurin ◽

V.M. Red’kov

Keyword(s):

Differential Equation ◽

Gordon Equation ◽

Order Differential Equation ◽

Coulomb Field ◽

Dirac Particle ◽

Quantization Rule ◽

Exact Analytical Solutions ◽

Relativistic Hydrogen ◽

Relativistic Hydrogen Atom

The known systems of radial equations describing the relativistic hydrogen atom on the base of the Dirac equation in Lobachevsky hyperbolic space is solved. The relevant 2-nd order differential equation has six regular singular points, its solutions of Frobenius type are constructed explicitly. To produce the quantization rule for energy values we have used the known condition for determination of the transcendental Frobenius solutions. This defines the energy spectrum which is physically interpretable and similar to the spectrum arising for the scalar Klein-Fock-Gordon equation in Lobachevsky space. In the present paper, exact analytical solutions referring to this spectrum are constructed. Convergence of the series involved is proved analytically and numerically. Squared integrability of the solutions is demonstrated numerically. It is shown that the spectrum coincides precisely with that previously found within the semi-classical approximation.

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Bifurcational Variations of the Structure of the Precessing Elliptic Trajectory of a Particle in the Coulomb Field Under the Action of Small Perturbations

Telecommunications and Radio Engineering ◽

10.1615/telecomradeng.v52.i11.40 ◽

1998 ◽

Vol 52 (11) ◽

pp. 17-19

Author(s):

D.B. Kostarev ◽

E. E. Getmanova ◽

A. G. Reuka

Keyword(s):

Coulomb Field ◽

Small Perturbations

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From the Vector to Scalar Perturbations Addition in the Stark Broadening Theory of Spectral Lines

Universe ◽

10.3390/universe7060176 ◽

2021 ◽

Vol 7 (6) ◽

pp. 176

Author(s):

Valery Astapenko ◽

Andrei Letunov ◽

Valery Lisitsa

Keyword(s):

Spectral Line ◽

Stark Effect ◽

Coulomb Field ◽

Spectral Lines ◽

Alternative Methods ◽

Scalar Perturbation ◽

Numerical Comparison ◽

Line Shapes ◽

Stark Effects ◽

The Impact

The effect of plasma Coulomb microfied dynamics on spectral line shapes is under consideration. The analytical solution of the problem is unachievable with famous Chandrasekhar–Von-Neumann results up to the present time. The alternative methods are connected with modeling of a real ion Coulomb field dynamics by approximate models. One of the most accurate theories of ions dynamics effect on line shapes in plasmas is the Frequency Fluctuation Model (FFM) tested by the comparison with plasma microfield numerical simulations. The goal of the present paper is to make a detailed comparison of the FFM results with analytical ones for the linear and quadratic Stark effects in different limiting cases. The main problem is connected with perturbation additions laws known to be vector for small particle velocities (static line shapes) and scalar for large velocities (the impact limit). The general solutions for line shapes known in the frame of scalar perturbation additions are used to test the FFM procedure. The difference between “scalar” and “vector” models is demonstrated both for linear and quadratic Stark effects. It is shown that correct transition from static to impact limits for linear Stark-effect needs in account of the dependence of electric field jumping frequency in FFM on the field strengths. However, the constant jumping frequency is quite satisfactory for description of the quadratic Stark-effect. The detailed numerical comparison for spectral line shapes in the frame of both scalar and vector perturbation additions with and without jumping frequency field dependence for the linear and quadratic Stark effects is presented.

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