arXiv subjects

R. S. Tutik

Publications and source records attributed to R. S. Tutik.

17 recordsLinked to original sources

arXiv2009

A new two-body relativistic potential model for pionic hydrogen

The new potential model for pionic hydrogen, constructed with the employment of the two-body relativistic equation, is offered. The relativistic equation, based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one, describes the effect of the proton spin and anomalous magnetic moment in accordance with the results of the quantum electrodynamics. Within this approach, using the experimental data on the strong energy level shift and width of the $1s$ state in pionic hydrogen as input, the pion-nucleon scattering lengths have been evaluated to be $a_{π^{-}p}=0.0860(6)m_π^{-1}$ and $a_{π^{0}n}=-0.1223(19)m_π^{-1}$.

hep-ph↗

arXiv2009

Oscillator model for the relativistic fermion-boson system

The solvable quantum mechanical model for the relativistic two-body system composed of spin-1/2 and spin-0 particles is constructed. The model includes the oscillator-type interaction through a combination of Lorentz-vector and -tensor potentials. The analytical expressions for the wave functions and the order of the energy levels are discussed.

quant-ph↗

arXiv2008

A new approach to the relativistic treatment of the fermion-boson system, based on the extension of the SL(2,C) group

A new technique for constructing the relativistic wave equation for the two-body system composed of the spin-1/2 and spin-0 particles is proposed. The method is based on the extension of the SL(2,C) group to the Sp(4,C) one. The obtained equation includes the interaction potentials, having both the Lorentz-vector and Lorentz-tensor structure, exactly describes the relativistic kinematics and possesses the correct one-particle limits. The comparison with results of other approaches to this problem is discussed.

hep-th↗

arXiv2007

The logarithmic perturbation theory for bound states in spherical-symmetric potentials via the $\hbar$-expansions

The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator and the screened Coulomb potential is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As examples, the perturbation expansions for the energy eigenvalues of the quartic anharmonic oscillator and the Debye potential are considered.

math-ph↗

arXiv2007

Relativistic wave equation for one spin-1/2 and one spin-0 particle

A new approach to the two-body problem based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one is developed. The wave equation with the Lorentz-scalar and Lorentz-vector potential interactions for the system of one spin-1/2 and one spin-0 particle with unequal masses is constructed.

hep-th↗

arXiv2007

Relativistic two-body equation based on the extension of the SL(2,C) group

A new approach to the two-body problem based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one is developed. The wave equation with various forms of including the interaction for the system of the spin-1/2 and spin-0 particles is constructed. For this system, it was found that the wave equation with a linear confinement potential involved in the non-minimal manner has an oscillator-like form and possesses the exact solution.

hep-th↗

arXiv2006

Perturbation theory for sextic doubly anharmonic oscillator

A simple method for the calculation of higher orders of the logarithmic perturbation theory for bound states of the spherical anharmonic oscillator is developed. The structure of the perturbation series for energy eigenvalues of the sextic doubly anharmonic oscillator is investigated. The recursion technique for deriving renormalized perturbation expansions is offered.

quant-ph↗

arXiv2006

A new perturbation technique for eigenenergies of the screened coulomb potential

The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem of the radial Shrodinger equation with the screened Coulomb potential is developed. Based upon h-expansions and new quantization conditions a novel procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained.

quant-ph↗

arXiv2006

Energy spectrum of the Dirac oscillator in the Coulomb field

The spectrum of the Dirac oscillator perturbed by the Coulomb potential is considered. The Regge trajectories for its bound states are obtained with the method of $\hbar$-expansion. It is shown that the split of the degenerate energy levels of the Dirac oscillator in the Coulomb field is approximately linear in the coupling constant.

physics.atom-ph↗

arXiv2006

Renormalization of expansions for Regge trajectories of the Schrödinger equation

A recursion technique for the renormalization of semiclassical expansions for the Regge trajectories of bound states of the Schrödinger equation is developed. As an application of the proposed technique, the two-parameter renormalization scheme of the Regge trajectories for the bound states in the Martin potential is considered.

quant-ph↗

arXiv2006

Regge trajectories of the Klein-Gordon equation with non-minimal interaction

A semiclassical method of deriving Regge trajectories for the bound states of the Klein-Gordon equation with the interaction introduced in a non-minimal way is proposed. The method is applied to construction of the quarkonium Regge trajectories. It is found that under the relativistic generalization of the Cornell potential the Regge trajectories of charmonium are in the same good agreement with experimental data for introducing the confinement part of potential either in the minimal, or non-minimal way.

hep-ph↗

arXiv2005

An alternative model for the Duffin-Kemmer-Petiau oscillator

A new oscillator model with different form of the non-minimal substitution within the framework of the Duffin-Kemmer-Petiau equation is offered. The model possesses exact solutions and a discrete spectrum of high degeneracy. The distinctive property of the proposed model is the lack of the spin-orbit interaction, being typical for other relativistic models with the non-minimal substitution, and the different value of the zero-point energy in comparison with that for the Duffin-Kemmer-Petiau oscillator described in the literature.

hep-th↗

arXiv2004

A new approach to the logarithmic perturbation theory for the spherical anharmonic oscillator

The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the quartic anharmonic oscillator are considered.

quant-ph↗

arXiv2002

Logarithmic perturbation theory for radial Klein-Gordon equation with screened Coulomb potentials via $\hbar$ expansions

The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component of a Lorentz four-vector and a Lorentz-scalar term, is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues for the Hulthén potential containing the vector part as well as the scalar component are considered.

quant-ph↗

arXiv2001

A recursion technique for deriving renormalized perturbation expansions for one-dimensional anharmonic oscillator

A new recursion procedure for deriving renormalized perturbation expansions for the one-dimensional anharmonic oscillator is offered. Based upon the $\hbar$-expansions and suitable quantization conditions, the recursion formulae obtained have the same simple form both for ground and excited states and can be easily applied to any renormalization scheme. As an example, the renormalized expansions for the sextic anharmonic oscillator are considered.

quant-ph↗

arXiv1999

A new approach to perturbation theory for a Dirac particle in a central field

The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the Dirac equation is developed. Avoiding disadvantages of the standard approach in the description of exited states, new handy recursion formulae with the same simple form both for ground and exited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues for the Yukawa potential containing the vector part as well as the scalar component are considered.

quant-ph↗

arXiv1999

Semiclassical treatment of logarithmic perturbation theory

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and exited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the harmonic oscillator perturbed by $λx^{6}$ are considered.

quant-ph↗