Orhan Bayrak - Academia.edu (original) (raw)

Papers by Orhan Bayrak

International Journal of Modern Physics E, 2006

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the ... more In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the no magnetic field case analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n = 2 − 10 and m = 0 − 1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.

International Journal of Modern Physics C

In this paper, we show an alternative and accurate solution of the radial Schrödinger equation fo... more In this paper, we show an alternative and accurate solution of the radial Schrödinger equation for the exponential cosine screened Coulomb potential within the framework of the asymptotic iteration method. Unlike other methods, which require approximations for the centrifugal or exponential terms, we show that it is possible to solve the full potential without making any approximations within the framework of this method. The bound state energy eigenvalues are obtained for any n and l values and the results are compared with the findings of different methods for several screening parameters. Moreover, we study the screening parameter delta = 0 case to obtain the energy eigenvalues and corresponding eigenfunctions of this potential in a closed-form.

The European Physical Journal A, 2015

The α-decay half-lives are calculated for heavy and superheavy nuclei for 52 ≤ Z ≤ 112 and 108 ≤ ... more The α-decay half-lives are calculated for heavy and superheavy nuclei for 52 ≤ Z ≤ 112 and 108 ≤ A ≤ 285 from the ground state to ground state α transitions within the framework of the Wentzel-Kramers-Brillouin (WKB) method and the Bohr-Sommerfeld quantization. In the calculations, the α-α single folding cluster potential obtained with the folded integral of the α-α potential with the α-cluster density distributions is used in order to model the nuclear interaction between the α-particle and core nucleus. While the results are very good agreement with the experimental ones in the heavy nuclei region especially for even-even nuclei, the smaller values than the experimental ones are obtained for superheavy nuclei. As both the density of the core and the interaction term in the folding integral include the α-clustering effects and in this way all cluster effects are taken into account in the model, the results of calculations are more physical and reasonable than the calculations done in the other models. The present method could be applied to light nuclei with different type nuclear densities.

Physica B: Condensed Matter, 2015

The impurity binding energy in the GaAs À Ga 1 À x Al x As system is studied with an anharmonic t... more The impurity binding energy in the GaAs À Ga 1 À x Al x As system is studied with an anharmonic type confinement potential by taking into account the influence of the external electric and magnetic fields within the framework of the effective mass approximation and asymptotic iteration method (AIM). The influence of the external electromagnetic fields and anharmonicity on a donor binding energy is examined systematically. It is shown that the donor binding energy is highly dependent on the external electric and magnetic fields and the confinement potential shapes. Both the electric and magnetic fields are increased, the binding energies increase for each of them. However, the behaviors of increase in the weak and strong fields' regimes have different character a bit. Furthermore, when the more anharmonicity is considered, the binding energy of donor slightly increases as well.

$Research paper thumbnail of Corrected analytical solution of the generalized Woods–Saxon potential for arbitrary <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">ℓ</mi></mrow><annotation encoding="application/x-tex">\ell </annotation></semantics></math>ℓ states$

Physica Scripta, 2014

The bound state solution of the radial Schrödinger equation with the generalized Woods-Saxon pote... more The bound state solution of the radial Schrödinger equation with the generalized Woods-Saxon potential is carefully examined by using the Pekeris approximation for arbitrary ℓ states. The energy eigenvalues and the corresponding eigenfunctions are analytically obtained for different n and ℓ quantum numbers. The obtained closed forms are applied to calculate the single particle energy levels of neutron orbiting around 56 Fe nucleus in order to check consistency between the analytical and Gamow code results. The analytical results are in good agreement with the results obtained by Gamow code for ℓ = 0.

Journal of Molecular Structure: THEOCHEM, 2007

We present the exact analytical solution of the radial Schrödinger equation for the deformed Hult... more We present the exact analytical solution of the radial Schrödinger equation for the deformed Hulthén and the Morse potentials within the framework of the Asymptotic Iteration Method. The bound state energy eigenvalues and corresponding wave functions are obtained explicitly. Our results are in excellent agreement with the findings of the other methods.

Open Physics, 2012

We present the elastic scattering of the 6 He+ 208 Pb and the 6 He+ 197 Au systems at the laborat... more We present the elastic scattering of the 6 He+ 208 Pb and the 6 He+ 197 Au systems at the laboratory energy of E lab =27 MeV within the framework of the McIntyre parametrization, and systematically investigate χ 2 /N analysis of both systems to obtain an excellent agreement between the theoretical results and the experimental data. We find large diffusivity parameters indicating long range absorption mechanisms. We also show that both systems lack both the nuclear and the Coulomb rainbow scattering for obtained S-matrix parameters.

Journal of Physics: Conference Series, 2015

ABSTRACT We systematically study the investigation of the influence of nuclear deformations of th... more ABSTRACT We systematically study the investigation of the influence of nuclear deformations of the cluster and daughter nuclei on the exotic cluster decay half-lives of heavy nuclei by the WKB method and the Bohr-Sommerfeld quantization condition. Even if the deformations of both cluster and daughter in the half-live values of cluster decays improve the results, considering the deformation of clusters is more efficient than the deformation of daughter for the heavy cluster decay half-live calculations. Moreover, taking into account of angle orientations of daughter and cluster provides a positive contributions to the results as well. The results would be useful for experimental researches in half-lives of exotic decays of some heavy nuclei and radium isotopes.

International Journal of Modern Physics E, 2005

Studying nuclear reactions near the Coulomb barrier shows a number of problems which have remaine... more Studying nuclear reactions near the Coulomb barrier shows a number of problems which have remained unsolved for a long time: The out-of-phase problem between theoretical 13 predictions and experimental data; the reproductions of the oscillatory structure near the Coulomb barrier; the consistent description of angular distributions together with 15 the excitation functions data are just some of these problems. In order to address and overcome these problems, by considering a comparative study of the shallow and deep 17 optical potentials, the elastic scattering angular distributions and excitation functions data of the 12 C+ 24 Mg reaction have been analyzed within the framework of the optical 19 model over a wide energy range. The potential depths near the Coulomb barrier according to the increasing energy and threshold anomaly are discussed in terms of the shallow 21 and deep potentials. Excellent agreement between theoretical results and measured data is obtained by using the optical model.

We present the exact and iterative solutions of the radial Schrodinger equation for a class of po... more We present the exact and iterative solutions of the radial Schrodinger equation for a class of potential, V (r) = A r2 − B r +Cr κ, for various values of κ from -2 to 2, for any n and l quantum states by applying the asymptotic iteration method. The global analysis of this potential family by using the asymptotic iteration method results in exact analytical solutions for the values of κ = 0, −1 and −2. Nevertheless, there are no analytical solutions for the cases κ = 1 and 2. Therefore, the energy eigenvalues are obtained numerically. Our results are in excellent agreement with the previous works.

Modern Physics Letters A, 2014

Bound state solutions of the Dirac equation for the generalized Woods-Saxon potential are examine... more Bound state solutions of the Dirac equation for the generalized Woods-Saxon potential are examined for arbitrary κ states by using the approximation to the Coulomb and centrifugal potentials in pseudospin and spin symmetry limits, respectively. The energy eigenvalues and corresponding eigenfunctions are obtained in closed forms. Some numerical examples are given for proton or anti-proton in a nuclei. The correlations between the energy splitting and some parameters of the effective potential in pseudospin symmetry limit are examined for several pseudospin doublets.

Physics of Atomic Nuclei, 2011

The results of the elastic scattering of 6 He+ 12 C system at E Lab =18 MeV by using the barrier ... more The results of the elastic scattering of 6 He+ 12 C system at E Lab =18 MeV by using the barrier and internal wave decomposition of the S -matrix element within the framework of the WKB method is presented. This is the rst detailed study for the interaction of the exotic 6 He nucleus on dierent stable nuclei by using a semiclassical method. In this paper, we show that in order to obtain the elastic scattering cross section of the 6 He+ 12 C system at energies close to the Coulomb barrier, it is vitally important to take into account the inner complex turning points in the calculations and the tunneling eects play a crucial role to explain the experimental data. The semiclassical results are compared with the experimental data as well as the quantum mechanical one. *

Physics of Atomic Nuclei, 2005

The investigation of the nuclear reactions near the Coulomb barrier poses a number of problematic... more The investigation of the nuclear reactions near the Coulomb barrier poses a number of problematic issues which have remained unsolved for a long time: The out-of-phase problem between theoretical predictions and experimental data; the reproduction of the oscillatory structure near the Coulomb barrier; the consistent description of angular distributions together with the excitation functions data are just some of these issues. To address and overcome them, we examine the elastic scattering of the 12 C+ 24 Mg system within the framework of the Optical model with two small potentials in addition to the nuclear potential. The experimental data has been analyzed in the laboratory system from 16.0 to 24.0 MeV and excellent agreement between theoretical results and the measured experimental data has been obtained by using this modified optical potential.

Physica Scripta, 2007

We present very accurate values for the bound state energy eigenvalues by solving the radial Schr... more We present very accurate values for the bound state energy eigenvalues by solving the radial Schrödinger equation for the Hulthén potential within the framework of the asymptotic iteration method (AIM) for any states and for different screening parameters without using any approximations required by other methods. The AIM results are compared with the results of the numerical integration, the generalized pseudospectral, the supersymmetry, the variational and the shifted 1/N expansion methods and they are in very good agreement for different screening parameter, δ, values.

Modern Physics Letters A, 2012

ABSTRACT The radial sensitivity of the elastic scattering of the weakly-bound 6Li and halo 6He nu... more ABSTRACT The radial sensitivity of the elastic scattering of the weakly-bound 6Li and halo 6He nuclei on medium-mass 64Zn target and heavy target 208Pb is examined around the Coulomb barrier energies. We present that very good agreement between theoretical and experimental results have been obtained with small χ2/N values. The fusion cross-section and volume integrals of the potentials have been deduced from the theoretical calculations for all studied systems at relevant energies. We have also analyzed the elastic scattering of the 6He+208Pb system at Elab = 14, 16, 18, 22, 27 MeV in order to investigate whether there is a dispersion relation between the real and imaginary parts of the optical potential.

Journal of Theoretical and Computational Chemistry, 2007

We present an alternative and accurate solution of the radial Schrödinger equation for the Hellma... more We present an alternative and accurate solution of the radial Schrödinger equation for the Hellmann potential within the framework of the asymptotic iteration method. We show that the bound state energy eigenvalues can be obtained easily for any n and values without using any approximations required by other methods. Our results are compared with the findings of other methods.

Journal of Physics B: Atomic, Molecular and Optical Physics, 2007

We present the exact and iterative solutions of the radial Schrödinger equation for a class of po... more We present the exact and iterative solutions of the radial Schrödinger equation for a class of potential, V (r) = A r 2 − B r + Cr κ , for various values of κ from -2 to 2, for any n and l quantum states by applying the asymptotic iteration method. The global analysis of this potential family by using the asymptotic iteration method results in exact analytical solutions for the values of κ = 0, −1 and −2. Nevertheless, there are no analytical solutions for the cases κ = 1 and 2. Therefore, the energy eigenvalues are obtained numerically. Our results are in excellent agreement with the previous works. PACS numbers: 03.65.Ge Keywords: asymptotic iteration method, eigenvalues and eigenfunctions, Kratzer, Modified Kratzer, Goldman-Krivchenkov, spiked harmonic oscillator, Coulomb plus linear and Coulomb plus harmonic oscillator potentials.

Journal of Physics A: Mathematical and Theoretical, 2007

In this paper, the energy eigenvalues and the corresponding spinors of the Dirac particles are ob... more In this paper, the energy eigenvalues and the corresponding spinors of the Dirac particles are obtained and the pseudospin symmetric solution of the attractive scalar and repulsive vector Morse potential for any spin-orbit quantum number κ is provided by using the Pekeris approximation within the framework of the asymptotic iteration method.

Journal of Physics A: Mathematical and General, 2006

In this article, we present the analytical solution of the radial Schrödinger equation for the Hu... more In this article, we present the analytical solution of the radial Schrödinger equation for the Hulthén potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any l states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different δ values. In order to demonstrate this, the results of the asymptotic iteration method are compared with the results of the supersymmetry, the numerical integration, the variational and the shifted 1/N expansion methods.