Hulthen Potential Research Articles

Relativistic spinless particles in the generalized asymmetric Woods–Saxon potential

In this study, the Klein–Gordon equation in one spatial dimension is solved exactly for the generalized asymmetric Woods–Saxon potential containing the various forms of physical potentials, such as the usual Woods–Saxon, asymmetric Hulthen, usual Hulthen, asymmetric cusp and usual cusp potentials. The solutions that describe the scattering and bound states of the Klein–Gordon particles are obtained in terms of the hypergeometric functions. Using the boundary conditions satisfied by the wave functions and considering the asymptotic behavior of the wave functions, we examine a condition for the transmission resonances of the relativistic spinless particles in view of the generalized asymmetric Woods–Saxon potential. Furthermore, dependence of the transmission coefficients on the generalized asymmetric Woods–Saxon potential parameters as well as the energies of Klein–Gordon particles is investigated numerically by using the Mathematica Software.

About the disposition of energy levels

The unique properties of central potential of the form −β e−rrγ were studied using the recently developed critical parameter technique. The particular cases of γ = 0 and γ = −1 yield, respectively, the exponential and Yukawa potentials widely used in atomic, molecular and nuclear physics. We found different behavior of the energy levels of this potential for three different ranges of the value of γ. For γ ⩾ 0 it was found that the energy of bound states with the same principal quantum number N decreases with increasing angular momentum ℓ. The Gaussian and Woods–Saxon potentials also show this behavior. In contrast, for −2 < γ ⩽ −1 increasing ℓ gives a higher energy, resembling the Hulthen potential. However, a potential with −1 < γ < 0 possesses mixed properties, which give rise to several interesting results. For one, the order of energy levels with different quantum numbers is not preserved when varying the parameter β. This leads to a quantum degeneracy of the states, and in fact, for a given value of γ we can find the values βthr for which two energy levels with different quantum numbers coincide. Another interesting phenomenon is the possibility, for some values of γ in this range, for two new energy levels with different quantum numbers to appear simultaneously when β reaches their common critical value.

ANALYTIC l-STATE SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR q-DEFORMED WOODS–SAXON PLUS GENERALIZED RING SHAPE POTENTIAL FOR THE TWO CASES OF EQUAL AND DIFFERENT MIXED VECTOR AND SCALAR POTENTIALS

The analytical expressions for the eigenvalues and eigenvectors of the Klein–Gordon equation for q-deformed Woods–Saxon plus new generalized ring shape potential are derived within the asymptotic iteration method in two cases, namely, the case of equal mixed vector and scalar potentials and the case when the vector potential is chosen to be equal to the q-deformed Woods–Saxon plus the new generalized ring-shaped potential while the scalar one is taken equal to the ring-shaped potential. The latter is considered as a small perturbation. The obtained eigenvalues are given in a closed form and the corresponding normalized eigenvectors, for any l, are formulated in terms of the generalized Jacobi polynomials for the radial part of the Klein–Gordon equation and associated Legendre polynomials for its angular one. When the shape deformation is canceled, we recover the same solutions previously obtained by the Nikiforov–Uvarov method for the standard spherical Woods–Saxon potential. It is also shown that, from the obtained results, we can derive the solutions of this problem for Hulthen potential.

A GENERALIZED SEMI-EMPIRICAL TC EXPRESSION OF THE ISOSUPERCONDUCTIVITY THEORY

As the international scientific community celebrates the first century of the discovery of superconductivity this year, 2011, an outstanding problem is achieving a generalized mechanism of the Cooper pair formation (CPF). In this current study, it has been shown that at short distances, the CPF is by a nonlinear, nonlocal and nonhamiltonian strong hadronic-type interactions due to deepwave-overlapping of spinning particles leading to Hulthen potential that is attractive between two electrons in singlet couplings while at large distance the CPF is by superexchange interaction which is purely a quantum mechanical affairs. It is observed that for both distances the control parameter responsible for the superconducting state is the effective valence z. Therefore a semiemperical Tc expression depending on the effective valence is obtained. This Tc expression gives the same results as the successful BCS Tc expression but unlike the latter whose predicting power is limited to 25 K, the former predicts higher temperatures even beyond room temperature. The implication is that unlike the BCS theory that is restricted to conventional superconductors, the isosuperconductivity theory can be used to account for the conventional and the non-conventional su-

S-wave solutions of spin-one DKP equation for a deformed Hulthén potential in (1+3) dimensions

We investigate spin-one particles by the relativistic Duffin-Kemmer-Petiau equation in the presence of a deformed Hulthen potential in three spatial dimensions. After a lengthy calculation, the exact s-state solutions are reported via the Nikiforov-Uvarov method.

Studying the general properties of potentials by means of dimensionless scaling variables

The general properties of the three-parametric Woods-Saxon potential and the two-parametric Hulthen and square-well potentials are studied by converting them to dimensionless scaling variables. The relations between the parameters of the potentials and such characteristics of a system as binding energies and the asymptotic normalization coefficients of wave functions are investigated.

Bound state solutions of the Klein - Gordon equation for deformed Hulthen potential with position dependent mass

Official journal of the Institute of Physics - Sri Lanka. Full text articles are available. The journal also has a website at http://www.ip-sl.org/sljp/The new email for the Editor is eic.ipsl@gmail.com.

Approximate Solutions to the Dirac Equation with Effective Mass for the Manning–Rosen Potential in N Dimensions

The solutions of the effective mass Dirac equation for the Manning–Rosen potential with the centrifugal term are studied approximately in N dimension. The relativistic energy spectrum and two-component spinor eigenfunctions are obtained by the asymptotic iteration method. We have also investigated eigenvalues of the effective mass Dirac–Manning–Rosen problem for α = 0 or α = 1. In this case, the Manning–Rosen potential reduces to the Hulthen potential.

Oscillator strengths based on the Möbius square potential under Schrödinger equation

By applying the NU method and an approximation to the centrifugal term, we have solved the Schrodinger equation in D-dimensions for the Mobius square potential which in some particular cases gives the Morse and Hulthen potentials. The eigenfunctions as well as the energy eigenvalues are obtained and some expectation values are reported. The important parameter of oscillator strength is obtained and discussed in terms of various parameters of the system.

Duffin–Kemmer–Petiau equation under a scalar and vector Hulthen potential; an ansatz solution to the corresponding Heun equation

Approximate analytical solutions of the spin-zero version of the Duffin-Kemmer-Petiau (DKP) equation are ob- tained via an elegant ansatz after successive transformations for the ground state. As the DKP equation under a scalar term appears as a differential equation that is more complicated than that of the Klein-Gordon equation, the solutions might open new insights to the corresponding physics.

ORBITALLY EXCITED STATES OF QUARKONIA IN A NONRELATIVISTIC MODEL

Having succeeded in predicting the S wave spectra and decays of [Formula: see text] and [Formula: see text] mesons, Bhaghyesh, K. B. Vijaya Kumar and A. P. Monteiro, J. Phys. G: Nucl. Part. Phys.38, 085001 (2011), in this article, we apply our nonrelativistic quark model to calculate the spectra and decays of the orbitally excited states (P- and D-waves) of heavy quarkonia. The full [Formula: see text] potential used in our model consists of a Hulthen potential and a confining linear potential. The spin hyperfine, spin-orbit and tensor interactions are introduced to obtain the masses of the P- and D-wave states. The three-dimensional harmonic oscillator wave function is employed as a trial wave function to obtain the mass spectra. The model parameters and the wave function that reproduce the mass spectra of [Formula: see text] and [Formula: see text] mesons are used to investigate their decay properties. The two-photon decay widths, two-gluon decay widths and E1 radiative decay widths are calculated. The obtained values are compared with the experimental results and those obtained from other theoretical models.

Galoisian approach for a Sturm-Liouville problem on the infinite interval

We study a Sturm-Liouville type eigenvalue problem for second-order differential equations on the infinite interval. Here the eigenfunctions are nonzero solutions exponentially decaying at infinity. We prove that at any discrete eigenvalue the differential equations are integrable in the setting of differential Galois theory under general assumptions. Our result is illustrated with two examples for a stationary Schroedinger equation having a generalized Hulthen potential and an eigenvalue problem for a traveling front in the Allen-Cahn equation.

Approximate Solution of Schrodinger Equation for Hulthen Potential plus Eckart Potential with Centrifugal Term in terms of Finite Romanovski Polynomials

The energy eigenvalues and eigenfunctions of Schrodinger equation for Hulthen potential plus Eckart potential with the centrifugal term are investigated approximately in terms of finite Romanovski polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials.

Heavy quarkonium spectra and its decays in a nonrelativistic model with Hulthen potential

In this paper, we have made a comprehensive study of S wave quarkonium spectra in the general framework of a nonrelativistic potential model. The full potential used in our model consists of a Hulthen potential and a confining linear potential. The spin hyperfine interaction is introduced to obtain the masses of the pseudoscalar and vector mesons. The three-dimensional harmonic oscillator wavefunction is used as a trial wavefunction to obtain the mass spectra. The model parameters and the wavefunction that reproduce the mass spectra of and mesons are used to investigate the decay constants, leptonic decay widths, two-photon and two-gluon decay widths, and radiative decay widths of the S wave and mesons. The obtained values are compared with the experimental results and with the values obtained from other theoretical models. The predictions from our model are found to be in good agreement with the experimental results.

Calculating the characteristics of neutron-deuteron and proton-deuteron systems in a two-body potential model

3H and 3He nuclei are considered in a two-body model (3H = n + d; 3He = p + d). Two independent approaches are used: in the first, interaction is described by the folding potential, while NN potentials are taken in the Hulthen form with allowance for violations of isotopic invariance. The second approach features phenomenological Hulthen and Yukawa Nd potentials used as Nd interaction. In both approaches, the binding energies, vertex constants, and asymptotic normalization coefficients in the N+d channel are calculated.

Path Integral Solution of PT-/non-PT-Symmetric and non-Hermitian Hulthen Potential

The wave functions and the energy spectrum of PT-/non-PT-Symmetric and non-Hermitian Hulthen potential are of an exponential type and are obtained via the path integral. The path integral is constructed using parametric time and point transformation.

Scattering of vector bosons by an asymmetric Hulthen potential

Exact solutions for the bound and scattering states of the spatially one-dimensional Duffin–Kemmer–Petiau equation for an asymmetric Hulthen potential are obtained in terms of the hypergeometric functions. These solutions are used to derive conditions for the existence of the transmission resonances. From this investigation, we show how the transmission coefficient depends on the energy of the particle and the strength of the potential barrier.

Dirac Equation with Coupling to 1/r Singular Vector Potentials for all Angular Momenta

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r^2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthen and Eckart potentials.

Approximate analytical solutions of the pseudospin symmetric Dirac equation for exponential-type potentials

The solvability of The Dirac equation is studied for the exponential-type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov-Uvarov method. The energy eigenvalue equation, and the corresponding Dirac spinors for Morse, Hulthen, and q-deformed Rosen-Morse potentials are obtained within the framework of an approximation to the spin-orbit coupling term, so the solutions are given for any value of the spin-orbit quantum number $\kappa=0$, or $\kappa \neq 0$.

Comparison study of finite element and basis set methods for finite size scaling

We compare two methods of obtaining critical parameters for a quantum Hamiltonian using a finite size scaling approach. A finite element and basis set method were used in conjunction with the finite size scaling to obtain the critical parameters for the Hulthen potential. The critical parameters obtained analytically were the coupling constant λc=12, the critical exponents for the energy α=2 and for the “correlation length” ν=1. The extrapolated results for finite size scaling with the basis set method are λc=0.49999, α=1.9960, and ν=0.99910. The results for the finite element solutions are λc=0.50184, α=1.99993, and ν=1.00079 for the linear interpolation and λc=0.50000, α=2.00011, and ν=1.00032 for the Hermite interpolation. The results for each method compare very well with the analytical results obtained for the Hulthen potential. However, the finite element method is easier to implement and may be combined with ab initio and density functional theory to obtain quantum critical parameters for more complex systems.