A semi-relativistic treatment of spinless particles subject to the nuclear Woods-Saxon potential (original) (raw)
Related papers
2015
The Woods-Saxon potential is probably the most studied and widely used short range potential in all of nuclear physics. For the angular momentum l= 0 case, Flügge had devised a method to obtain an analytical expression for the bound state energies of the radial time-independent Schrӧdinger equation for a neutron confined in a Woods-Saxon potential well. In this study, we extend Flügge's method to solve the radial Schrӧdinger equation for a neutron within the Woods-Saxon potential and the centrifugal potential for arbitrary values of l. Here, the Pekeris method is used to deal with the centrifugal term. We obtain an analytical expression for the bound states, valid for arbitrary angular momentum, and show that our expression reduces to that of Flügge, which applies to the l= 0 case. The numerical computations performed also show very good agreement with our analytical expression.
Approximate l-State Solutions of a Spin-0 Particle for Woods-Saxon Potential
Arxiv preprint arXiv:0901.2773, 2009
The radial part of Klein-Gordon equation is solved for the Woods-Saxon potential within the framework of an approximation to the centrifugal barrier. The bound states and the corresponding normalized eigenfunctions of the Woods-Saxon potential are computed by using the Nikiforov-Uvarov method. The results are consistent with the ones obtained in the case of generalized Woods-Saxon potential. The solutions of the Schrödinger equation by using the same approximation are also studied as a special case, and obtained the consistent results with the ones obtained before.
Zeitschrift für Naturforschung A, 2013
We present analytical bound state solutions of the spin-zero particles in the Klein-Gordon (KG) equation in presence of an unequal mixture of scalar and vector Woods-Saxon potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a parametric Nikiforov-Uvarov (NU) method. Our numerical energy eigenvalues demonstrate the existence of inter-dimensional degeneracy amongst energy states of the KG-Woods-Saxon problem. The dependence of the energy levels on the dimension D is numerically discussed for spatial dimensions D = 2 - 6.
2010
We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. In the framework of the spin and pseudospin symmetry concept, the approximately analytical bound state energy eigenvalues and the corresponding upper-and lower-spinor components of the two Dirac particles are obtained, in closed form, by means of the Nikiforov-Uvarov method which is based on solving the second-order linear differential equation by reducing it to a generalized equation of hypergeometric type. The special cases κ = ±1 (l = l = 0, s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. Also, the non-relativistic results are compared with the other works.
Relativistic Study of the Spinless Salpeter Equation with a Modified Hylleraas Potential
Ukrainian Journal of Physics
We have solved the Spinless Salpeter Equation (SSE) with a modified Hylleraas potential within the Nikiforov–Uvarov method. The energy eigenvalues and the corresponding wave functions for this system expressed in terms of the Jacobi polynomial are obtained. With the help of an approximation scheme, the potential barrier has been evaluated. The results obtained can be applied in nuclear physics, chemical physics, atomic physics, molecular chemistry, and other related areas, for example, can be used to study the binding energy and interaction of some diatomic molecules. By adjusting some potential parameters, our potential reduces to the Rosen–Morse and Hulthen potentials. We have present also the numerical data on the energy spectra for this system.
Physica Scripta, 2014
An exact analytical treatment is presented, in the momentum space, for the one-dimensional spinless Salpeter equation describing two particles with unequal masses interacting via a Coulomb-type potential. We derive the exact energy equation for bound states and work out the associated wave functions. The obtained energy eigenvalues are shown to agree very well with exact numerical calculations and also the analytical upper bounds available in the literature.
Few-Body Systems, 2018
In this paper, we explore the analytical solutions for both bound and scattering states of the Klein-Gordon equation with the multiparameter potential which describes atomic, diatomic and polyatomic molecular structures via the standard method by applying a Pekeris-type approximation to the centrifugal potential. For the bound states, we obtain the energy eigenvalues and the corresponding normalized eigenfunctions in terms of hypergeometric functions. In the scattering states, the phase shift relation is derived. Besides, we investigate the special potentials, which are defined in the literature and derived from to the multiparameter potential. Finally, by using the obtained relations, we give the results both for bound and scattering states numerically and graphically.
Physica Scripta, 2014
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.
The zero-mass spinless Salpeter equation with a regularized inverse square potential
We present a detailed study for the classical and the quantum motion of a relativistic massless particle in an inverse square potential. The classical treatment shows that it is possible to find trajectories for which the system has a positive total energy and yet the particle remains bound to the potential center. The quantum approach to the problem is based on the exact solution of the corresponding semirelativistic spinless Salpeter equation for bound states. The connection between the classical and the quantum descriptions is made via the comparison of the associated probability densities for momentum.