Effective-Mass Dirac Equation for Woods-Saxon Potential: Scattering, Bound States and Resonances

Abstract

Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions. Transmission and reflection coefficients are calculated by using behavior of the wave functions at infinity. The same analysis is done for the constant mass case. It is also pointed out that our results are in agreement with those obtained in literature. Meanwhile, an analytic expression is obtained for the transmission resonance and observed that the expressions for bound states and resonances are equal for the energy values $E=\pm m$.

20 pages, 6 figures

References in corpus (16)

• Effective Mass of One 4he Atom in Liquid 3he
• Solution of the Dirac equation with position-dependent mass in the Coulomb field
• Nonrelativistic Green's function for systems with position-dependent mass
• The Woods-Saxon Potential in the Dirac Equation
• Scattering of a Klein-Gordon particle by a Woods-Saxon potential
• Supercriticality and Transmission Resonances in the Dirac equation
• Bound states of the Klein-Gordon equation in the presence of short-range potentials
• New exact solution of the one dimensional Dirac Equation for the Woods-Saxon potential within the effective mass case
• Nucleon-nucleus real potential of Woods-Saxon shape between -60 and +60 MeV for the 40<A<208 nuclei
• Scattering of a relativistic scalar particle by a cusp potential
• Relativistic scattering with spatially-dependent effective mass in the Dirac equation
• Low Momentum Scattering in the Dirac Equation
• Scattering in the PT-symmetric Coulomb potential
• J-matrix method of scattering in one dimension: The nonrelativistic theory
• Tunneling and transmission resonances of a Dirac particle by a double barrier
• Scattering solutions of the spinless Salpeter equation

Cited by in corpus (8)

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• $\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
• Scattering, bound and quasi-bound states of the generalized symmetric Woods-Saxon potential
• Scattering state of Klein-Gordon Particles by q-parameter hyperbolic Poschl-Teller potential
• Exact solution and coherent states of an asymmetric oscillator with position-dependent mass
• Comparative effect of an addition of a surface term to the Woods-Saxon potential on the thermodynamics of a nucleon
• Surface Interaction Effects to a Klein-Gordon Particle Embedded in a Woods-Saxon Potential Well in terms of Thermodynamic Functions
• Thermodynamic Properties of a Nucleon under the Generalized Symmetric Woods-Saxon Potential in Flourine 17 Isotope