On the Solution of the Generalized Symmetric Woods-Saxon Potential in the Dirac Equation

Year 2018, Issue: 2, 435 - 438, 19.08.2018

Bekir Can Lutfuoglu

Abstract

In this work, we present a solution to the Dirac
equation that is coupled with vector and scalar generalized symmetric
Woods-Saxon potential energy in one plus one space-time.  The chosen potential energy has a flexible
structure to examine four different physical problems. The potential energy can
be a barrier or well depend on being attractive or repulsive. Furthermore, the
included surface effects can be attractive or repulsive. Therefore, in one
class a potential barrier occurs with a pocket or an extra barrier nearby the
effective radius. Similar effects occur in the potential well whether the
surface effects are repulsive or attractive. Here we use the usual
two-component approach. We obtain the solutions in hypergeometric function
form.

Keywords

Dirac equation , Scalar and vector potential energies , Generalized symmetric , Woods-Saxon potential energy

References

• Bayrak, O. & Aciksoz, E.. (2015). Corrected analytical solution of the generalized Woods-Saxon potential for arbitrary ℓ states. Phys. Scr., 90, 015302. Brandan, M. E. & Satchler, G. R.. (1997). The interaction between light heavy-ions and what it tells us, Phys. Rep., 285, 143–243. Chabab, M., El Batoul, A., Hassanabadi, H., Oulne, M., & Zare, S.. (2016). Scattering states of Dirac particle equation with position-dependent mass under the cusp potential. Eur. Phys. J. Plus, 131(11). Costa, L.S., Prudente, F. V., Acioli, P. H., Soares Neto, J. J. & Vianna, J. D. M.. (1999). A study of confned quantum systems using the Woods-Saxon potential, J. Phys. B: At., Mol. Opt. Phys., 32, 2461–2470. Dirac, P. A. M.. (1928). The quantum theory of the electron, Proc. Roy. Soc. A117, 610-628. Flügge, S.. (1974). Pratical Quantum Mechanics. Berlin: Spinger. Hosseinpour, M., Andrade, F.M., Silva, E.O., & Hassanabadi, H. (2017). Scattering and bound states for the Hulthén potential in a cosmic string background. Eur. Phys. J. C, 77: 270. Klein, O.. (1926). Quantentheorie und fünfdimensionale Relativitätstheorie, Z. Phys., 37, 895-906. Lee, D. -H.. (2009). Surface states of topological insulators: The dirac fermion in curved two-dimensional spaces. Phys. Rev. Lett., 103, 196804. Lütfüoğlu, B. C., Akdeniz, F.& Bayrak, O.. (2016). Scattering, bound, and quasi-bound states of the generalized symmetric Woods-Saxon potential, J. Math. Phys., 57, 032103. Lütfüoğlu, B. C.. (2018). Comparative Effect of an Addition of a Surface Term to Woods-Saxon Potential on Thermodynamics of a Nucleon, Commun. Theor. Phys., 69, 23-27. Lütfüoğlu, B. C.. (2018). Surface interaction effects to a Klein-Gordon particle embedded in a Woods-Saxon potential well in terms of thermodynamic functions, Can. J. Phys., 96, 843-850. Lütfüoğlu, B. C, Lipovsky, J. & Kriz, J..(2018) Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential, Eur. Phys. J. Plus, 133, 17. Lütfüoğlu, B. C.. (2018). An investigation of the bound-state solutions of the Klein-Gordon equation for the generalized Woods-Saxon potential in spin symmetry and pseudo-spin symmetry limits, Eur. Phys. J. Plus, 133, 309. Rojas, C. & Villalba, V. M. (2005). Scattering of a Klein-Gordon particle by a Woods-Saxon potential, Phys. Rev. A, 71, 052101. Satchler, G. R.. (1983). Direct Nuclear Reaction. Oxford: Oxford University Press. Woods, R. D. & Saxon, D. S.. (1954). Diffuse Surface Optical Model for Nucleon-Nuclei Scattering, Phys. Rev., 95, 577-578. Zaichenko, A. K.& Ol’khovskii, V. S.. (1976) Analytic solutions of the problem of scattering by potentials of the Eckart class, Theor. Math. Phys., 27, 475–477.