Scattering, bound, and quasi-bound states of the generalized symmetric Woods-Saxon potential

Abstract

The exact analytical solutions of the Schrödinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients are analytically obtained. Then, the correlations between the potential parameters and the reflection-transmission coefficients are investigated, and a transmission resonance condition is derived. Occurrence of the transmission resonance has been shown when incident energy of the particle is equal to one of the resonance energies of the quasi-bound states.

Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential

“…The superposition of Coulomb and Woods-Saxon interaction can be described by Modified Woods-Saxon potential (MWSP) [33]. Recently in order to give a better description of the energy barrier at the surface of atomic nucleus that nucleons suffer, Generalized Symmetric Woods-Saxon potential (GSWSP) was proposed [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53].…”

Comparative Effect of an Addition of a Surface Term to Woods-Saxon Potential on Thermodynamics of a Nucleon

“…In order to take the surface effect into account, an additional term to the WS potential is widely used [39][40][41]. The WS potential combined with the additional terms are called GSWS potential.…”

“…Because of the symmetry of the potential, even E e n and odd E o n energy eigenvalues arise, which are studied extensively in the reference [41] and evaluated to be…”

“…In section 2, we interpret the forms of the WS and GSWS potentials, and corresponding energy eigenvalues, for a massive non-relativistic confined particle, using the formalism proposed by [41]. In section 3, we give a brief summary on the thermodynamic functions, that are calculated in the following section for the two potentials.…”

“…Such potential wells can be used to model any system, in which a particle is trapped in a finite space, as well as the effects, such as non-zero l, spin-orbit coupling [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55].…”