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

Abstract

Recently, scattering of a Klein-Gordon particle in the presence of mixed scalar-vector generalized symmetric Woods-Saxon potential was investigated for the spin symmetric and the pseudo-spin symmetric limits in one spatial dimension. In this manuscript, the bound state solutions of the Klein-Gordon equation with mixed scalar-vector generalized symmetric Woods-Saxon potential are examined analytically within the framework of spin and pseudo-spin symmetry limits. We prove that the occurrence of bound state energy spectrum exists only in the spin symmetric limit, while in the pseudo-spin symmetric limit, the bound state spectrum does not exist. Besides the theoretical proof, the Newton-Raphson numerical methods are used to calculate the bound state energy spectra of a neutral Kaon particle, confined in a generalized symmetric Woods-Saxon potential, energy well constituted with repulsive or attractive surface interactions, for the spin and pseudo-spin symmetric limits, respectively. Numerical results are consistent with the non-existence of the bound state energy spectrum in the pseudo-spin symmetric limit.

A comparative interpretation of the thermodynamic functions of a relativistic bound state problem proposed with an attractive or a repulsive surface effect

“…Another discussion that we made in the previous article [49], was on the appearance of a "barrier" for the repulsive and a "pocket" for the attractive surface effects. There, we showed such effects appear if and only if |W 0 | > V 0 condition is satisfied.…”

“…In section II, we introduce the GSWSP energy and then we demonstrate the comparisons of the potential energies used. In section III, we present a very brief solution of the KG equation that was obtained in our previous paper [49]. We divide the section IV into two subsections.…”

“…First, we explored the scattering solution in the KG equation in the limits of the spin symmetry (SS) and pseudospin symmetry (PSS) [47]. Then, BCL analyzed the bound state solution in the same limits, he observed a very surprising result, such that only in the SS limit a bound state spectrum could have existed [49]. He compared the WSP with GSWSP energies in the context of statistical mechanics first in the non-relativistic [46] and then in the relativistic approaches [48].…”

“…We introduce this additional term and describe its physical meaning in section II. GWSP energy is examined in various papers as well [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50].…”

Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

“…The Nikiforov-Uvarov method [8], factorization method [9], Laplace transform approach [10], and the path integral method [11] and shifted 1/N expansion approach [12,13] are used for solving radial and azimuthal parts of the wave equations exactly or quasiexactly in l ≠ 0 for various potentials. Additionally, there are numerous interesting research works about the KFG equation with physical potentials by using different methods in the literature [14][15][16][17][18][19][20][21][22][23][24][25][26]. Among them, as an example, in Ref.…”