Behavior of spin-0 particles in the generalized Woods-Saxon potential field

We notice that there is inconsistency in the analytical solution of the Woods-Saxon or modified Woods-Saxon potential for the Klein-Gordon equation in literature. The physical boundary conditions cannot be satisfied with the energy eigenvalues and corresponding wave functions obtained by using the Nikiforov-Uvarov or Asymptotic Iteration Methods for the Woods-Saxon or modified Woods-Saxon potentials. The Nikiforov-Uvarov or Asymptotic Iteration methods cannot take into account the correct behavior of the wave function at the vicinity r=R. In this thesis, we examine the analytical solution of the Klein-Gordon equation to determine the energy eigenvalue and corresponding wave function of the Generalized Woods-Saxon potential for L=0 state by using the properties of Hypergeometric functions. We obtain the bound state energy eigenvalues and corresponding wave functions in the closed forms. We discuss the correlations between the potential parameters and energy eigenvalues for π0 particles under moving the Generalized Woods-Saxon potential field and determine the critical V0 values inducing pair creation for other constant potential parameters. In this thesis, we show that some solutions of Woods-Saxon or modified Woods-Saxon potentials for the Klein Gordon equation are inaccurate. Using a more general form of the Woods-Saxon potential, we have obtained analytical solutions that provide boundary conditions. These analytical solutions could be used to describe the behavior of other interacting systems.