1/Nenergy-formulae for relativistic two-body Coulomb and Yukawa systems with arbitrary masses

Abstract

Energy formulae for two-particle Klein-Gordon systems subjected to Coulomb and Yukawa potentials are derived to first l/N-order. The energies obtained in this manner incorporate the influence of the mass-asymmetry via the parameter 6 = (M:mi)*. Certain Coulomb-inspired extrapolations to Dirac-particle systems, having the meaning of dominant contributions, are taken into account. Numerical results are presented.

Approximate Analytical Solutions of the Dirac Equation for Yukawa Potential Plus Tensor Interaction with Any κ-Value

“…Yukawa potential [7][8][9][10][11][12][13][14][15] has also received a great deal of attention in view of the methods by which the potential has been studied. Some of them used to solving the wave equations are the 1/N -expansion [16] and shifted 1/N -expansion methods [17], studying the potential by using the Raygleih-Schrödinger perturbation expansion [18], a group-theoretical approach by using the Fock transformation [3], the variational self-consistent field molecular-orbital method [18], the J-matrix method [19], a new approximation scheme proposed to study the bound states of potential [20], studying in terms of the hypervirial theorems [21] and a numerical solution of the Schrödinger equation for the present potential [22].…”