Energy Levels of Spin-1/2 Particles with Yukawa Interaction

Abstract

In this article, Yukawa interaction is used to study the relativistic spin-1/2 particles and obtain their energy levels. The role of Yukawa potential on the spin and pseudospin symmetry solution is investigated systematically by solving the Dirac equation with attractive scalar S(r) and repulsive vector V(r) potentials. Bound state spectrum and wave functions of Yukawa potential are obtained. It is found that the energy eigenvalues strongly depend on the potential parameters.

Spin and pseudospin solutions to Dirac equation and its thermodynamic properties using hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential

“…In mathematical physics, the Dirac equation with pseudo scalar potential can be handled as a Sturm-Liouville problem while the bound state spectrum of Dirac equation is relevant for the study of Zakharaov-Shabat eigenvalue problem which is applicable in the study of isospectral flow of soliton in plasma [31][32][33][34] . The solutions of Dirac equation with various considerable potentials within spin and pseudospin symmetries have been obtained by different authors using different methods such as: factorisation method 35,36 , asymptotic iteration method 37,38 , Laplace transform technique 39 , Supersymmetric quantum mechanics approach [40][41][42] , path integral formulation [43][44][45] , Nikiforov-Uvarov method 46,47 and others.…”

Investigations on the Relativistic Interactions in One-Electron Atoms with Modified Yukawa Potential for Spin 1/2 Particles

“…which known by Yukawa potential on based to the main reference [22]: potentials is given by [18][19][20][21][22]:…”

“…11 31 here M are E the fermions' mass and the relativistic energy while can be expressed as [18][19][20][21][22]: …”

“…In very recent years the energy levels of atoms, nuclei, and hadrons have been studied by several analytic methods in the case the two relativistic equations Klein-Gordon and Dirac for certain potentials of the physical interest , some of these potentials are known to play important roles in many fields, one of such potential is the Yukawa potential has been a subject of many studies, it is a central potential of nuclear shell model in addition to used in nonrelativistic quantum mechanics to study the interactions between nonrelativistic particles, in atomic and molecular physics, it represents a screened Coulomb potential due to the cloud of electronic charges around the nucleus, on the other hand, it has also been used to describe the interaction between charged particles in plasma, solid and colloidal suspensions [22]. It is well known that the ordinary quantum structures obey the standard Weyl-Heisenberg algebra in both Schrödinger and Heisenberg (the operators are depended on time) pictures ((HP) and (SP)), respectively, as (Throughout this paper the natural unit denote to the ordinary quantum Hamiltonian operator for Yukawa potential.…”

“…The plan of recently work is as follows: In next section, we briefly review the Dirac equation with Yukawa potential on based to refs. [18][19][20][21][22]. In section three, we give a description of the Bopp's shift method for (m.d.e.)…”