Based on the investigation of the asymptotic behaviour of the polarization loop function for charged n scalar particles in an external gauge field, we determine the interaction Hamiltonian including relativistic corrections. The mass spectrum of the bound state is analytically derived. The mechanism for arising of the constituent mass of the relativistic bound-state forming particles is explained. The mass and the constituent mass of the two-, three- and n-body relativistic bound states are calculated taking into account relativistic corrections. The corrections arising due to the one- and two-loop electron polarization to the energy spectrum of muonic hydrogen with orbital and radial excitations are calculated.
Based on the investigation of the asymptotic behaviour of the polarization loop function for charged n scalar particles in an external gauge field, we determine the interaction Hamiltonian including the relativistic corrections. The energy eigenvalues of spherical symmetric potentials for two-particle bound state systems with relativistic corrections are analytically derived. The energy spectra of linear and funnel potentials with orbital and radial excitations are determined. The energy spectrum of a superposition of Coulomb and Yukawa potentials is also determined. Our result shows that the energy spectrum with the relativistic corrections for the linear, harmonic oscillator and funnel potentials is smaller than the upper boundaries for the energy spectrum established in the framework of the spinless Salpeter equation for the orbital and radial excited states. The relativistic corrections to the energy spectrum of a superposition of the attractive Coulomb potential and the Yukawa (exponentially screened Coulomb) potentials are very small.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.