The -order Foldy–Wouthuysen Hamiltonian and relativistic corrections to Coulomb systems

Abstract

The order nonrelativistic Hamiltonians of scalar, spinor and vector particles in the electromagnetic field are studied by applying the Douglas–Kroll–Hess approach. The result of the spin-1/2 spinor agrees with the Hamiltonian of the nonrelativistic quantum electrodynamics (Zhou et al 2019 Phys. Rev. A 100 012513). Additionally, the -order relativistic correction to few-electron Coulomb systems and the -order relativistic correction to two-electron Coulomb systems are derived. The singularities of Hamiltonians of Coulomb systems are separated out and cancelled. The regularized Hamiltonians up to -order for scalar and electron in the Coulomb field are obtained. Their numerical results agree with the relativistic theory. The regularized Hamiltonian, up to for few-electrons in the Coulomb field, is also derived.