The mα8 -order Foldy–Wouthuysen Hamiltonian and relativistic corrections to Coulomb systems

Abstract

Abstract The m α 8 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 m α 6 -order relativistic correction to few-electron Coulomb systems and the m α 8 -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 m α 8 -order for scalar and electron in the Coulomb field are obtained. Their numerical results agree with the relativistic theory. The regularized Hamiltonian, up to m α 6 for few-electrons in the Coulomb field, is also derived.