Higher-order effective Hamiltonian for light atomic systems

Abstract

We present the derivation of the effective higher-order Hamiltonian, which gives $m{\alpha }^6$ contribution to energy levels of an arbitrary light atom. The derivation is based on the Foldy-Wouthuysen transformation of the one-particle Dirac Hamiltonian followed by perturbative expansion of the many particle Green function. The obtained results can be used for the high precision calculation of relativistic effects in atomic systems.

19 pages, Phys. Rev. A, to be published

References in corpus (4)

• Ionization Potential of the Helium Atom
• Quantum Electrodynamics of the Helium Atom
• Recursion relations for Hylleraas three-electron integral
• Hyperfine splitting of $2^3{S}_1$ state in He${}^3$

Cited by in corpus (39)

• ${\alpha }^4$ Ry corrections to singlet states of helium
• Ground state wave function and energy of the lithium atom
• The full infrared spectrum of molecular hydrogen
• Relativistic, QED, and finite nuclear mass corrections for low-lying states of Li and Be${}^{+}$
• Constraints on extra dimensions from precision molecular spectroscopy
• Improved theory of helium fine structure
• Reexamination of helium fine structure
• Helium energy levels including $m{\alpha }^6$ corrections
• Higher-order recoil corrections for triplet states of the helium atom
• Ab initio potential energy curve for the ground state of beryllium dimer
• Quantum electrodynamics corrections to the $2P$ fine splitting in Li
• Foldy-Wouthuysen Transformation, Scalar Potentials and Gravity
• NRQED approach to the fine and hyperfine structure corrections of order $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ -- Application to the hydrogen atom
• Extended Hylleraas three-electron integral
• Hyperfine structure in the H${}_2^{+}$ and HD${}^{+}$ molecular ions at $m{\alpha }^6$ order
• Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules
• D1 and D2 lines in ${}^{6,7}$Li including QED effects
• Nonradiative ${\alpha }^{7}m$ QED effects in Lamb shift of helium triplet states
• Testing Standard Model extensions with few-electron ions
• The Bethe-Salpeter QED wave equation for bound-state computations of atoms and molecules
• Calculation of Araki-Sucher correction for many-electron systems
• Non-relativistic expansion of single-nucleon Dirac equation: Comparison between Foldy-Wouthuysen transformation and similarity renormalization group
• Potential energy curve for the $a^3{\Sigma }_u^{+}$ state of lithium dimer with Slater-type orbitals
• Pre-Born-Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen
• QED corrections of order alpha (Zalpha)^2 E_F to the hyperfine splitting of P_1/2 and P_3/2 states in hydrogenlike ions
• Quantum electrodynamics of two-body systems with arbitrary masses
• Atomic Bethe logarithm in the mean-field approximation
• Two-body $P$-state energies at ${\alpha }^6$ order
• Calculation of size for bound-state constituents
• Gauge invariance and relativistic effects in photon absorption and scattering by matter
• Foldy-Wouthuysen Transformation in Strong Magnetic Fields and Relativistic Corrections for Quantum Cyclotron Energy Levels
• High-precision solution of the Dirac Equation for the hydrogen molecular ion by an iterative method
• Self-Energy Correction to the Bound-Electron g Factor of P States
• Foldy-Wouthuysen Transformation for a Spinning Particle with Anomalous Magnetic Moment
• Relativistic (Z alpha)^2-Corrections and Leading Quantum Electrodynamic Corrections to the Two-Photon Decay Rate of Ionic States
• Eighth-Order Foldy-Wouthuysen Transformation
• Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian
• Proton radius puzzle in Hamiltonian dynamics
• Nonrelativistic quantum electrodynamic approach to polarizabilities of light atoms