Atomic Bethe logarithm in the mean-field approximation

Abstract

In this work we develop and implement a method for calculation of the Bethe logarithm for many-electron atoms. This quantity is required to evaluate the leading-order quantum electrodynamics correction to the energy and properties of atomic and molecular systems beyond the Dirac theory (the Lamb shift). The proposed formalism is based on the mean-field representation of the ground-state electronic wavefunction and of the response functions required in the Schwartz method [C. Schwartz, Phys. Rev. {\bf 123}, 1700 (1961)]. We discuss difficulties encountered in the calculations with the emphasis on the specific basis set requirements in the vicinity of the atomic nucleus. This problem is circumvented by introducing a modified basis set of exponential functions which are able to accurately represent the gradient of hydrogen-like orbitals. The Bethe logarithm is computed for ground electronic states of atoms from hydrogen to magnesium and, additionally, for argon. Whenever possible, the results are compared with the available reference data from the literature. In general, the mean-field approximation introduces a surprisingly small error in the calculated values, suggesting that the electron correlation effects are of minor importance in determination of the Bethe logarithm. Finally, we propose a robust scheme to evaluate the Lamb shift for arbitrary light molecular systems at little computational cost. As an illustration, the method is used to calculate Lamb shifts of the vibrational levels of the nitrogen molecule.

References in corpus (25)

• The radiative potential method for calculations of QED radiative corrections to energy levels and electromagnetic amplitudes in many-electron atoms
• Model operator approach to the Lamb shift calculations in relativistic many-electron atoms
• Higher-order effective Hamiltonian for light atomic systems
• AMBiT: A program for high-precision relativistic atomic structure calculations
• Second virial coefficients for helium-4 and helium-3 from accurate relativistic interaction potential
• Testing quantum electrodynamics in the lowest singlet states of beryllium atom
• 4-component relativistic Hamiltonian with effective QED potentials for molecular calculations
• Complete basis set extrapolation of electronic correlation energies using the Riemann zeta function
• Ab initio potential energy curve for the ground state of beryllium dimer
• Calculation of the nonrelativistic Bethe logarithm in the velocity gauge
• Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. I. Coulomb and hybrid integrals
• Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. III. Case study of the beryllium dimer
• Bethe logarithm for the helium atom
• Ab initio properties of the NaLi molecule in the $a^3{\Sigma }^{+}$ electronic state
• Model-QED operator for superheavy elements
• D1 and D2 lines in ${}^{6,7}$Li including QED effects
• Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. II. Neumann expansion of the exchange integrals
• Theoretical determination of polarizability and magnetic susceptibility of neon
• First-principles calculation of the frequency-dependent dipole polarizability of argon
• Evaluation of the Bethe logarithm: from atom to chemical reaction
• Analytical two-center integrals over Slater geminal functions
• Calculation of Araki-Sucher correction for many-electron systems
• 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
• Calculation of STOs electron repulsion integrals by ellipsoidal expansion and large-order approximations

Cited by in corpus (3)

• Bound-state relativistic quantum electrodynamics: a perspective for precision physics with atoms and molecules
• Diamagnetic susceptibility of neon and argon including leading relativistic effects
• Applicability of the Dirac-Fock method combined with Core Polarization in calculations of alkali atoms