Electron Self-energy Corrections Research Articles

Electron self-energy corrections using the Welton concept for atomic structure calculations

The high level of accuracy achieved by atomic experiments in recent time has shone a spotlight on the need for a similarly high level of accuracy in atomic structure calculations, and in particular, QED prediction. A method of electron self-energy correction originally derived from the Welton idea by Lowe et al. (2013) (LCG-Welton method) has now been fully incorporated into the popular atomic structural package, GRASP2K, which we have introduced in this paper. A series of benchmark tests and results are presented, which enables the comparison of the implementations of different versions of GRASP2K, and the implementations on different platforms or operating systems. Test results presented in this paper demonstrate that these new implementations maintain the overall consistency and stability of the program across various platforms, while at the same time improve the accuracy of final energies. Our calculations for hydrogenic Lyα1,2 transitions show excellent agreement with experiment, to within less than 0.5 eV. On helium-like systems, our calculations show an improvement from the previous GRASP2K screening method. The new results from electronic self-energy contribution using the LCG-Welton method is more consistent with current standards in the literature, where they now fit within experimental variability of up to 0.1 eV. An option for users to adjust the gauge factor in the electric component of the transition rate has also been added to facilitate further investigation of this particular topic.

One-loop binding corrections to the electron g factor

We calculate the one-loop electron self-energy correction of order $\alpha\,(Z\,\alpha)^5$ to the bound electron $g$ factor. Our result is in agreement with the extrapolated numerical value and paves the way for the calculation of the analogous, but as yet unknown two-loop correction.

Dynamical breakdown of parity and time-reversal invariance in the many-body theory of graphene

We show that, at sufficiently large strength of the long-range Coulomb interaction, a mass term breaking parity (so-called Haldane mass) is dynamically generated in the many-body theory of Dirac fermions describing the graphene layer. While the tendency towards chiral symmetry breaking is stronger than for the dynamical breakdown of parity at spatial dimension D > 2, we find that the situation is reversed at D = 2. The need to regularize the many-body theory in a gauge-invariant manner (taking the limit D = 2 - \epsilon) is what leads to the dominance of the parity-breaking pattern in graphene. We compute the critical coupling for the generation of a parity-breaking mass from the finite radius of convergence of the ladder series supplemented with electron self-energy corrections, finding a value quite close to the effective interaction strength for graphene in vacuum after including Fermi velocity renormalization and static RPA screening of the Coulomb interaction.

Higher-order renormalization of graphene many-body theory

We study the many-body theory of graphene Dirac quasiparticles interacting via the long-range Coulomb potential, taking as a starting point the ladder approximation to different vertex functions. We test in this way the low-energy behavior of the electron system beyond the simple logarithmic dependence of electronic correlators on the high-energy cutoff, which is characteristic of the large-N approximation. We show that the graphene many-body theory is perfectly renormalizable in the ladder approximation, as all higher powers in the cutoff dependence can be absorbed into the redefinition of a finite number of parameters (namely, the Fermi velocity and the weight of the fields) that remain free of infrared divergences even at the charge neutrality point. We illustrate this fact in the case of the vertex for the current density, where a complete cancellation between the cutoff dependences of vertex and electron self-energy corrections becomes crucial for the preservation of the gauge invariance of the theory. The other potentially divergent vertex corresponds to the staggered (sublattice odd) charge density, which is made cutoff independent by a redefinition in the scale of the density operator. This allows to compute a well-defined, scale invariant anomalous dimension to all orders in the ladder series, which becomes singular at a value of the interaction strength marking the onset of chiral symmetry breaking (and gap opening) in the Dirac field theory. The critical coupling we obtain in this way matches with great accuracy the value found with a quite different method, based on the resolution of the gap equation, thus reassuring the predictability of our renormalization approach.

Electron self-energy effects on chiral symmetry breaking in graphene

We investigate the excitonic instability in the theory of Dirac fermions in graphene with long-range Coulomb interaction. We analyze the electron-hole vertex relevant for exciton condensation in the ladder approximation, showing that it blows up at a critical value of the interaction strength \alpha = e^2/4\pi v_F sensitive to further many-body corrections. Under static screening of the interaction, we find that taking into account electron self-energy corrections increases the critical coupling to \alpha_c \approx 2.09, for a number N = 4 of two-component Dirac fermions. We show that the dynamical screening of the interaction has however the opposite effect of enhancing the instability, which turns out to develop then at \alpha_c \approx 0.99 for N = 4, bringing the question of whether that critical value can be reached by the effective coupling in real graphene samples at the low-energy scales of the exciton condensation.

Quantum electrodynamic corrections for the valence shell in heavy many-electron atoms

We present quantum electrodynamic (QED) calculations within the picture of bound-state QED for the frequency-dependent Breit interaction between electrons, the vacuum polarization, and the electron self-energy correction starting from the Dirac-Coulomb Hamiltonian for the ionization potentials of the group 1, 2, 11, 12, 13, and 18 elements of the periodic table, and down to the superheavy elements up to nuclear charge Z=120. The results for the s-block elements are in very good agreement with earlier studies by Labzowsky et al. [Phys. Rev. A 59, 2707 (1999)]. We discuss the influence of the variational versus perturbative treatment of the Breit interaction for valence-space ionization potentials. We argue that the lowest-order QED contributions become as important as the Breit interaction for ionization potentials out of the valence s shell.

Spin Wave Excitations in the Ferromagnetic Phase of Iron –Study with a Tight-Binding Model–

Spin wave excitations and the electron self-energy corrections in the ferromagnetic phase of iron are studied using the Naval Research Laboratory tight-binding model. It is found that the spin wave excitation spectrum obtained with this model is in good agreement with the experimental results. Transverse spin fluctuations contribute to the self-energy and reduce the band width uniformly, but does not cause a prominent kink structure in the quasiparticle dispersion near the fermi level. Comparison with recent angle-resolved photoemission experiments on Fe is made.

Enlarged paramagnetism by electron–electron exchange interactions in n-type modulation doped Cd1−xMnxTe/Cd1−x−yMnxMgyTe single quantum wells

Electron spin polarization is studied on n-type modulation doped Cd1−xMnxTe/Cd1−x−yMnxMgyTe single quantum wells. The influence of the electron–electron exchange interaction on the electron spin polarization is discussed. In magnetic fields, the electronic states undergo an initial giant splitting due to the s–d and p–d exchange interactions with localized magnetic moments. Such a giant Zeeman splitting creates an initial spin polarization which will be further enlarged due to the many-body effects of the electron self-energy corrections.

A new approach to the direct renormalization of the bound electron self-energy

A new practical expression for the first-order electron self-energy correction is presented in the coordinate space. It is derived within the adiabatic formalism and decomposed into several parts. For each part a direct renormalization procedure is introduced which avoids the commonly used potential expansion and the Feynman regulated photon propagator. As a simple illustration, the direct renormalization method is applied to terms of the sum over intermediate states in the expansion for the bound electron self-energy of the hydrogen-like ions. It is shown that these renormalized terms give reasonable estimates for the self-energy shift in ground and excited states for different values of the nuclear charge Z including the 1S 1 2 state of the hydrogen-like uranium.

Alpha (Z alpha )2EF correction to hyperfine splitting in hydrogenic atoms.

The electron self-energy correction of the order \ensuremath{\alpha}(Z\ensuremath{\alpha}${)}^{2}$${\mathit{E}}_{\mathit{F}}$ to the ground-state hyperfine splitting in hydrogenic atoms is calculated using a semianalytical method. The correction is divided into three parts by introducing two auxiliary parameters. The low-energy part corresponds to the nonrelativistic limit, where photon energy is of the order m${\mathrm{\ensuremath{\alpha}}}^{2}$, and the effective hyperfine interaction is given by ${\mathrm{\ensuremath{\delta}}}^{3}$(r). In the middle-energy part electron and photon momenta are of the order m\ensuremath{\alpha} and m, respectively. This part is calculated using on-shell electron form factors. The high-energy part corresponds to the S-matrix amplitude for the forward scattering. The final value does not depend on auxiliary parameters and amounts to \ensuremath{\Delta}E=(\ensuremath{\alpha}/\ensuremath{\pi})(Z\ensuremath{\alpha}${)}^{2}$${\mathit{E}}_{\mathit{F}}$\ifmmode\times\else\texttimes\fi{}17.122. It is larger than the previous value of Sapirstein \ensuremath{\sim}15.10(29) and significantly alters theoretical predictions. \textcopyright{} 1996 The American Physical Society.

Electron Cyclotron Resonance in CdS

Electron cyclotron resonance has been observed in single-crystal CdS platelets at temperatures below 4.2\ifmmode^\circ\else\textdegree\fi{}K. The single resonance seen in all orientations is consistent with a single-ellipsoid conduction-band model for CdS. The cyclotron effective masses measured with the crystal $c$ axis parallel and perpendicular to the magnetic field are $\frac{{{m}^{*}}_{c\mathrm{II}B}}{{m}_{o}}=0.171$ and $\frac{{{m}^{*}}_{c\ensuremath{\perp}B}}{{m}_{o}}=0.162$, implying that the constant-energy surfaces near the conduction-band minimum are oblate spheroids having transverse and longitudinal effective masses $\frac{{{m}_{t}}^{*}}{{m}_{o}}=0.171$ and $\frac{{{m}_{l}}^{*}}{{m}_{o}}=0.153$. The effective mass values determined from cyclotron resonance are 15% lower than those measured in other experiments. The difference cannot be due to depolarization or optical polaron effects, but can be accounted for in terms of an electron self-energy correction resulting from the piezoelectric electron-phonon interaction in CdS. Electron collision times of order ${10}^{\ensuremath{-}11}$ sec were calculated from the 70-Gc/sec cyclotron resonance data taken between 1.25 and 4.2\ifmmode^\circ\else\textdegree\fi{}K. The magnitude and temperature dependence of the collision times are best described by the theoretical predictions for piezoelectric scattering along with possibly a small neutral-impurity scattering contribution.