Functional Form of the Imaginary Part of the Atomic Polarizability

The dynamic atomic polarizability describes the response of the atom to incoming electromagnetic radiation. The functional form of the imaginary part of the polarizability for small driving frequencies omega has been a matter of long-standing discussion, with both a linear dependence and an omega^3 dependence being presented as candidate formulas. The imaginary part of the polarizability enters the expressions of a number of fundamental physical processes which involve the thermal dissipation of energy, such as blackbody friction, and non-contact friction. Here, we solve the long-standing problem by calculating the imaginary part of the polarizability in both the length (d.E) as well as the velocity-gauge (p.A) form of the dipole interaction, verify the gauge invariance, and find general expressions applicable to atomic theory; the omega^3 form is obtained in both gauges. The seagull term in the velocity gauge is found to be crucial in establishing gauge invariance.Comment: 10 pages; RevTeX; accepted for publication in Eur.Phys.J.

Techniques in Analytic Lamb Shift Calculations

Quantum electrodynamics has been the first theory to emerge from the ideas of regularization and renormalization, and the coupling of the fermions to the virtual excitations of the electromagnetic field. Today, bound-state quantum electrodynamics provides us with accurate theoretical predictions for the transition energies relevant to simple atomic systems, and steady theoretical progress relies on advances in calculational techniques, as well as numerical algorithms. In this brief review, we discuss one particular aspect connected with the recent progress: the evaluation of relativistic corrections to the one-loop bound-state self-energy in a hydrogenlike ion of low nuclear charge number, for excited non-S states, up to the order of alpha (Zalpha)^6 in units of the electron mass. A few details of calculations formerly reported in the literature are discussed, and results for 6F, 7F, 6G and 7G states are given.Comment: 16 pages, LaTe

Toward high-precision values of the self energy of non-S states in hydrogen and hydrogen-like ions

The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between 20 and 110 are given for a large number of states. The self-energy is the largest contribution of Quantum Electrodynamics (QED) to the energy levels of these atomic systems. These results greatly expand the number of levels for which the self energy is known with a controlled and high precision. Applications include the adjustment of the Rydberg constant and atomic calculations that take into account QED effects.Comment: Minor changes since previous versio

Renormalization of the Periodic Scalar Field Theory by Polchinski's Renormalization Group Method

The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this work we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go beyond the local potential approximation in the gradient expansion in order to clarify the supposed role of the field-dependent wave-function renormalization. The well-known Coleman fixed point of the sine-Gordon model is recovered after linearization, whereas the flow exhibits strong dependence on the choice of the renormalization scheme when non-linear terms are kept. The RG flow is compared to those obtained in the Wegner-Houghton approach and in the dilute gas approximation for the two-dimensional Coulomb-gas.Comment: 14 pages, LaTeX, 1 figure; J. Phys. G (in press

Renormalization-Group Analysis of the Generalized sine-Gordon Model and of the Coulomb Gas for d >= 3 Dimensions

Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d >= 3 of dimensions by means of Wegner's and Houghton's, and by way of the real-space RG approaches. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions d >= 3, independent of the dimensionality, and in sharp contrast to the special case d = 2. For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations), that the blocked potential tends to a constant effective potential in the infrared (IR) limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used.Comment: 19 pages, 8 figure

Double-Logarithmic Two-Loop Self-Energy Corrections to the Lamb Shift

Self-energy corrections involving logarithms of the parameter Zalpha can often be derived within a simplified approach, avoiding calculational difficulties typical of the problematic non-logarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by alpha the fine-structure constant). For some logarithmic corrections, it is sufficient to consider internal properties of the electron characterized by form factors. We provide a detailed derivation of related self-energy ``potentials'' that give rise to the logarithmic corrections; these potentials are local in coordinate space. We focus on the double-logarithmic two-loop coefficient B_62 for P states and states with higher angular momenta in hydrogenlike systems. We complement the discussion by a systematic derivation of B_62 based on nonrelativistic quantum electrodynamics (NRQED). In particular, we find that an additional double logarithm generated by the loop-after-loop diagram cancels when the entire gauge-invariant set of two-loop self-energy diagrams is considered. This double logarithm is not contained in the effective-potential approach.Comment: 14 pages, 1 figure; references added and typographical errors corrected; to appear in Phys. Rev.

On the applicability of the layered sine-Gordon model for Josephson-coupled high-T_c layered superconductors

We find a mapping of the layered sine-Gordon model to an equivalent gas of topological excitations and determine the long-range interaction potentials of the topological defects. This enables us to make a detailed comparison to the so-called layered vortex gas, which can be obtained from the layered Ginzburg-Landau model. The layered sine-Gordon model has been proposed in the literature as a candidate field-theoretical model for Josephson-coupled high-T_c superconductors, and the implications of our analysis for the applicability of the layered sine-Gordon model to high-T_c superconductors are discussed. We are led to the conjecture that the layered sine--Gordon and the layered vortex gas models belong to different universality classes. The determination of the critical temperature of the layered sine-Gordon model is based on a renormalization-group analysis.Comment: 7 pages, accepted for publication in J. Phys.: Condens. Matte

Reexamining Blackbody Shifts for Hydrogenlike Ions

We investigate blackbody-induced energy shifts for low-lying levels of atomic systems, with a special emphasis on transitions used in current and planned high-precision experiments on atomic hydrogen and ionized helium. Fine-structure- and Lamb-shift-induced blackbody shifts are found to increase with the square of the nuclear charge number, whereas blackbody shifts due to virtual transitions decrease with increasing nuclear charge as the fourth power of the nuclear charge. We also investigate the decay width acquired by the ground state of atomic hydrogen, due to interaction with blackbody photons. The corresponding width is due to an instability against excitation to higher excited atomic levels, and due to blackbody-induced ionization. These effects limit the lifetime of even the most fundamental, a priori absolutely stable, asymptotic state of atomic theory, namely, the ground state of atomic hydrogen

Polarization operator approach to electron-positron pair production in combined laser and Coulomb fields

The optical theorem is applied to the process of electron-positron pair creation in the superposition of a nuclear Coulomb and a strong laser field. We derive new representations for the total production rate as two-fold integrals, both for circular laser polarization and for the general case of elliptic polarization, which has not been treated before. Our approach allows us to obtain by analytical means the asymptotic behaviour of the pair creation rate for various limits of interest. In particular, we consider pair production by two-photon absorption and show that, close to the energetic threshold of this process, the rate obeys a power law in the laser frequency with different exponents for linear and circular laser polarization. With the help of the upcoming x-ray laser sources our results could be tested experimentally.Comment: 10 pages, 3 figure

Semi-Analytic Approach to Higher-Order Corrections in Simple Muonic Bound Systems: Vacuum Polarization, Self-Energy and Radiative-Recoil

The current discrepancy of theory and experiment observed recently in muonic hydrogen necessitates a reinvestigation of all corrections to contribute to the Lamb shift in muonic hydrogen muH, muonic deuterium muD, the muonic 3He ion, as well as in the muonic 4He ion. Here, we choose a semi-analytic approach and evaluate a number of higher-order corrections to vacuum polarization (VP) semi-analytically, while remaining integrals over the spectral density of VP are performed numerically. We obtain semi-analytic results for the second-order correction, and for the relativistic correction to VP. The self-energy correction to VP is calculated, including the perturbations of the Bethe logarithms by vacuum polarization. Subleading logarithmic terms in the radiative-recoil correction to the 2S-2P Lamb shift of order alpha (Zalpha)^5 mu^3 ln(Zalpha)/(m_mu m_N) are also obtained. All calculations are nonperturbative in the mass ratio of orbiting particle and nucleus.Comment: 10 pages; svjour style; to appear in the European Physical Journal