arXiv subjects

Krzysztof Pachucki

Publications and source records attributed to Krzysztof Pachucki.

116 records · Page 7Linked to original sources

arXiv2003

Two-Loop Bethe Logarithms

We calculate the two-loop Bethe logarithm correction to atomic energy levels in hydrogen-like systems. The two-loop Bethe logarithm is a low-energy quantum electrodynamic (QED) effect involving multiple summations over virtual excited atomic states. Although much smaller in absolute magnitude than the well-known one-loop Bethe logarithm, the two-loop analog is quite significant when compared to the current experimental accuracy of the 1S-2S transition: it contributes -8.19 and -0.84 kHz for the 1S and the 2S state, respectively. The two-loop Bethe logarithm has been the largest unknown correction to the hydrogen Lamb shift to date. Together with the ongoing measurement of the proton charge radius at the Paul Scherrer Institute its calculation will bring theoretical and experimental accuracy for the Lamb shift in atomic hydrogen to the level of 10^(-7).

hep-ph↗

arXiv2003

Two-Loop QED Bound-State Calculations and Squared Decay Rates

We discuss the epsilon-method as used in various recent QED bound-state calculations by considering mathematical model examples. Recently obtained results for higher-order self-energy binding corrections at the two-loop level are reviewed. Problems associated with the interpretation of squared decay rates as radiative bound-state energy level shifts are discussed. We briefly expand on the relation of squared decay rates to nonresonant and radiative corrections to the Lorentzian line shape, including their dependence on the experimental process under study.

hep-ph↗

arXiv2002

Two-Loop Self-Energy Corrections to the Fine-Structure

We investigate two-loop higher-order binding corrections to the fine structure, which contribute to the spin-dependent part of the Lamb shift. Our calculation focuses on the so-called ``two-loop self-energy'' involving two virtual closed photon loops. For bound states, this correction has proven to be notoriously difficult to evaluate. The calculation of the binding corrections to the bound-state two-loop self-energy is simplified by a separate treatment of hard and soft virtual photons. The two photon-energy scales are matched at the end of the calculation. We explain the significance of the mathematical methods employed in the calculation in a more general context, and present results for the fine-structure difference of the two-loop self-energy through the order of $α^8$.

hep-ph↗

arXiv2001

Forbidden transitions in the helium atom

Nonrelativistically forbidden, single-photon transition rates between low lying states of the helium atom are rigorously derived within quantum electrodynamics theory. Equivalence of velocity and length gauges, including relativistic corrections is explicitly demonstrated. Numerical calculations of matrix elements are performed with the use of high precision variational wave functions and compared to former results.

physics.atom-ph↗

arXiv2001

Hyperfine splitting of $2^3S_1$ state in He$^3$

Relativistic corrections to the hyperfine splitting are calculated for the triplet $2^3S_1$ state of the helium isotope He$^3$. High precision variational wave functions are employed, where the electron-electron correlations are well accounted for. Due to the unknown nuclear structure a comparison with the experimental result is performed via He$^{3+}$ hyperfine splitting. Surprisingly, the second order contribution due to Fermi interaction, in spite of the additional small factor $m/M$, is very significant.

physics.atom-ph↗

arXiv2000

Logarithmic two-loop corrections to the Lamb shift in hydrogen

Higher order $(α/π)^2 (Z α)^6$ logarithmic corrections to the hydrogen Lamb shift are calculated. The results obtained show the two-loop contribution has a very peculiar behavior, and significantly alter the theoretical predictions for low lying S-states.

physics.atom-ph↗

arXiv1999

Proton structure effects in muonic hydrogen

The proton structure effects, including finite size, polarizability and self-energy is considered and their influence on energy levels of muonic hydrogen is recalculated. A new theoretical prediction for the Lamb shift is presented together with improved values of all known QED contributions.

physics.atom-ph↗

arXiv1997

Complete Result for Positronium Energy Levels at Order alpha^6 m

We have completed theoretical predictions for positronium energy levels through order alpha^6 m by the calculation of the spin independent, radiative recoil correction. This contribution is significant and amounts to 10.64 MHz for the 1S state. We further perform detailed comparison of theoretical predictions to experimental results for 1S-2S and 2S-2P transitions.

hep-ph↗