1,643 research outputs found
Calculation of Hydrogenic Bethe Logarithms for Rydberg States
We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all
states with principal quantum numbers n <= 200. While, in principle, the
calculation of the Bethe logarithm is a rather easy computational problem
involving only the nonrelativistic (Schroedinger) theory of the hydrogen atom,
certain calculational difficulties affect highly excited states, and in
particular states for which the principal quantum number is much larger than
the orbital angular momentum quantum number. Two evaluation methods are
contrasted. One of these is based on the calculation of the principal value of
a specific integral over a virtual photon energy. The other method relies
directly on the spectral representation of the Schroedinger-Coulomb propagator.
Selected numerical results are presented. The full set of values is available
at quant-ph/0504002.Comment: 10 pages, RevTe
Self-energy values for P states in hydrogen and low-Z hydrogenlike ions
We describe a nonperturbative (in Zalpha) numerical evaluation of the
one-photon electron self energy for 3P_{1/2}, 3P_{3/2}, 4P_{1/2} and 4P_{3/2}
states in hydrogenlike atomic systems with charge numbers Z=1 to 5. The
numerical results are found to be in agreement with known terms in the
expansion of the self energy in powers of Zalpha and lead to improved
theoretical predictions for the self-energy shift of these states.Comment: 3 pages, RevTe
Perturbation Approach to the Self Energy of non-S Hydrogenic States
We present results on the self-energy correction to the energy levels of
hydrogen and hydrogenlike ions. The self energy represents the largest QED
correction to the relativistic (Dirac-Coulomb) energy of a bound electron. We
focus on the perturbation expansion of the self energy of non-S states, and
provide estimates of the so-called A60 perturbative coefficient, which can be
considered as a relativistic Bethe logarithm. Precise values of A60 are given
for many P, D, F and G states, while estimates are given for other electronic
states. These results can be used in high-precision spectroscopy experiments in
hydrogen and hydrogenlike ions. They yield the best available estimate of the
self-energy correction of many atomic states.Comment: 18 pages (in 2-column format), 21 figures. Version 2 (June 20, 2003)
includes minor modification
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).Comment: 4 pages, RevTe
Thermal Correction to the Molar Polarizability of a Boltzmann Gas
Metrology in atomic physics has been crucial for a number of advanced determinations of fundamental constants. In addition to very precise frequency measurements, the molar polarizability of an atomic gas has recently also been measured very accurately. Part of the motivation for the measurements is due to ongoing efforts to redefine the International System of Units (SI), for which an accurate value of the Boltzmann constant is needed. Here we calculate the dominant shift of the molar polarizability in an atomic gas due to thermal effects. It is given by the relativistic correction to the dipole interaction, which emerges when the probing electric field is Lorentz transformed into the rest frame of the atoms that undergo thermal motion. While this effect is small when compared to currently available experimental accuracy, the relativistic correction to the dipole interaction is much larger than the thermal shift of the polarizability induced by blackbody radiation
Electron Self-Energy for the K and L Shells at Low Nuclear Charge
A nonperturbative numerical evaluation of the one-photon electron self-energy for the K- and L-shell states of hydrogenlike ions with nuclear charge numbers Z =1 to 5 is described. Our calculation for the 1S1/2 state has a numerical uncertainty of 0.8 Hz in atomic hydrogen, and for the L-shell states (2S1/2 , 2P1/2 , and 2P3/2) the numerical uncertainty is 1.0 Hz. The method of evaluation for the ground state and for the excited states is described in detail. The numerical results are compared to results based on known terms in the expansion of the self-energy in powers of Zα
Lamb Shift of 3P and 4P States and the Determination of α
The fine-structure interval of P states in hydrogenlike systems can be determined theoretically with high precision, because the energy levels of P states are only slightly influenced by the structure of the nucleus. Therefore a measurement of the fine structure may serve as an excellent test of QED in bound systems, or alternatively as a means of determining the fine-structure constant a with very high precision. In this paper an improved analytic calculation of higher-order binding corrections to the one-loop self-energy of 3P and 4P states in hydrogenlike systems with a low nuclear charge number Z is presented. The method of calculation has been described earlier by Jentschura and Pachucki [Phys. Rev. A 54, 1853 (1996)], and is applied here to the excited P states. Because of the more complicated nature of the wave functions and the bound-state poles corresponding to decay of the excited states, the calculations are more complex. Comparison of the analytic results to the extrapolated numerical data for high-Z ions [Mohr and Kim, Phys. Rev. A 45, 2727 (1992)] serves as an independent test of the analytic evaluation. Theoretical values for the Lamb shift of the P states and for the fine-structure splittings are given
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