Atomic Energy Levels with QED and Contribution of the Screened Self-Energy

We present an introduction to the principles behind atomic energy level calculations with Quantum Electrodynamics (QED) and the two-time Green's function method; this method allows one to calculate an effective Hamiltonian that contains all QED effects and that can be used to predict QED Lamb shifts of degenerate, quasidegenerate and isolated atomic levels.Comment: 4 pages, 6 figures, summary of a talk given at the QED2000 Conference held in Trieste, Italy in Oct. 200

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

Characterization of a CCD array for Bragg spectroscopy

The average pixel distance as well as the relative orientation of an array of 6 CCD detectors have been measured with accuracies of about 0.5 nm and 50 $\mu$rad, respectively. Such a precision satisfies the needs of modern crystal spectroscopy experiments in the field of exotic atoms and highly charged ions. Two different measurements have been performed by illuminating masks in front of the detector array by remote sources of radiation. In one case, an aluminum mask was irradiated with X-rays and in a second attempt, a nanometric quartz wafer was illuminated by a light bulb. Both methods gave consistent results with a smaller error for the optical method. In addition, the thermal expansion of the CCD detectors was characterized between -105 C and -40 C.Comment: Submitted to Review of Scientific Instrument

Precise calculation of transition frequencies of hydrogen and deuterium based on a least-squares analysis

We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to obtain precise and optimal predictions for hydrogen and deuterium transition frequencies. Some of the predicted transition frequencies have relative uncertainties more than an order of magnitude smaller than that of the g-factor of the electron, which was previously the most accurate prediction of QED.Comment: 4 pages, RevTe

High Resolution He-like Argon And Sulfur Spectra From The PSI ECRIT

We present new results on the X-ray spectroscopy of multicharged argon, sulfur and chlorine obtained with the Electron Cyclotron Resonance Ion Trap (ECRIT) in operation at the Paul Scherrer Institut (Villigen, Switzerland). We used a Johann-type Bragg spectrometer with a spherically-bent crystal, with an energy resolution of about 0.4 eV. The ECRIT itself is of a hybrid type, with a superconducting split coil magnet, special iron inserts which provides the mirror field, and a permanent magnetic hexapole. The high frequency was provided by a 6.4 GHz microwave emitter. We obtained high intensity X-ray spectra of multicharged F-like to He-like argon, sulfur and chlorine with one 1s hole. In particular, we observed the 1s2s^{3}S_1 \to 1s^2^{1}S_0 M1 and 1s2p^{3}P_2 \to 1s^2^{1}S_0 M2 transitions in He-like argon, sulfur and chlorine with unprecedented statistics and resolution. The energies of the observed lines are being determined with good accuracy using the He-like M1 line as a reference

Relativistic and Radiative Energy Shifts for Rydberg States

We investigate relativistic and quantum electrodynamic effects for highly-excited bound states in hydrogenlike systems (Rydberg states). In particular, hydrogenic one-loop Bethe logarithms are calculated for all circular states (l = n-1) in the range 20 <= n <= 60 and successfully compared to an existing asymptotic expansion for large principal quantum number n. We provide accurate expansions of the Bethe logarithm for large values of n, for S, P and circular Rydberg states. These three expansions are expected to give any Bethe logarithms for principal quantum number n > 20 to an accuracy of five to seven decimal digits, within the specified manifolds of atomic states. Within the numerical accuracy, the results constitute unified, general formulas for quantum electrodynamic corrections whose validity is not restricted to a single atomic state. The results are relevant for accurate predictions of radiative shifts of Rydberg states and for the description of the recently investigated laser-dressed Lamb shift, which is observable in a strong coherent-wave light field.Comment: 8 pages; RevTeX

A High Efficiency Ultra High Vacuum Compatible Flat Field Spectrometer for EUV Wavelengths

A custom, flat field, extreme ultraviolet EUV spectrometer built specifically for use with low power light sources that operate under ultrahigh vacuum conditions is reported. The spectral range of the spectrometer extends from 4 nm to 40 nm. The instrument optimizes the light gathering power and signal to noise ratio while achieving good resolution. A detailed description of the spectrometer and design considerations are presented, as well as a novel procedure that could be used to obtain a synthetic wavelength calibration with the aid of only a single known spectral feature. This synthetic wavelength calibration is compared to a standard wavelength calibration obtained from previously reported spectral lines of Xe, Ar and Ne ions recorded with this spectrometer

The Lamb shift in muonic hydrogen and the proton radius

By means of pulsed laser spectroscopy applied to muonic hydrogen (μ− p) we have measured the 2S F = 1 1/2 − 2PF = 2 3/2 transition frequency to be 49881.88(76) GHz. By comparing this measurement with its theoretical prediction based on bound-state QED we have determined a proton radius value of rp = 0.84184 (67) fm. This new value is an order of magnitude preciser than previous results but disagrees by 5 standard deviations from the CODATA and the electronproton scattering values. An overview of the present effort attempting to solve the observed discrepancy is given. Using the measured isotope shift of the 1S-2S transition in regular hydrogen and deuterium also the rms charge radius of the deuteron rd = 2.12809 (31) fm has been determined. Moreover we present here the motivations for the measurements of the μ 4He + and μ 3He + 2S-2P splittings. The alpha and triton charge radii are extracted from these measurements with relative accuracies of few 10 − 4. Measurements could help to solve the observed discrepancy, lead to the best test of hydrogen-like energy levels and provide crucial tests for few-nucleon ab-initio theories and potentials

The Lamb shift in muonic hydrogen

The long quest for a measurement of the Lamb shift in muonic hydrogen is over. Last year we measured the 2S1/2F=1–2P3/2F=2 energy splitting (Pohl et al., Nature, 466, 213 (2010)) in μp with an experimental accuracy of 15 ppm, twice better than our proposed goal. Using current QED calculations of the fine, hyperfine, QED, and finite size contributions, we obtain a root-mean-square proton charge radius of rp = 0.841 84 (67) fm. This value is 10 times more precise, but 5 standard deviations smaller, than the 2006 CODATA value of rp. The origin of this discrepancy is not known. Our measurement, together with precise measurements of the 1S–2S transition in regular hydrogen and deuterium, gives improved values of the Rydberg constant, R∞ = 10 973 731.568 160 (16) m⁻¹ and the rms charge radius of the deuteron rd = 2.128 09 (31) fm