1s Lamb Shift Research Articles

High-resolution X-ray emission study for Xe^{54+} on Xe collisions

We report on an experiment conducted at the ESR storage ring aiming at the study of the X-ray emission of text {Xe}^{54+} ions colliding with Xe atoms at a beam energy of 50 MeV/u. The radiation resulting from the ion–atom interaction was observed using a high-resolution spectrometer based on metallic–magnetic calorimeter technology. In order to benchmark the capabilities of these detectors for high-precision atomic physics experiments, we identified several transitions from H-like and He-like xenon and determined their energies. Furthermore, the 1s-Lamb shift in text {Xe}^{53+} was estimated using the measured line energies. The results are compared with previous experimental studies and theoretical predictions.Graphicalabstract

X-ray Spectroscopy Based on Micro-Calorimeters at Internal Targets of Storage Rings

With metallic-magnetic calorimeters (MMCs), promising detectors for high-precision X-ray spectrometry in atomic and fundamental physics experiments are available. In this work, we present a pilot experiment based on a maXs-30 type MMC-spectrometer for recording X-rays emitted in collisions of lithium-like uranium ions with a molecular nitrogen gas jet in the internal target of the ESR storage ring of the GSI. Sample spectra have been measured, and a multitude of X-ray transitions have been unambiguously identified. As a first test and for comparison with data recorded at an EBIT, the 2s Lamb shift in lithium-like uranium was estimated.

The Lamb shift of the 1s state in hydrogen: Two-loop and three-loop contributions

We consider the 1s Lamb shift in hydrogen and helium ions, a quantity, required for an accurate determination of the Rydberg constant and the proton charge radius by means of hydrogen spectroscopy, as well as for precision tests of the bound-state QED. The dominant QED contribution to the uncertainty originates from α8m external-field contributions (i.e., the contributions at the non-recoil limit). We discuss the two- and three-loop cases and in particular, we revisit calculations of the coefficients B61,B60,C50 in standard notation.We have found a missing logarithmic contribution of order α2(Zα)6m. We have also obtained leading pure self-energy logarithmic contributions of order α2(Zα)8m and α2(Zα)9m and estimated the subleading terms of order α2(Zα)7m, α2(Zα)8m, and α2(Zα)9m. The determination of those higher-order contributions enabled us to improve the overall accuracy of the evaluation of the two-loop self-energy of the electron.We investigated the asymptotic behavior of the integrand related to the next-to-leading three-loop term (order α3(Zα)5m, coefficient C50 in standard notation) and applied it to approximate integration over the loop momentum. Our result for contributions to the 1s Lamb shift for the total three loop next-to-leading term is (−3.3±10.5)(α3/π3)(Zα)5m.Altogether, we have completed the evaluation of the logarithmic contributions to the 1s Lamb shift of order α8m and reduced the overall α8m uncertainty by approximately a factor of three for H, D, and He+ as compared with the most recent CODATA compilation.

Microcalorimeters for X-Ray Spectroscopy of Highly Charged Ions at Storage Rings

X-ray spectroscopy of highly charged heavy ions is an important tool for the investigation of many topics in atomic physics. Such highly charged ions, in particular hydrogen-like uranium, are investigated at heavy ion storage rings, where high charge states can be produced in large quantities, stored for long times and cooled to low momentum spread of the ion beam. One prominent example is the determination of the 1s Lamb Shift in hydrogen-like heavy ions, which has been investigated at the Experimental Storage Ring (ESR) at the GSI Helmholtz Centre for Heavy Ion Research. Due to the large electron binding energies, the energies of the corresponding photon transitions are located in the X-ray regime. To determine the transition energies with high accuracy, highly resolving X-ray spectrometers are needed. One concept of such spectrometers is the concept of microcalorimeters, which, in contrast to semiconductor detectors, uses the detection of heat rather than charge to detect energy. Such detectors have been developed and successfully applied in experiments at the ESR. For experiments at the Facility for Antiproton and Ion Research (FAIR), the Stored Particles and Atoms Collaboration (SPARC) pursues the development of new microcalorimeter concepts and larger detector arrays. Next to fundamental investigations on quantum electrodynamics such as the 1s Lamb Shift or electron–electron interactions in two- and three-electron systems, X-ray spectroscopy may be extended towards nuclear physics investigations like the determination of nuclear charge radii.

Wavelength-dispersive spectroscopy in the hard x-ray regime of a heavy highly-charged ion: the 1s Lamb shift in hydrogen-like gold

Accurate spectroscopy of highly-charged high-Z ions in a storage ring is demonstrated to be feasible by the use of specially adapted crystal optics. The method has been applied for the measurement of the 1s Lamb shift in hydrogen-like gold (Au+78) in a storage ring through spectroscopy of the Lyman x-rays. This measurement represents the first result obtained for a high-Z element using high-resolution wavelength-dispersive spectroscopy in the hard x-ray regime, paving the way for sensitivity to higher-order QED effects.

Precise determination of the 1s Lamb shift in hydrogen-like lead and gold using microcalorimeters

Quantum electrodynamics in very strong Coulomb fields is one scope which has not yet been tested experimentally with sufficient accuracy to really determine whether the perturbative approach is valid. One sensitive test is the determination of the 1s Lamb shift in highly-charged very heavy ions. The 1s Lamb shift of hydrogen-like lead (Pb81+) and gold (Au78+) has been determined using the novel detector concept of silicon microcalorimeters for the detection of hard x-rays. The results of eV for lead and eV for gold are within the error bars in good agreement with theoretical predictions. To our knowledge, for hydrogen-like lead, this represents the most accurate determination of the 1s Lamb shift.

Precise determination of the 1s Lamb Shift in hydrogen-like heavy ions at the ESR storage ring using microcalorimeters

The precise determination of the energy of the Lyman α1 and α2 lines in hydrogen-like heavy ions provides a sensitive test of quantum electrodynamics in very strong Coulomb fields. To improve the precision of such experiments, the new detector concept of microcalorimeters, which detect the temperature change of an absorber after an incoming particle or photon has deposited its energy as heat, is now exploited. The microcalorimeters for x-rays used in these experiments consist of arrays of silicon thermometers and x-ray absorbers made of high-Z material. With such detectors, a relative energy resolution of about 1 per mille is obtained in the energy regime of 50–100 keV. Two successful measurement campaigns to determine the 1s Lamb Shift in Pb81+ and Au78+ have been completed: a prototype array has been applied successfully for the determination of the 1s Lamb Shift of Pb81+ at the ESR storage ring at GSI in a first test experiment. Based on the results of this test, a full array with 32 pixels has been equipped and has recently been applied to determine the 1s Lamb Shift in Au78+ ions. The energy of the Lyman-α1 line agrees within error bars well with theoretical predictions. The obtained accuracy is already comparable to the best accuracy obtained with conventional germanium detectors for hydrogen-like uranium.

Theory of Lamb Shift in Muonic Hydrogen

There has been for a while a large discrepancy between the values of the proton charge radius measured by the Lamb shift in muonic hydrogen and by other methods. It has already been clear that theory of muonic hydrogen is reliable at the level of this discrepancy and an error there cannot be a reason for the contradiction. Still the status of theory at the level of the uncertainty of the muonic-hydrogen experiment (which is two orders of magnitude below the discrepancy level) requires an additional clarification. Here, we revisit theory of the 2p − 2s Lamb shift in muonic hydrogen. We summarize all the theoretical contributions in order α5m, including pure quantum electrodynamics (QED) ones as well as those which involve the proton-structure effects. Certain enhanced higher-order effects are also discussed. We basically confirm former QED calculations of other authors, present a review of recent calculations of the proton-structure effects, and treat self-consistently higher-order proton-finite-size corrections. We also overview theory of the 2p states. Eventually, we derive a value of the root-mean-square proton charge radius. It is found to be 0.840 29(55) fm, which is slightly different from that previously published in the literature (0.840 87(39) fm [Antognini et al., Science 339, 417 (2013)]).

Pure bound field corrections to the atomic energy levels and the proton size puzzle

Reinforcement of the puzzle about the proton charge radius, rE, stimulated by the recent experiment with muonic hydrogen (Antognini et al. Science, 339, 417 (2013)) induced new discussions on the subject, and now some physicists are ready to adopt the exotic properties of the muon, lying beyond the Standard Model, to explain the difference between the results of muonic hydrogen experiments (rE = 0.840 87(39) fm) and the CODATA-2010 value rE = 0.8775(51) fm based on electron–proton scattering and hydrogen spectroscopy. In the present contribution we suggest a way to achieve progress in the entire problem via paying attention on some logical inconsistency of fundamental equations of atomic physics, constructed by analogy with corresponding classical equations without, however, taking into account the purely bound nature of electromagnetic fields generated by the electrically bound particles in stationary energy states. We suggest eliminating this inconsistency via introducing some appropriate correcting factors into these equations, which explicitly involve the requirement of total momentum conservation in the system “bound particles and their fields” in the absence of electromagnetic radiation. We further show that this approach allows us not only to eliminate long-standing discrepancies between theory and experiment in the precise physics of simple atoms, but also yields the same estimation (though with different uncertainties) for the proton size in the classic 2S–2P Lamb shift in hydrogen, 1S Lamb shift in hydrogen, and 2S–2P Lamb shift in muonic hydrogen, with the mean value rE = 0.841 fm. Finally, we suggest the crucial experiment for verification of the validity of pure bound field corrections: the measurement of decay rate of bound moun in various meso-atoms, especially at large Z, where the standard calculations and our predictions essentially deviate from each other, and some of the available experimental results (Yovanovitch. Phys. Rev. 117, 1580 (1960)) strongly support our approach.

Precision experiments and fundamental physics at low energies – Part I

Precision experiments and fundamental physics at low energies – Part I

Frequency‐comb spectroscopy of the hydrogen 1S‐3S and 1S‐3D transitions

AbstractAn observation of the 1S‐3S and 1S‐3D two‐photon transitions in an atomic hydrogen beam using direct frequency‐comb spectroscopy in a Doppler‐free arrangement is reported. The measurements of these transition frequencies may be used for an improved determination of the Rydberg constant and the 1S Lamb shift and could shed light on the current discrepancy in the determination of the proton charge radius. Concurrently, a frequency comb well‐suited for high‐precision, Doppler‐free spectroscopy in the deep ultraviolet (DUV) wavelength region is demonstrated.

Going from classical to quantum description of bound charged particles II: Implications for the atomic physics

This paper is the continuation of the analysis of bound quantum systems started in part I (A.L. Kholmetskii, T. Yarman and O.V. Missevitch, Going from classical to quantum description of bound charged particles. I: Basic concepts and assertions), which is based on a novel approach to the transition from classical to quantum description of electrically bound charges, involving the requirement of energy-momentum conservation for the bound electromagnetic (EM) field, when the EM radiation is forbidden. It has been shown that the modified expression for the energy levels of hydrogenic atoms within such a pure bound field theory (PBFT) provides the same gross and fine structure of energy levels, like in the standard theory. At the same time, at the scale of hyperfine interactions, our approach, in general, does evoke some important corrections to the energy levels. Part of such corrections, like the spin-spin splitting in the hydrogen atom, is less than the present theoretical/experimental uncertainties in the evaluation of hyperfine contributions into the atomic levels. But the most interesting result is the appearance of a number of significant corrections (the 1S -2S interval and 1S spin-spin interval in positronium, 1S and 2S -2P Lamb shift in light hydrogenic atoms), which improve considerably the convergence between theoretical predictions and experimental results. In particular, the corrected 1S -2S interval and 1S spin-spin splitting in positronium practically eliminate the existing up-to-date discrepancy between theoretical and experimental data. The re-estimated classic 2S -2P Lamb shift as well as ground-state Lamb shift in the hydrogen atom lead to the proton charge radius r p = 0.841(6) fm (from 2S -2P Lamb shift), and r p = 0.846(22) fm (from 1S Lamb shift), which perfectly agrees with the latest estimation of proton size via the measurement of 2S -2P Lamb shift in muonic hydrogen, i.e. r p = 0.84184(67) fm. Finally, we consider the decay of bound muons in meso-atoms and achieve a quantitative agreement between experimental data and the results obtained through our approach.

Illuminating the proton radius conundrum: the μHe+ Lamb shiftThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

We plan to measure several 2S–2P transition frequencies in μ4He+ and μ3He+ by means of laser spectroscopy with an accuracy of 50 ppm. This will lead to a determination of the corresponding nuclear rms charge radii with a relative accuracy of 3 × 10−4, limited by the uncertainty of the nuclear polarization contribution. First, these measurements will help to solve the proton radius puzzle. Second, these very precise nuclear radii are benchmarks for ab initio few-nucleon theories and potentials. Finally when combined with an ongoing measurement of the 1S–2S transition in He+, these measurements will lead to an enhanced bound-state QED test of the 1S Lamb shift in He+.

2S state and Lamb shift in muonic hydrogen

The metastable 2S state in muonic hydrogen is particularily interesting because a measurement of the Lamb shift could reduce the uncertainty in the proton charge radius by an order of magnitude. The most important prerequisite for such a measurement is a sufficiently large population and lifetime of the 2S state. We have determined the long-lived and short-lived 2S population, the deexcitation mechanisms and lifetimes, and the cascade time in μp.

Fine and hyperfine structure of P-wave levels in muonic hydrogen

Corrections of order α5 and α6 are calculated for muonic hydrogen in the fine-structure interval ΔEfs = E(2P3/2) − E(2P1/2) and in the hyperfine structure of the 2P1/2-and 2P3/2-wave energy levels. The resulting values of ΔEfs = 8352.08 µeV, ΔẼhfs(2P1/2) = 7819.80 µeV, and ΔẼhfs(2P3/2) = 3248.03 µeV provide reliable guidelines in performing a comparison with relevant experimental data and in more precisely extracting the experimental value of the (2P–2S) Lamb shift in the muonic-hydrogen atom.

Powerful fast triggerable 6 μm laser for the muonic hydrogen 2S-Lamb shift experiment

Laser spectroscopy of the 2S-Lamb shift in muonic hydrogen (μ −p) is being performed at the Paul Scherrer Institute, Switzerland, to determine the root-mean-square (rms) proton charge radius with 10 −3 precision. A multistage laser system has been developed which provides 0.2 mJ pulse energy tunable at 6 μm wavelength. An excimer pumped dye laser is used to drive a titanium sapphire (Ti:Sa) system whose wavelength is then shifted to 6 μm using a multipass Raman cell filled with hydrogen. The short cavity length of the Ti:Sa oscillator (7 cm) guarantees a pulse width of 7 ns and a pulse energy of 1.2 mJ at 708 nm, a wavelength controlled by a mono-mode cw-Ti:Sa laser. The laser is triggered at a maximum 60 s −1 repetition rate by muons entering the apparatus at random times. A new type of multipass cavity has been developed to provide a homogeneously illuminated volume (25 × 7 × 170 mm 3).

The muonic hydrogen Lamb-shift experiment

The charge radius of the proton, the simplest nucleus, is known from electron-scattering experiments only with a surprisingly low precision of about 2%. The poor knowledge of the proton charge radius restricts tests of bound-state quantum electrodynamics (QED) to the precision level of about 6 × 10–6, although the experimental data themselves (1S Lamb shift in hydrogen) have reached a precision of 2 × 10–6. The determination of the proton charge radius with an accuracy of 10–3 is the main goal of our experiment, opening a way to check bound-state QED predictions to a level of 10–7. The principle is to measure the 2S–2P energy difference in muonic hydrogen (µ–p) by infrared laser spectroscopy. The first data were taken in the second half of 2003. Muons from our unique very-low-energy muon beam are stopped at a rate of ~100 s–1 in 0.6 mbar H2 gas where the lifetime of the formed µp(2S) atoms is about 1.3 µs. An incoming muon triggers a pulsed multistage laser system that delivers ~0.2 mJ at λ ≈ 6 µm. Following the laser excitation µp(2S) → µp(2P) we observe the 1.9 keV X-rays from 2P–1S transitions using large area avalanche photodiodes. The resonance frequency, and, hence, the Lamb shift and the proton radius, is determined by measuring the intensity of these X-rays as a function of the laser wavelength. A broad range of laser frequencies was scanned in 2003 and the analysis is currently under way. PACS Nos.: 36.10.Dr, 14.20.Dh, 42.62.Fi

Planar LAAPDs: temperature dependence, performance, and application in low-energy X-ray spectroscopy

An experiment measuring the 2S Lamb shift in muonic hydrogen ( μ - p ) was performed at the Paul Scherrer Institute, Switzerland. It required small and compact detectors for 1.9 keV X-rays (2P–1S transition) with an energy resolution around 25% at 2 keV, a time resolution better than 100 ns, a large solid angle coverage, and insensitivity to a 5 T magnetic field. We chose Large Area Avalanche Photodiodes (LAAPDs) from Radiation Monitoring Devices as X-ray detectors, and they were used during the last data taking period in 2003. For X-ray spectroscopy applications, these LAAPDs have to be cooled in order to suppress the dark current noise; hence, a series of tests were performed to choose the optimal operation temperature. Specifically, the temperature dependence of gain, energy resolution, dark current, excess noise factor, and detector response linearity was studied. Finally, details of the LAAPDs application in the muonic hydrogen experiment as well as their response to α particles are presented.

Using a microcalorimeter to measure the Lamb shift in hydrogenic gold and uranium on cooled, decelerated ion beams

A precise determination of the Lamb shift from photons emitted by highly charged, one electron ions represents one of the most sensitive tests of QED in strong electromagnetic fields. Recent progress in the production and cooling of intense beams of fully stripped Au and U in the SIS/ESR synchrotron storage ring at GSI, Darmstadt has made it possible to obtain precision spectroscopy of these ions. A fully stripped beam of either Au79+ or U92+ ions is injected, stored and cooled in the ESR and interacts with an internal gas target. The capture of an electron and the subsequent population of a 2p or 3p state will lead to a decay by either Lyman or Balmer X-ray emission. Although measurements of the 1s Lamb shift in U with Ge ionization detectors accurate to ∼3% have provided a test of QED for the high Z domain, the experimental errors (±13eV) are about one order of magnitude larger than the accuracy theoreticians presently claim (±1eV). We present the results from initial broad band experiments using NTD Ge microcalorimeters to measure the 2s Lamb Shift in Au and U at the ESR. The broad band coverage of the microcalorimeter makes it possible to reduce the systematic uncertainties in the Doppler corrections while the high-energy resolution reduces the statistical error in the absolute energy calibration.

Absolute wavelength measurement of the Lyman-α transition of hydrogen-like silicon

The wavelengths of the 1s1/2–2p1/2 and 1s1/2–2p3/2 Lyman-α transitions have been measured in hydrogenic silicon with an accuracy of 70 ppm. The measurement was carried out with an electron-beam ion trap with a calibrated double-faced monolithic crystal that enabled absolute measurements of the transition wavelengths. The values for the Lyman-α wavelengths are λLyα1 = 6.180 49(44) Å and λLyα2 = 6.185 56(66) Å. The wavelengths are in good agreement with calculations and allow a determination of the 1s Lamb shift to within 28% in a region that has received little experimental attention. PACS Nos.:32.30Rj, 31.30Jv