P. Indelicato

Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen

Proton Still Too Small Despite a protons tiny size, it is possible to measure its radius based on its charge or magnetization distributions. Traditional measurements of proton radius were based on the scattering between protons and electrons. Recently, a precision measurement of a line in the spectrum of muonium—an atom consisting of a proton and a muon, instead of an electron—revealed a radius inconsistent with that deduced from scattering studies. Antognini et al. (p. 417; see the Perspective by Margolis) examined a different spectral line of muonium, with results less dependent on theoretical analyses, yet still inconsistent with the scattering result; in fact, the discrepancy increased. A precision spectroscopic measurement of the proton radius indicates a growing discrepancy with respect to scattering results. [Also see Perspective by Margolis] Accurate knowledge of the charge and Zemach radii of the proton is essential, not only for understanding its structure but also as input for tests of bound-state quantum electrodynamics and its predictions for the energy levels of hydrogen. These radii may be extracted from the laser spectroscopy of muonic hydrogen (μp, that is, a proton orbited by a muon). We measured the 2S1/2F=0-2P3/2F=1 transition frequency in μp to be 54611.16(1.05) gigahertz (numbers in parentheses indicate one standard deviation of uncertainty) and reevaluated the 2S1/2F=1-2P3/2F=2 transition frequency, yielding 49881.35(65) gigahertz. From the measurements, we determined the Zemach radius, rZ = 1.082(37) femtometers, and the magnetic radius, rM = 0.87(6) femtometer, of the proton. We also extracted the charge radius, rE = 0.84087(39) femtometer, with an order of magnitude more precision than the 2010-CODATA value and at 7σ variance with respect to it, thus reinforcing the proton radius puzzle.

Thin-Disk Yb:YAG Oscillator-Amplifier Laser, ASE, and Effective Yb:YAG Lifetime

We report on a thin-disk Yb:YAG laser made from a Q-switched oscillator and a multipass amplifier delivering pulses of 48 mJ at 1030 nm. The peculiar requirements for this laser are the short delay time (< 500 ns) between electronic trigger and optical output pulse and the time randomness with which these triggers occur (with trigger to next trigger delay ges 1.5 ms). Details concerning the oscillator dynamics (-switching cycle, intensity stabilization), and the peculiar amplifier layout are given. Simulations of the beam propagation in the amplifier based on the Collins integral and the measured aspherical components of the disk reproduce well the measured beam intensity profiles (with higher order intensity moments) and gains. Measurements of the thermal lens and ASE effects of the disk are also presented. A novel method to deduce the effective Yb:YAG upper state lifetime (under real laser operation and including ASE effects) is presented. That knowledge is necessary to determine gain and stored energy in the active medium and to understand the limiting factors for energy scaling of thin-disk lasers.

M1, M2 and hyperfine-induced decay rates in Mg-like ions of Co, Ni and Cu measured at a heavy-ion storage ring

The optical decay rates of the 3s3p 3 P o level in Mg-like ions of 59 Co, 58 Ni and 63,65 Cu have been measured at a heavy-ion storage ring. The measurement is sensitive to M1, M2 and hyperfine-induced decay rates. The measurement precision is just about high enough to detect the difference in the isotope effect on the level lifetime in the ions 63,65 Cu 17+ . We also discuss our findings when trying to measure the hyperfine-induced decay of the lowest triplet level, 3s3p 3 P o , in the two Cu isotopes.

Laser spectroscopy of muonic deuterium

The deuteron is too small, too The radius of the proton has remained a point of debate ever since the spectroscopy of muonic hydrogen indicated a large discrepancy from the previously accepted value. Pohl et al. add an important clue for solving this so-called proton radius puzzle. They determined the charge radius of the deuteron, a nucleus consisting of a proton and a neutron, from the transition frequencies in muonic deuterium. Mirroring the proton radius puzzle, the radius of the deuteron was several standard deviations smaller than the value inferred from previous spectroscopic measurements of electronic deuterium. This independent discrepancy points to experimental or theoretical error or even to physics beyond the standard model. Science, this issue p. 669 The charge radius of the deuteron is several standard deviations smaller than the previously accepted value. The deuteron is the simplest compound nucleus, composed of one proton and one neutron. Deuteron properties such as the root-mean-square charge radius rd and the polarizability serve as important benchmarks for understanding the nuclear forces and structure. Muonic deuterium μd is the exotic atom formed by a deuteron and a negative muon μ–. We measured three 2S-2P transitions in μd and obtain rd = 2.12562(78) fm, which is 2.7 times more accurate but 7.5σ smaller than the CODATA-2010 value rd = 2.1424(21) fm. The μd value is also 3.5σ smaller than the rd value from electronic deuterium spectroscopy. The smaller rd, when combined with the electronic isotope shift, yields a “small” proton radius rp, similar to the one from muonic hydrogen, amplifying the proton radius puzzle.

Self-energy correction to the bound-electron g factor in H-like ions.

The one-loop self-energy correction to the 1s-electron g factor is evaluated to all orders in Zalpha with an accuracy essentially better than that of previous calculations of this correction. As a result, the uncertainty of the theoretical prediction for the bound-electron g factor in H-like carbon is reduced by a factor of 3. This improves the total accuracy of the recent electron-mass determination [T. Beier, Phys. Rev. Lett. 88, 011603 (2002)]]. The new value of the electron mass is found to be m(e)=0.000 548 579 909 3 (3) u.

QED and relativistic corrections in superheavy elements

Abstract.In this paper we review the different relativistic and QED contributions to energies, ionic radii, transition probabilities and Landé g-factors in super-heavy elements, with the help of the MultiConfiguration Dirac-Fock method (MCDF). The effects of taking into account the Breit interaction to all orders by including it in the self-consistent field process are demonstrated. State of the art radiative corrections are included in the calculation and discussed. We also study the non-relativistic limit of MCDF calculation and find that the non-relativistic offset can be unexpectedly large.

Quantum similarity study of atomic density functions: Insights from information theory and the role of relativistic effects

A novel quantum similarity measure (QSM) is constructed based on concepts from information theory. In an application of QSM to atoms, the new QSM and its corresponding quantum similarity index (QSI) are evaluated throughout the periodic table, using the atomic electron densities and shape functions calculated in the Hartree-Fock approximation. The periodicity of Mendeleevs table is regained for the first time through the evaluation of a QSM. Evaluation of the information theory based QSI demonstrates, however, that the patterns of periodicity are lost due to the renormalization of the QSM, yielding chemically less appealing results for the QSI. A comparison of the information content of a given atom on top of a group with the information content of the elements in the subsequent rows reveals another periodicity pattern. Relativistic effects on the electronic density functions of atoms are investigated. Their importance is quantified in a QSI study by comparing for each atom, the density functions evaluated in the Hartree-Fock and Dirac-Fock approximations. The smooth decreasing of the relevant QSI along the periodic table illustrates in a quantitative way the increase of relativistic corrections with the nuclear charge.

Multiconfiguration Dirac-Fock studies of two-electron ions. I. Electron-electron interaction

The self-consistent multiconfiguration Dirac-Fock method is used to obtain total energies of helium-like ions. The authors first discuss foundations and gauge dependence of the model from the standpoint of quantum electrodynamics. Retardation contributions to energies are considered and relativistic correlation energies presented, which result in non-negligible shifts. Numerical data and scaling laws are given and interpreted.

Evaluation of the self-energy correction to the g factor of S states in H-like ions

A detailed description of the numerical procedure is presented for the evaluation of the one-loop self-energy correction to the g factor of an electron in the 1s and 2s states in H-like ions to all orders in Z{alpha}.

Balmer α transitions in antiprotonic hydrogen and deuterium

Abstract The strong-interaction shifts ϵ and broadenings Γ of the 2p levels in antiprotonic hydrogen and deuterium have been measured for the first time with a crystal spectrometer. In hydrogen, the 2 3 P 0 hyperfine state could be resolved from the three close-lying states 2 3 P 2 , 2 1 P 1 , and 2 3 P 1 . The hadronic shift was determined to be ϵ 2 3 P 0 =+139±28 meV (attractive). The value found for Γ 2 3 P 0 =120±25 meV is much larger than the spin-averaged 2p-level broadening Γ bal 2p as determined from earlier experiments measuring the intensity balance. The average shift of the three unresolved states is consistent with zero and a mean broadening of Γ 2( 3 P 2 , 1 P 1 , 3 P 1 ) =38±9 meV was measured. In deuterium, the spin-averaged hadronic shift and broadening were found to be ϵ 2p =−243±26 meV (repulsive) and Γ 2p =489±30 meV.