QED confronts the radius of the proton

Recent results on muonic hydrogen (Pohl et al., 2010) [1] and the ones compiled by CODATA on ordinary hydrogen and ep-scattering (Mohr et al., 2008) [2] are 5σ away from each other. Two reasons justify a further look at this subject: (1) One of the approximations used in Pohl et al. (2010) [1] is not valid for muonic hydrogen. This amounts to a shift of the proton's radius by ∼3 of the standard deviations of Pohl et al. (2010) [1], in the “right” direction of data-reconciliation. In field-theory terms, the error is a mismatch of renormalization scales. Once corrected, the proton radius “runs”, much as the QCD coupling “constant” does. (2) The result of Pohl et al. (2010) [1] requires a choice of the “third Zemach moment”. Its published independent determination is based on an analysis with a p  -value – the probability of obtaining data with equal or lesser agreement with the adopted (fit form-factor) hypothesis – of 3.92×¹⁰⁻¹²$3.92\times {10}^{-12}$. In this sense, this quantity is not empirically known. Its value would regulate the level of “tension” between muonic- and ordinary-hydrogen results, currently at most  ∼4σ$\sim 4\sigma$. There is no tension between the results of Pohl et al. (2010) [1] and the proton radius determined with help of the analyticity of its form-factors.     

Lamb shift in muonic hydrogen—I. Verification and update of theoretical predictions

In view of the recently observed discrepancy of theory and experiment for muonic hydrogen [R. Pohl et al., Nature 466 (2010) 213], we reexamine the theory on which the quantum electrodynamic (QED) predictions are based. In particular, we update the theory of the 2P–2S Lamb shift, by calculating the self-energy of the bound muon in the full Coulomb + vacuum polarization (Uehling) potential. We also investigate the relativistic two-body corrections to the vacuum polarization shift, and we analyze the influence of the shape of the nuclear charge distribution on the proton radius determination. The uncertainty associated with the third Zemach moment 〈r³〉₂ in the determination of the proton radius from the measurement is estimated. An updated theoretical prediction for the 2S–2P transition is given.     

Double-beta decay Q values of Cd and Te

The Q values of the ¹¹⁶Cd and ¹³⁰Te double-beta decaying nuclei were determined by using a Penning trap mass spectrometer. The new atomic mass difference between ¹¹⁶Cd and ¹¹⁶Sn of 2813.50(13) keV differs by 4.5 keV and is 30 times more precise than the previous value of 2809(4) keV. The new value for ¹³⁰Te, 2526.97(23) keV is close to the Canadian Penning trap value of 2527.01 ± 0.32 keV (Scielzo et al., 2009) [1], but differs from the Florida State University trap value of 2527.518 ± 0.013 keV (Redshaw et al., 2009) [2] by 0.55 keV (2σ). These values are sufficiently precise for ongoing neutrinoless double-beta decay searches in ¹¹⁶Cd and ¹³⁰Te. Hence, our Q values were used to compute accurate phase-space integrals for these double-beta decay nuclei. In addition, experimental two-neutrino double-beta decay nuclear matrix elements were determined and compared with the theoretical values. The neutrinoless double-beta decay half-lives for these nuclei were estimated using our precise phase-space integrals and considering the range of the best available matrix elements values.     

The RMS charge radius of the proton and Zemach moments

On the basis of recent precise measurements of the electric form factor of the proton, the Zemach moments, needed as input parameters for the determination of the proton rms radius from the measurement of the Lamb shift in muonic hydrogen, are calculated. It turns out that the new moments give an uncertainty as large as the presently stated error of the recent Lamb shift measurement of Pohl et al. De Rújula's idea of a large Zemach moment in order to reconcile the five standard deviation discrepancy between the muonic Lamb shift determination and the result of electronic experiments is shown to be in clear contradiction with experiment. Alternative explanations are touched upon.     

Nuclear structure corrections in muonic deuterium

The muonic hydrogen experiment measuring the 2P-2S transition energy [R. Pohl et?al., Nature (London) 466, 213 (2010)] is significantly discrepant with theoretical predictions based on quantum electrodynamics. A possible approach to resolve this conundrum is to compare experimental values with theoretical predictions in another system, muonic deuterium μD. The only correction which might be questioned in μD is that due to the deuteron polarizability. We investigate this effect in detail and observe cancellation with the elastic contribution. The total value obtained for the deuteron structure correction in the 2P-2S transition is 1.680(16)?meV.     

Colossal dielectric constant in high entropy oxides

Entropic contributions to the stability of solids are very well understood and the mixing entropy has been used for forming various solids, for instance such as inverse spinels, see Nawrotsky et al., J. Inorg. Nucl. Chem. 29 , 2701 (1967) [1]. A particular development was related to high entropy alloys by Yeh et al., Adv. Eng. Mater. 6 , 299 (2004) [2] and Cantor et al., Mater. Sci. Eng. A 375–377 , 213 (2004) [3] (for recent reviews see Zhang et al., Prog. Mater. Sci. 61 , 1 (2014) [4] and Tsai et al., Mater. Res. Lett. 2 , 107 (2014) [5]) in which the configurational disorder is responsible for forming simple solid solutions and which are thoroughly studied for various applications especially due to their mechanical properties, e.g. Gludovatz et al., Science 345 , 1153 (2014) [6] and Lu et al., Sci. Rep. 4 , 6200 (2014) [7], but also electrical properties, Kozelj et al., Phys. Rev. Lett. 113 , 107001 (2014) [8], hydrogen storage, Kao et al., Int. J. Hydrogen Energy 35 , 9046 (2010) [9], magnetic properties, Zhang et al., Sci. Rep. 3 , 1455 (2013) [10]. Many unexplored compositions and properties still remain for this class of materials due to their large phase space. In a recent report it has been shown that the configurational disorder can be used for stabilizing simple solid solutions of oxides, which should normally not form solid solutions, see Rost et al., Nature Commun. 6 , 8485 (2015) [11] these new materials were called ”entropy‐stabilized oxides”. In this pioneering report, it was shown that mixing five equimolar binary oxides yielded, after heating at high temperature and quenching, an unexpected rock salt structure compound with statistical distribution of the cations in a face centered cubic lattice. Following this seminal study, we show here that these high entropy oxides (named HEOx hereafter) can be substituted by aliovalent elements with a charge compensation mechanism. This possibility largely increases the potential development of new materials by widening their (already complex) phase space. As a first example, we report here that at least one HEOx composition exhibits colossal dielectric constants, which could make it very promising for applications as large‐k dielectric materials. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Analysis of high temperature ammonia spectra from 780 to 2100 cm

A recently-recorded set [Hargreaves et al., Astrophys. J., in press] of Fourier transform emission spectra of hot ammonia is analyzed using a variational line list. Approximately 3350 lines are newly assigned to mainly hot bands from vibrational states as high as v₂ = 2. 431 new energy levels of these states are experimentally determined, considerably extending the range of known rotationally-excited states. Comparisons with a recent study of high J levels in the ground and first vibrational states [Yu et al., J. Chem. Phys., 133 (2010) 174317] suggests that while the line assignments presented in that work are correct, their energy level predictions suffer from problems associated with the use of very high-order perturbation series in the effective Hamiltonian. It is suggested that variational calculations provide a more stable method for analyzing spectra involving highly-excited states of ammonia.     

Derivation of Absolute Depth-Intensity Spectrum under Standard Rock from the Recently Estimated Primary Cosmic Ray Spectrum

Using the recently derived primary cosmic ray nucleon spectrum from JACEE and GSFC balloon flight data and Fermilab results for pp → π^± + X anything inclusive reaction data in the light of Feynman scaling the depth-intensity spectrum under standard rock has been estimated. A precisely constructed range-energy relation has been applied in this analysis. The derived spectrum when corrected for range fluctuation agrees approximately with the experimental data under standard rocks measured by MIYAZAKI , BARTON , CASTAGNOLI et al., MEYER et al., BERGAMASCO et al., SHELDON et al. and BASCHIERA et al.     

Physics of novel site controlled InGaAs quantum dots on (1 1 1) oriented substrates

Recent work has shown that site-controlled dots (QD) grown on (1 1 1)B GaAs substrates, pre-patterned with tetrahedral pyramidal recesses (Baier et al., 2006) [1], (Pelucchi et al., 2007) [2], (Zhu et al., 2007) [3] are suitable for the generation of single and entangled photons (Young et al., 2009) [4]. We recently introduced InGaAs/GaAs site controlled QD structures which demonstrated record breaking spectral purity, and we showed that increasing the indium concentration of the active region allows easy tunability of the emission wavelength (Mereni et al., 2009) [5], [6]. We present here the first theoretical analysis of the emission energies and optical properties of this system as a function of QD height and In concentration. We model the dots using an 8 band k.p theory chosen to provide the best convergence and performance for structures oriented specifically along the (1 1 1) crystallographic direction.     

Spin squeezing: transforming one-axis twisting into two-axis twisting

Squeezed spin states possess unique quantum correlation or entanglement and are significantly promising for advancing quantum information processing and quantum metrology. In recent back-to-back publications [C. Gross et al., Nature (London) 464, 1165 (2010) and Max F. Riedel et al., Nature (London) 464, 1170 (2010)], reduced spin fluctuations are observed leading to spin squeezing at -8.2 and -2.5 dB, respectively, in two-component atomic condensates exhibiting one-axis-twisting interactions. The noise reduction limit for the one-axis twisting scales as ∝1/N(2/3), which for a condensate with N～10(3) atoms is about 100 times below the standard quantum limit. We present a scheme using repeated Rabi pulses capable of transforming the one-axis-twisting spin squeezing into the two-axis-twisting type, leading to Heisenberg limited noise reduction ∝1/N or an extra tenfold improvement for N～10(3).     

Theory of the 2S–2P Lamb shift and 2S hyperfine splitting in muonic hydrogen

The 7σ$7\sigma$ discrepancy between the proton rms charge radius from muonic hydrogen and the CODATA-2010 value from hydrogen spectroscopy and electron-scattering has caused considerable discussions. Here, we review the theory of the 2S–2P Lamb shift and 2S hyperfine splitting in muonic hydrogen combining the published contributions and theoretical approaches. The prediction of these quantities is necessary for the determination of both proton charge and Zemach radii from the two 2S–2P transition frequencies measured in muonic hydrogen; see Pohl et al. (2010) [9] and Antognini et al. (2013) [71].     

Proton radius,Darwin-Foldy term and radiative corrections

We discuss the role of the so-called Darwin-Foldy term in the evaluation of the proton and deuteron charge radii from atomic hydrogen spectroscopy and nuclear scattering data. The question of whether this term should be included or excluded from the nuclear radius has been controversially discussed in the literature. We attempt to clarify which literature values correspond to which conventions. A detailed discussion of the conventions appears useful because a recent experiment [R. Pohl et al., Nature 466, 213 (2010)] has indicated that there is a discrepancy between the proton charge radii inferred from ordinary (“electronic”) atomic hydrogen and muonic hydrogen. We also investigate the role of quantum electrodynamic radiative corrections in the determination of nuclear radii from scattering data, and propose a definition of the nuclear self energy which is compatible with the subtraction of the radiative corrections in scattering experiments.     

Aharonov–Bohm effects in magnetohydrodynamics

It is shown that an Aharonov–Bohm (AB) effect exists in magnetohydrodynamics (MHD). This effect is best described in terms of the MHD variational variables (Kats, 2004; Yahalom and Lynden-Bell, 2008; Yahalom, 2010) [1], [10], [12]. If a MHD flow has a non-trivial topology some of the functions appearing in the MHD Lagrangian are non-single-valued. These functions have properties similar to the phases in the AB celebrated effect (Aharonov and Bohm, 1959; van Oudenaarden et al., 1998) [2], [3]. While the manifestation of the quantum AB effect is in interference fringe patterns (Tonomura et al., 1982) [4], the manifestation of the MHD Aharonov–Bohm effects are through new dynamical conservation laws.     

The problems with M

M² is now widely used to characterize the quality of laser radiation. In the paraxial approach the inequality M²1 holds, if M² is defined by the second moments. Nevertheless, in some publications M²<1 is presented, either theoretically or experimentally (Wang et al., Optik 1995;100(1):8; Lu et al., Optik 1995;100(2):91; Wang et al., Optics and Laser Technology 1999;31:151). In particular, it is stated that for a superposition of axially shifted Gaussian spherical beams, M² can become smaller than one (Wang et al., Optics and Laser Technology 1999;31:151). These problems with M² are briefly summarized.     

Do moving basal dislocations in sapphire (α-Al2O3) have non-stoichiometric cores?

An idealized crystal structure for sapphire (α-Al₂O₃) (perfect oxygen hcp packing, flat cation planes perpendicular to [0 0 0 1]) has been used by Kronberg [Acta. Metall. 5 (1957)] and many others over the past 50 years to describe basal slip and basal twinning at the atomic level. However, it was recognized a decade ago [Bilde-Sørensen et al., Acta Mater. 44 2145 (1996); Pirouz et al., Acta Mater. 44 2153 (1996)] that the actual structure of sapphire allows much simpler atomic mechanisms to be postulated for basal slip and basal twinning. These models are supported by convincing arguments derived from chemical and structural considerations.

Recently, a climb-dissociated basal dislocation in the boundary of a manufactured bicrystal was observed by atomic resolution transmission electron microscopy [Shibata et al., Science 316 82 (2007)]. The images were interpreted as indicating non-stoichiometric charged dislocation cores and it was inferred that, during dislocation motion on the basal plane, the basal dislocations had to move according to a variant of Kronberg's mechanism. This conclusion is difficult to reconcile, with (i) the models based on the actual structure [Bilde-Sørensen et al., Acta Mater. 44 2145 (1996); Pirouz et al., Acta Mater. 44 2153 (1996)], (ii) weak beam TEM images [Lagerlöf et al., in Proceedings of the Electron Microscopy Society of America, edited by G.W. Baily (San Francisco Press, 1982), p.554], which contradict important implications of this variant of Kronberg's model, (iii) implications concerning dislocation motion in ionic materials, and (iv) the possibility that interface dislocations can be subject to entirely different constraints than apply to gliding lattice dislocations.     

Improving Einstein–Podolsky–Rosen steering inequalities with state information

We discuss the relationship between entropic Einstein–Podolsky–Rosen (EPR)-steering inequalities and their underlying uncertainty relations along with the hypothesis that improved uncertainty relations lead to tighter EPR-steering inequalities. In particular, we discuss how using information about the state of a quantum system affects one?s ability to witness EPR-steering. As an example, we consider the recent improvement to the entropic uncertainty relation between pairs of discrete observables (Berta et al., 2010 [10]). By considering the assumptions that enter into the development of a steering inequality, we derive correct steering inequalities from these improved uncertainty relations and find that they are identical to ones already developed (Schneeloch et al., 2013 [9]). In addition, we consider how one can use state information to improve our ability to witness EPR-steering, and develop a new continuous variable symmetric EPR-steering inequality as a result.     

Simultaneous Space and Time Synchronization Using Shared Entangled Qubits

This paper generalizes the quantum clock synchronization protocol of Josza, et al., [Richard Jozsa, et al.,Phys. Rev. Lett. 85 (2000) 2010] to synchronize space and time simultaneously.     

The strongest magnetic barrier in the DIII-D tokamak and comparison with the ASDEX UG

Magnetic perturbations in tokamaks lead to the formation of magnetic islands, chaotic field lines, and the destruction of flux surfaces. Controlling or reducing transport along chaotic field lines is a key challenge in magnetically confined fusion plasmas. A local control method was proposed by Chandre et al. [Nucl. Fusion 46, 33–45 (2006)] to build barriers to magnetic field line diffusion by addition of a small second-order control term localized in the phase space to the field line Hamiltonian. Formation and existence of such magnetic barriers in Ohmically heated tokamaks (OHT), ASDEX UG and piecewise analytic DIII-D [Luxon, J.L.; Davis, L.E., Fusion Technol. 8, 441 (1985)] plasma equilibria was predicted by the authors [Ali, H.; Punjabi, A., Plasma Phys. Control. Fusion 49, 1565–1582 (2007)]. Very recently, this prediction for the DIII-D has been corroborated [Volpe, F.A., et al., Nucl. Fusion 52, 054017 (2012)] by field-line tracing calculations, using experimentally constrained Equilibrium Fit (EFIT) [Lao, et al., Nucl. Fusion 25, 1611 (1985)] DIII-D equilibria perturbed to include the vacuum field from the internal coils utilized in the experiments. This second-order approach is applied to the DIII-D tokamak to build noble irrational magnetic barriers inside the chaos created by the locked resonant magnetic perturbations (RMPs) (m, n)=(3, 1)+(4, 1), with m and n the poloidal and toroidal mode numbers of the Fourier expansion of the magnetic perturbation with amplitude δ. A piecewise, analytic, accurate, axisymmetric generating function for the trajectories of magnetic field lines in the DIII-D is constructed in magnetic coordinates from the experimental EFIT Grad-Shafranov solver [Lao, L, et al., Fusion Sci. Technol. 48, 968 (2005)] for the shot 115,467 at 3000 ms in the DIII-D. A symplectic mathematical map is used to integrate field lines in the DIII-D. A numerical algorithm [Ali, H., et al., Radiat. Eff. Def. Solids Inc. Plasma Sc. Plasma Tech. 165, 83 (2010)] based on continued fraction decomposition of the rotational transform labeling the barriers for selecting and identifying the strongest noble irrational barrier is used. The results are compared and contrasted with our previous results on the ASDEX UG. About six times stronger a barrier can be built in the DIII-D than in the ASDEX UG. High magnetic shear near the separatrix in the DIII-D is inferred as the possible cause of this. Implications of this for the DIII-D and the International Thermonuclear Experimental Reactor (ITER) are discussed.     

The role of a dipole-coupled but not dipole-probed state in probe absorption with multilevel coupling

We study the impact on weak-probe spectra from the presence of a state for which the electric-dipole transition is allowed for coupling but forbidden for probing. Such is the ⁸⁵Rb ²P_3/2(F′ = 1) state, providing D2-line hfs transitions in Λ-configurations are considered with the 5²S_1/2(F = 2) and 5²S_1/2(F = 3) states in the role of the ground-states for coupling and probing, respectively. The multilevel EIT/Autler-Townes spectra were simulated with coupling field frequency fixed at various values in the range encompassing the atomic resonances. Collisionless (cold) atoms are assumed, and all decoherence rates, other than those related to the natural decay rates, are neglected. The general conclusion is that a state which is not directly involved in probe absorption can still considerably shape absorption spectra (due to multiphoton transitions), and its influence (negative for some applications) has to be carefully considered, even for the coupling-field-induced Rabi frequency values not exceeding the natural linewidth. A particular attention is paid to how the F′ = 1 state effects the narrow resonances, such as those of EIT origin or a “distant wing” of the Autler-Townes splitting, because resonances of these types are of interest, e.g., for developing quantum memory protocols [Sheremet et al., PRA82 (2010) 033838].