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Radiative corrections to electronic structure are characterized by perturbative expansions in $\alpha$ and $Z\alpha$, where $\alpha$ is the fine-structure constant and $Z$ is the nuclear charge. A formulation of the leading-order $\alpha(Z\alpha)$ Uehling contribution to the renormalized vacuum polarization is reported in a form that is convenient for implementation in computational studies of the relativistic electronic structures of molecules. Benchmark calculations based on these methods are reported that include the leading-order vacuum polarization effects within relativistic mean-field methods for the E119$^+$ ion and the closed-shell diatomic species E119F., Comment: 10 pages, 3 tables, 6 figures

We outline a general formalism for treating vacuum polarization phenomena within an effective field expansion. The coupling between source charges and virtual fields is examined from the perspectives of electrostatic potentials, induced charge densities and form factors in momentum space. A strategy for the efficient calculation of vacuum polarization potentials is outlined, implemented, and applied towards the construction of fitting potentials that are suitable for molecular electronic structure calculations, which enclose no overall charge by construction. The order $\alpha(Z \alpha)$, $\alpha (Z \alpha)^{3}$ and $\alpha^{2}(Z\alpha)$ effects of a Gaussian nuclear charge on the electron-positron field are applied variationally towards the E119F molecule, as well as the order $\alpha(Z \alpha)$ effects arising from the virtual muon and charged pion fields., Comment: 14 pages, 9 figures, 2 tables

Young double-slit experiments using monochromatic hard X-rays with the energy of 25 keV are presented. The experiments were performed at a synchrotron source with a distance of 110 m between the interferometer and the detector to produce an interference pattern with a sufficiently broad period that could be adequately sampled by a photon-counting detector with 75 micrometre pixels. In the single-particle version of the experiment, over one million image frames with a single registered photon in each one were collected. The sum of these frames showed a clear presence of the interference pattern with the expected period. Subsequent analysis provided an objective estimation of the minimal number of detected photons required to determine, in accordance with the Rose criterion, the presence of the photon interference. Apart from a general theoretical interest, these investigations were aimed at exploring the possibility of medical X-ray phase-contrast imaging in photon-counting mode at minimal radiation doses., Comment: 18 pages, 10 figures

Signal-to-noise ratio and spatial resolution are quantitatively analysed in the context of in-line (propagation based) X-ray phase-contrast imaging. It is known that free-space propagation of a coherent X-ray beam from the imaged object to the detector plane, followed by phase retrieval in accordance with Paganin's method, can increase the signal-to-noise in the resultant images without deteriorating the spatial resolution. This results in violation of the noise-resolution uncertainty principle and demonstrates "unreasonable" effectiveness of the method. On the other hand, when the process of free-space propagation is performed in software, using the detected intensity distribution in the object plane, it cannot reproduce the same effectiveness, due to the amplification, during free-space propagation, of photon shot noise in the object-plane intensity. We show that the performance of Paganin's method is determined by just two dimensionless parameters: the Fresnel number and the ratio of the phase shift to the logarithm of intensity in the object plane. The relevant theoretical analysis is performed first, followed by computer simulations and then by a brief test using experimental images collected at a synchrotron beamline. More extensive experimental tests will be presented in the second part of this paper., Comment: 26 pages, 2 figures, 2 tables, 56 references

A method is proposed for high-resolution, three-dimensional reconstruction of internal structure of objects from planar transmission images. The described approach can be used with any form of radiation or matter waves, in principle, provided that the depth of field is smaller than the thickness of the sample. The physical optics basis for the method is elucidated and the reconstruction algorithm is presented in detail. A simulated example demonstrates an application of the method to three-dimensional electron transmission imaging of a nanoparticle under realistic radiation dose and spatial resolution constraints. It is envisaged that the method can be applicable in high-resolution transmission electron microscopy, soft X-ray microscopy, ultrasound imaging and other areas., Comment: 20 pages, 5 figures

It has been argued that in atomic-resolution transmission electron microscopy (TEM) of sparse weakly scattering structures, such as small biological molecules, multiple electron scattering usually has only a small effect, while the in-molecule Fresnel diffraction can be significant due to the intrinsically shallow depth of focus. These facts suggest that the three-dimensional reconstruction of such structures from defocus image series collected at multiple rotational orientations of a molecule can be effectively performed for each atom separately, using the incoherent first Born approximation. The corresponding reconstruction method, termed here Differential Holographic Tomography, is developed theoretically and demonstrated computationally on several numerical models of biological molecules. It is shown that the method is capable of accurate reconstruction of the locations of atoms in a molecule from TEM data collected at a small number of random orientations of the molecule, with one or more defocus images per orientation. Possible applications to cryogenic electron microscopy and other areas are briefly discussed., Comment: 32 pages, 8 figures, version 5c (a few typos have been found in the previous version and fixed in the current version)

A method for extracting the dark-field signal in propagation-based phase-contrast imaging is proposed. In the case of objects consisting predominantly of a single material, or several different materials with similar ratios of the real decrement to the imaginary part of the complex refractive index, the proposed method requires a single image for extraction of the dark-field signal in two-dimensional projection imaging. In the case of three-dimensional tomographic imaging, the method needs only one image to be collected at each projection angle. A preliminary example demonstrates that this method can improve the visualization of microcalcifications in propagation-based X-ray breast cancer imaging. It is suggested that the proposed approach may be useful in other forms of biomedical imaging, where it can help one to obtain additional small-angle scattering information without increasing the radiation dose to the sample.

The relative roles of multiple electron scattering and in-molecule free-space propagation in transmission electron microscopy of small molecules are discussed. It is argued that while multiple scattering tends to have only a moderate effect in this case, the in-molecule Fresnel diffraction is likely to be significant due to the shallow depth of focus under the relevant experimental conditions. As a consequence, diffraction tomography based on the first Born or first Rytov approximation represents a more suitable method for the reconstruction of three-dimensional distribution of the electrostatic potential in this context, compared to conventional computed tomography which is intrinsically based on the projection approximation. A simplified method for diffraction tomography is proposed and tested on numerically simulated examples., Comment: 11 pages, 3 figures

A practical method utilising three-dimensional image pattern matching is proposed which, in principle, is capable of unambiguous determination of the types and positions of atoms in small molecules from defocus series collected at only a few different angular orientations of the molecule. Numerical tests of the method are presented using multislice calculations of defocus series of small biological molecules. The proposed technique can in future gain from Bayesian or machine-learning approaches and is likely to be useful in cryogenic electron microscopy., Comment: 19 pages, 5 figures

A generic computational imaging setup is considered which assumes sequential illumination of a semi-transparent object by an arbitrary set of structured illumination patterns. For each incident illumination pattern, all transmitted light is collected by a photon-counting bucket (single-pixel) detector. The transmission coefficients measured in this way are then used to reconstruct the spatial distribution of the object's projected transmission. It is demonstrated that the squared spatial resolution of such a setup is usually equal to the ratio of the image area to the number of linearly independent illumination patterns. If the noise in the measured transmission coefficients is dominated by photon shot noise, then the ratio of the spatially-averaged squared mean signal to the spatially-averaged noise variance in the "flat" distribution reconstructed in the absence of the object, is equal to the average number of registered photons when the illumination patterns are orthogonal. The signal-to-noise ratio in a reconstructed transmission distribution is always lower in the case of non-orthogonal illumination patterns due to spatial correlations in the measured data. Examples of imaging methods relevant to the presented analysis include conventional imaging with a pixelated detector, computational ghost imaging, compressive sensing, super-resolution imaging and computed tomography., Comment: Minor corrections and clarifications compared to the original version

The effectiveness of reconstructive imaging using the Homogeneous Transport of Intensity equation may be regarded as "unreasonable", because it has been shown to significantly increase signal-to-noise ratio while preserving spatial resolution, compared to equivalent conventional absorption-based imaging techniques at the same photon fluence. We reconcile this surprising behaviour by analysing the propagation of noise in typical in-line holography experiments. This analysis indicates that novel imaging techniques may be designed which produce high signal-to-noise images at low radiation doses without sacrificing spatial resolution.

Ionization of atoms and molecules in strong laser fields is a fundamental process in many fields of research, especially in the emerging field of attosecond science. So far, demonstrably accurate data have only been acquired for atomic hydrogen (H), a species that is accessible to few investigators. Here we present measurements of the ionization yield for argon, krypton, and xenon with percentlevel accuracy, calibrated using H, in a laser regime widely used in attosecond science. We derive a transferrable calibration standard for laser peak intensity, accurate to 1.3%, that is based on a simple reference curve. In addition, our measurements provide a much-needed benchmark for testing models of ionisation in noble-gas atoms, such as the widely employed single-active electron approximation., Comment: Article: 5 pages, 2 figures, submitted to PRL (manuscript number LZ14457). Supplementary information: 7 pages, 6 figures, appended to end of main Article

As dipolar gases become more readily accessible in experiment there is a need to develop a comprehensive theoretical framework of the few-body physics of these systems. Here, we extend the coupled-pair approach developed for the unitary two-component Fermi gas to a few-body system of dipolar bosons in a spherical harmonic trap. The long range and anisotropy of the dipole-dipole interaction is handled by a flexible and efficient correlated gaussian basis with stochastically variational optimisation. We calculate the eigenenergy spectrum and structural properties of two and three trapped bosonic dipoles. This demonstrates the efficiency and flexibility of the coupled-pair approach at dealing with systems with complex interactions., Comment: 6 pages, 5 figures Extra references, typos and grammar corrected. Improved discussion of method, results unchanged

We present a coupled pair approach for studying few-body physics in harmonically trapped ultracold gases. The method is applied to a two-component Fermi system of $N$ particles. A stochastically variational gaussian expansion method is applied, focusing on optimization of the two-body correlations present in the strongly interacting, or unitary, limit. The groundstate energy of the four-, six- and eight-body problem with equal spin populations is calculated with high accuracy and minimal computational effort. We also calculate the structural properties of these systems and discuss their implication for the many-body ultracold gas and other few-body calculations., Comment: 7 pages, 4 figures

We analytically determine the properties of three interacting fermions in a harmonic trap subject to an external rotation. Thermodynamic quantities such as the entropy and energy are calculated from the third order quantum virial expansion. By parameterizing the solutions in the rotating frame we find that the energy and entropy are universal for all rotations in the strongly interacting regime. Additionally, we find that rotation suppresses the onset of itinerant ferromagnetism in strongly interacting repulsive three-body systems., Comment: 5 pages with 3 figures

We analytically determine the properties of two interacting particles in a harmonic trap subject to a rotation or a uniform synthetic magnetic field, where the spherical symmetry of the relative Hamiltonian is preserved. Thermodynamic quantities such as the entropy and energy are calculated via the second order quantum cluster expansion. We find that in the strongly interacting regime the energy is universal, however the entropy changes as a function of the rotation or synthetic magnetic field strength., Comment: 4 pages, 2 figures

We present the first experimental data on strong-field ionization of atomic hydrogen by few-cycle laser pulses. We obtain quantitative agreement at the 10% level between the data and an {\it ab initio} simulation over a wide range of laser intensities and electron energies.