Tables for form factors and anomalous dispersion are widely used in the UV, x-ray, and y-ray communities, and have existed for a considerable period of time. Much of the recent theoretical basis for these was contributed by Cromer, Mann, and Liberman while much of the experimental data were synthesized by Henke et al. More recent developments in both areas have led to new and revised tables. These works have employed numerous simplifications compared to detailed relativistic S-matrix calculations; the latter do not lend themselves to convenient tabular application for the range of Z and energy of general interest. Conversely, the former tables appear to have large regions of limited validity throughout the range of Z and energies, and in particular have important limitations with regard to extrapolation to energies outside tabulated ranges. In the present study, the primary interactions of x-rays with isolated atoms from Z=1 (hydrogen) to Z=92 (uranium) are described and computed within a self-consistent Dirac–Hartree–Fock framework. This has general application across the range of energy from 1–10 eV to 400–1000 keV, with limitations (described below) as the low- and high-energy extremes are approached. Tabulations are provided for the f1 and f2 components of the form factors, together with the photoelectric attenuation coefficient for the atom, μ, and the value for the K-shell, μK, as functions of energy and wavelength. Also provided are estimated correction factors as described in the text, conversion factors, and a simple estimate for the sum of the scattering contributions (from an isolated atom). The method used herein is primarily theoretical and considers intermediate assumptions which limit the precision and applicability of previous theoretical tabulations. Particular concern involves the application of the dispersion relation to derive Re(f) from photoelectric absorption cross-sections. The revised formulation presented here explicitly avoids most of the limitations of previous works. Revised formulae can lead to significant qualitative and quantitative improvement, particularly above 30–60 keV energies, near absorption edges, and at 0.03 keV to 3 keV energies. Recent experimental syntheses are often complementary to this approach. Examples are given where the revised theoretical tables are in better agreement with experiment than are those based on experimental syntheses.

A new tabulation of atomic form factors is discussed brie¯y, extending the validity of the isolated atom approximation and serving as a baseline for near-edge solid-state and XAFS investigations. This is detailed by Chantler [J. Phys. Chem. Ref. Data, (2000), 29, 597±1048] and is the latest component of the FFAST tabulation of NIST.

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We report a new test of quantum electrodynamics (QED) for the w (1s2p 1 P1 → 1s 2 1 S0) X-ray resonance line transition energy in helium-like titanium. This measurement is one of few sensitive to two-electron QED contributions. Systematic errors such as Doppler shifts are minimised in our experiment by trapping and stripping Ti atoms in an Electron Beam Ion Trap (EBIT) and by applying absolute wavelength standards to calibrate the dispersion function of a curved-crystal spectrometer. We also report a more general systematic discrepancy between QED theory and experiment for the w transition energy in helium-like ions for Z > 20. When all of the data available in the literature forZ = 16 − 92 is taken into account, the divergence is seen to grow as approximately Z 3 with a statistical significance on the coefficient that rises to the level of five standard deviations. Our result for titanium alone, 4749.85(7) eV for the w-line, deviates from the most recent ab initio prediction by three times our experimental uncertainty and by more than ten times the currently estimated uncertainty in the theoretical prediction.PACS numbers: 31.30.jf, 12.20.Fv, 34.50.Fa, 32.30.Rj Quantum electrodynamics (QED) is a cornerstone of modern theoretical physics. New activity on this topic has been stimulated by the announcement of a five-sigma inconsistency between a 15 ppm (parts per million) measurement of an atomic transition frequency in muonic hydrogen [1] and independent measurements of the proton size, linked together by QED calculations. The high sensitivity of such a measurement to QED is derived in part from the large mass of the bound lepton which shrinks the orbital radius. Another way to reduce the orbital radius and study magnified QED effects is to measure transitions in highly charged ions of increasing Z. QED processes scale as various powers of Zα and significantly affect the quantum observable, namely transition energies. Moreover, in the high-Z range, some of the perturbative expansions fail, so that theoretical methods very different from those used for hydrogen are required. Since QED treatment of low-Z and high-Z systems are undertaken with significantly different starting points and mathematical techniques, precise measurements for ions in the mid-Z range will guide the long-pursued development of a unified computational methodology with very accurate predictions for the entire domain Z < 100 [2,3].Advances in QED theory have been sufficient that one can go beyond one-lepton systems (either free or bound) and explore the three-body quantum problem to high precision, including the investigation of helium-like * Electronic address: chantler@unimelb.edu.au atomic systems with two electrons bound to a nucleus. Here the two-electron QED contributions that are entirely absent in one-electron systems can be probed and compared to various theoretical formulations. In this work, we report a measurement of the strongest resonant transition 1s2p1 P 1 → 1s 2 1 S 0 in He-like Ti (Ti 20+ ), and present a divergence that is...

This work presents the x-ray extended range technique for measuring x-ray mass attenuation coefficients. This technique includes the use of multiple foil attenuators at each energy investigated, allowing independent tests of detector linearity and of the harmonic contributions to the monochromated synchrotron beam. Measurements over a wide energy range allow the uncertainty of local foil thickness to be minimized by the calibration of thin sample measurements to those of thick samples. The use of an extended criterion for sample thickness selection allows direct determination of dominant systematics, with an improvement of accuracies compared to previous measurements by up to factors of 20. Resulting accuracies for attenuation coefficients of copper ͑8.84 to 20 keV͒ are 0.27-0.5 %, with reproducibility of 0.02%. We also extract the imaginary component of the form factor from the data with the same accuracy. Results are compared to theoretical calculations near and away from the absorption edge. The accuracy challenges available theoretical calculations, and observed discrepancies of 10% between current theory and experiments can now be addressed.Compilations of experimental data of PE over the last decade show large variations of up to 30%, although many authors have claimed 1% precision or better using various experimental techniques ͓16,17͔. These variations are due to unresolved systematics relating to sample thickness determination and purity, detector linearity, harmonic contamination of the x-ray beam, scattering, energy calibration, and beam divergence. The most reliable results quoted in the literature relate to the work of Creagh and Hubbell ͓17͔, Gerward ͓18͔, and Mika et al. and Chantler and Barnea ͓19͔. We have recently adapted the techniques of these authors and developed them to be appropriate for synchrotron research ͓16,20͔.The availability of modern synchrotron radiation brought near-edge absorption of x-rays within the reach of many fields of research. Previously, conventional x-ray diffraction PHYSICAL REVIEW A, VOLUME 64, 062506