Resonant X-ray excitation of the nuclear clock isomer 45Sc.

Resonant oscillators with stable frequencies and large quality factors help us to keep track of time with high precision. Examples range from quartz crystal oscillators in wristwatches to atomic oscillators in atomic clocks, which are, at present, our most precise time measurement devices1. The search for more stable and convenient reference oscillators is continuing2-6. Nuclear oscillators are better than atomic oscillators because of their naturally higher quality factors and higher resilience against external perturbations7-9. One of the most promising cases is an ultra-narrow nuclear resonance transition in 45Sc between the ground state and the 12.4-keV isomeric state with a long lifetime of 0.47 s (ref. 10). The scientific potential of 45Sc was realized long ago, but applications require 45Sc resonant excitation, which in turn requires accelerator-driven, high-brightness X-ray sources11 that have become available only recently. Here we report on resonant X-ray excitation of the 45Sc isomeric state by irradiation of Sc-metal foil with 12.4-keV photon pulses from a state-of-the-art X-ray free-electron laser and subsequent detection of nuclear decay products. Simultaneously, the transition energy was determined as [Formula: see text] with an uncertainty that is two orders of magnitude smaller than the previously known values. These advancements enable the application of this isomer in extreme metrology, nuclear clock technology, ultra-high-precision spectroscopy and similar applications.

Effects of energy spread on brightness and coherence of undulator sources.

The (spectral) brightness for partially transverse coherent sources such as synchrotron radiation and free-electron laser sources can be defined as the maximum of the Wigner distribution. Then, the brightness includes information on both coherence and wavefront characteristics of the radiation field. For undulator sources, it is customary to approximate the single-electron electric field at resonance with a Gaussian beam, leading to great simplifications. Attempts to account for the modified spatial and angular profile of the undulator radiation in the presence of detuning due to energy spread, currently build on the simplified brightness expression derived under the assumption of Gaussian beams. The influence of energy spread on undulator radiation properties is becoming important in view of diffraction-limited rings with ultralow emittance coming on-line. Here the effects of energy spread on the brightness of undulator radiation at resonance are discussed, as well as relevant relations with coherence properties.

Ultra-high-resolution inelastic X-ray scattering at high-repetition-rate self-seeded X-ray free-electron lasers.

Inelastic X-ray scattering (IXS) is an important tool for studies of equilibrium dynamics in condensed matter. A new spectrometer recently proposed for ultra-high-resolution IXS (UHRIX) has achieved 0.6 meV and 0.25 nm(-1) spectral and momentum-transfer resolutions, respectively. However, further improvements down to 0.1 meV and 0.02 nm(-1) are required to close the gap in energy-momentum space between high- and low-frequency probes. It is shown that this goal can be achieved by further optimizing the X-ray optics and by increasing the spectral flux of the incident X-ray pulses. UHRIX performs best at energies from 5 to 10 keV, where a combination of self-seeding and undulator tapering at the SASE-2 beamline of the European XFEL promises up to a 100-fold increase in average spectral flux compared with nominal SASE pulses at saturation, or three orders of magnitude more than what is possible with storage-ring-based radiation sources. Wave-optics calculations show that about 7 × 10(12) photons s(-1) in a 90 µeV bandwidth can be achieved on the sample. This will provide unique new possibilities for dynamics studies by IXS.

Brightness of synchrotron radiation from undulators and bending magnets.

The maximum of the Wigner distribution (WD) of synchrotron radiation (SR) fields is considered as a possible definition of SR source brightness. Such a figure of merit was originally introduced in the SR community by Kim [(1986), Nucl. Instrum. Methods Phys. Res. A, 246, 71-76]. The brightness defined in this way is always positive and, in the geometrical optics limit, can be interpreted as the maximum density of photon flux in phase space. For undulator and bending magnet radiation from a single electron, the WD function can be explicitly calculated. In the case of an electron beam with a finite emittance the brightness is given by the maximum of the convolution of a single electron WD function and the probability distribution of the electrons in phase space. In the particular case when both electron beam size and electron beam divergence dominate over the diffraction size and the diffraction angle, one can use a geometrical optics approach. However, there are intermediate regimes when only the electron beam size or the electron beam divergence dominate. In these asymptotic cases the geometrical optics approach is still applicable, and the brightness definition used here yields back once more to the maximum photon flux density in phase space. In these intermediate regimes a significant numerical disagreement is found between exact calculations and the approximation for undulator brightness currently used in the literature. The WD formalism is extended to a satisfactory theory for the brightness of a bending magnet. It is found that in the intermediate regimes the usually accepted approximation for bending magnet brightness turns out to be inconsistent even parametrically.

Perspectives for imaging single protein molecules with the present design of the European XFEL.

The Single Particles, Clusters and Biomolecules & Serial Femtosecond Crystallography (SPB/SFX) instrument at the European XFEL is located behind the SASE1 undulator and aims to support imaging and structure determination of biological specimen between about 0.1 µm and 1 µm size. The instrument is designed to work at photon energies from 3 keV up to 16 keV. Here, we propose a cost-effective proof-of-principle experiment, aiming to demonstrate the actual feasibility of a single molecule diffraction experiment at the European XFEL. To this end, we assume self-seeding capabilities at SASE1 and we suggest to make use of the baseline European XFEL accelerator complex-with the addition of a slotted-foil setup-and of the SPB/SFX instrument. As a first step towards the realization of an actual experiment, we developed a complete package of computational tools for start-to-end simulations predicting its performance. Single biomolecule imaging capabilities at the European XFEL can be reached by exploiting special modes of operation of the accelerator complex and of the SASE1 undulator. The output peak power can be increased up to more than 1.5 TW, which allows to relax the requirements on the focusing efficiency of the optics and to reach the required fluence without changing the present design of the SPB/SFX instrument. Explicit simulations are presented using the 15-nm size RNA Polymerase II molecule as a case study. Noisy diffraction patterns were generated and they were processed to generate the 3D intensity distribution. We discuss requirements to the signal-to-background ratio needed to obtain a correct pattern orientation. When these are fulfilled, our results indicate that one can achieve diffraction without destruction with about 0.1 photons per Shannon pixel per shot at 4 Å resolution with 10(13) photons in a 4 fs pulse at 4 keV photon energy and in a 0.3 µm focus, corresponding to a fluence of 10(14) photons/µm(2). We assume negligible structured background. At this signal level, one needs only about 30 000 diffraction patterns to recover full 3D information. At the highest repetition rate manageable by detectors at European XFEL, one will be able to accumulate these data within a fraction of an hour, even assuming a relatively low hit probability of about a percent.