Mean Shift Cluster Recognition Method Implementation in the Nested Sampling Algorithm

Testing quantum electrodynamics in extreme fields using helium-like uranium

Quantum electrodynamics (QED), the quantum field theory that describes the interaction between light and matter, is commonly regarded as the best-tested quantum theory in modern physics. However, this claim is mostly based on extremely precise studies performed in the domain of relatively low field strengths and light atoms and ions1-6. In the realm of very strong electromagnetic fields such as in the heaviest highly charged ions (with nuclear charge Z ≫ 1), QED calculations enter a qualitatively different, non-perturbative regime. Yet, the corresponding experimental studies are very challenging, and theoretical predictions are only partially tested. Here we present an experiment sensitive to higher-order QED effects and electron-electron interactions in the high-Z regime. This is achieved by using a multi-reference method based on Doppler-tuned X-ray emission from stored relativistic uranium ions with different charge states. The energy of the 1s1/22p3/2 J = 2 → 1s1/22s1/2 J = 1 intrashell transition in the heaviest two-electron ion (U90+) is obtained with an accuracy of 37 ppm. Furthermore, a comparison of uranium ions with different numbers of bound electrons enables us to disentangle and to test separately the one-electron higher-order QED effects and the bound electron-electron interaction terms without the uncertainty related to the nuclear radius. Moreover, our experimental result can discriminate between several state-of-the-art theoretical approaches and provides an important benchmark for calculations in the strong-field domain.

Shape and Satellite Studies of Highly Charged Ions X-ray Spectra Using Bayesian Methods

High-accuracy spectroscopy commonly requires dedicated investigation into the choice of spectral line modelling to avoid the introduction of unwanted systematic errors. For such a kind of problem, the analysis of χ2 and likelihood are normally implemented to choose among models. However, these standard practices are affected by several problems and, in the first place, they are useless if there is no clear indication in favour of a specific model. Such issues are solved by Bayesian statistics, in the context of which a probability can be assigned to different hypotheses, i.e., models, from the analysis of the same set of data. Model probabilities are obtained from the integration of the likelihood function over the model parameter space with the evaluation of the so-called Bayesian evidence. Here, some practical applications are presented within the context of the analysis of recent high-accuracy X-ray spectroscopy data of highly charged uranium ion transitions. The method to determine the most plausible profile is discussed in detail. The study of the possible presence of satellite peaks is also presented.

Assessing Search and Unsupervised Clustering Algorithms in Nested Sampling

Nested sampling is an efficient method for calculating Bayesian evidence in data analysis and partition functions of potential energies. It is based on an exploration using a dynamical set of sampling points that evolves to higher values of the sampled function. When several maxima are present, this exploration can be a very difficult task. Different codes implement different strategies. Local maxima are generally treated separately, applying cluster recognition of the sampling points based on machine learning methods. We present here the development and implementation of different search and clustering methods on the nested_fit code. Slice sampling and the uniform search method are added in addition to the random walk already implemented. Three new cluster recognition methods are also developed. The efficiency of the different strategies, in terms of accuracy and number of likelihood calls, is compared considering a series of benchmark tests, including model comparison and a harmonic energy potential. Slice sampling proves to be the most stable and accurate search strategy. The different clustering methods present similar results but with very different computing time and scaling. Different choices of the stopping criterion of the algorithm, another critical issue of nested sampling, are also investigated with the harmonic energy potential.

Surface Chemistry of Gold Nanoparticles Produced by Laser Ablation in Pure and Saline Water

Pulsed laser ablation in liquid (PLAL) is a powerful method for producing nanoparticle colloids with a long-term stability despite the absence of stabilizing organic agents. The colloid stability involves different reactivities and chemical equilibria with complex ionic-specific effects at the nanoparticle/solvent interface which must be strongly influenced by their chemical composition. In this work, the surface composition of PLAL-produced gold nanoparticles in alkaline and saline (NaBr) water is investigated by X-ray photoelectron spectroscopy on free-flying nanoparticles, exempt from any substrate or radiation damage artifact. The Au 4f photoelectron spectra with a depth profiling investigation are used to evaluate the degree of nanoparticle surface oxidation. In alkaline water, the results preclude any surface oxidation contrary to the case of nanoparticles produced in NaBr solution. In addition, the analysis of Br 3d core-level photoelectron spectra agrees with a clear signature of Br on the nanoparticle surface, which is confirmed by a specific valence band feature. This experimental study is supported by DFT calculations, evaluating the energy balance of halide adsorption on different configurations of gold surfaces including oxidation or adsorbed salts.