Adaptive Covariance Estimation with model selection

We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud

Detailed analysis of shake structures in the KLL Auger spectrum of H2S

Shake processes of different origin are identified in the KLL Auger spectrum of H2S with unprecedented detail. The KLL Auger spectrum is presented together with the S 1s−1 photoelectron spectrum including the S 1s−1V−1nλ and S 1s−12p−1nλ shake-up satellites with V−1 and nλ indicating a hole in the valence shell and an unoccupied molecular orbital, respectively. By using different photon energies between 2476 and 4150 eV to record the KLL Auger spectra two different shake-up processes responsible for the satellite lines are identified. The first process is a shake-up during the Auger decay of the S 1s−1 core hole and can be described by S 1s−1→2p−2V−1nλ. The second process is the Auger decay of the shake-up satellite in the ionization process leading to S 1s−1V−1nλ→2p−2V−1nλ transitions. By combining the results of photoelectron and Auger spectra the involved V−1nλ levels are assigned

Resonant Inelastic X-ray Scattering of Methyl Chloride at the Chlorine K Edge

We present a combined experimental and theoretical study of isolated CH3Cl molecules using resonant inelastic x-ray scattering (RIXS). The high-resolution spectra allow extraction of information about nuclear dynamics in the core-excited molecule. Polarization-resolved RIXS spectra exhibit linear dichroism in the spin-orbit intensities, a result interpreted as due to chemical environment and singlet-triplet exchange in the molecular core levels. From analysis of the polarization-resolved data, Cl 2px, y and 2pz electronic populations can be determined

Simulation of Auger decay dynamics in the hard X-ray regime: HCl as a showcase

Auger decay after photoexcitation or photoemission of an electron from a deep inner shell in the hard X-ray regime can be rather complex, implying a multitude of phenomena such as multiple-step cascades, post-collision interaction (PCI), and electronic state-lifetime interference. Furthermore, in a molecule nuclear motion can also be triggered. Here we discuss a comprehensive theoretical method which allows us to analyze in great detail Auger spectra measured around an inner-shell ionization threshold. HCl photoexcited or photoionized around the deep Cl 1s threshold is chosen as a showcase. Our method allows calculating Auger cross sections considering the nature of the ground, intermediate and final states (bound or dissociative), and the evolution of the relaxation process, including both electron and nuclear dynamics. In particular, we show that we can understand and reproduce a so-called experimental 2D-map, consisting of a series of resonant Auger spectra measured at different photon energies, therefore obtaining a detailed picture of all above-mentioned dynamical phenomena at once

Ultrafast nuclear dynamics in the doubly-core-ionized water molecule observed via Auger spectroscopy

We present a combined experimental and theoretical study of the Auger-emission spectrum following double core ionization and excitation of gas-phase water molecules with hard-x-ray synchrotron radiation above the O K−2 threshold. We observe an indication of ultrafast proton motion occurring within the 1.5 fs lifetime of the double-core-hole (DCH) states in water. Furthermore, we have identified symmetric and antisymmetric dissociation modes characteristic for particular DCH states. Our results serve as a fundamental reference for state-of-the-art studies of DCH dynamic processes in liquid water both at synchrotron and free-electron-laser facilities

Postcollision interaction effects in KLL Auger spectra following argon 1s photoionization

Postcollision interaction effects on the Auger decay of a deep core hole are studied both experimentally and theoretically. KL2,3L2,3 decay spectra of the Ar 1s vacancy are measured with high-energy resolution with excess photon energies ranging from 0 to 200 eV above the ionization threshold. Interaction of the Auger electron with the photoelectron and the ion field manifests itself in the Auger spectra as a distortion of the energy distribution of the Auger electron close to threshold. Moreover, recapture of the photoelectron due to energy exchange is dominating in the low-photon-energy range above threshold. The experimental results are compared with calculations based on the semiclassical approach to the postcollision interaction. The energies of the discrete levels and individual recapture cross sections are computed in the Hartree-Fock approximation. Good agreement is found between the calculated and experimental spectra, validating the model used

Cationic double K-hole pre-edge states of CS2 and SF6

Recent advances in X-ray instrumentation have made it possible to measure the spectra of an essentially unexplored class of electronic states associated with double inner-shell vacancies. Using the technique of single electron spectroscopy, spectra of states in CS2 and SF6 with a double hole in the K-shell and one electron exited to a normally unoccupied orbital have been obtained. The spectra are interpreted with the aid of a high-level theoretical model giving excellent agreement with the experiment. The results shed new light on the important distinction between direct and conjugate shake-up in a molecular context. In particular, systematic similarities and differences between pre-edge states near single core holes investigated in X-ray absorption spectra and the corresponding states near double core holes studied here are brought out

Deep-core photoionization of krypton atoms below and above the 1s ionization threshold

Electronic relaxation of atomic Kr below and above the 1s ionization threshold is investigated experimentally using hard x-ray photoelectron spectroscopy. The experimental results are interpreted with the aid of relativistic Dirac-Fock calculations. The 1s orbital core-hole lifetime is extracted and the satellite's structures accompanying the photoelectron main line are assigned. Auger spectra recorded below and above the K edge are also investigated. In particular, the Auger cascade originating from vacancies of different origin in the L shell is analyzed in great detail. Competition between radiative KL versus nonradiative KLL Auger emission is emphasized

Experimental observation and theoretical calculations of rydberg series in hollow lithium atomic states

Several extended Rydberg series have been experimentally identified in triply excited states of hollow lithium, by use of electron spectrometry and synchrotron radiation at the Advanced Light Source. Energies, partial cross sections, and quantum defects have also been calculated using the R-matrix approximation. Our results show that the two inner electrons stay in a core-excited state of given symmetry while the behavior of the third electron is mostly governed by the nuclear potential screened by the two inner electrons