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

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

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

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

Double-core-hole states in CH3CN: Pre-edge structures and chemical-shift contributions

Spectra reflecting the formation of single-site double-core-hole pre-edge states involving the N 1s and C 1s core levels of acetonitrile have been recorded by means of high-resolution single-channel photoelectron spectroscopy using hard X-ray excitation. The data are interpreted with the aid of ab initio quantum chemical calculations, which take into account the direct or conjugate nature of this type of electronic states. Furthermore, the photoelectron spectra of N 1s and C 1s singly core-ionized states have been measured. From these spectra, the chemical shift between the two C 1s−1 states is estimated. Finally, by utilizing C 1s single and double core-ionization potentials, initial and final state effects for the two inequivalent carbon atoms have been investigated