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The atomic X-ray absorption spectrum (XAS) of a core-level in an absorbing atom is separated into states in the discrete part of the spectrum called "bounds final states" or "Rydberg states" below the ionization potential (IP) and "states in the continuum" part of the spectrum above the ionization potential due to excitations of the photoelectron in the vacuum.
The discrete spectrum is defined as the set of normal eigenvalues or, equivalently, as the set of isolated points of the spectrum such that the corresponding Riesz projector is of finite rank. As such, the discrete spectrum is a strict subset of the point spectrum, i.e., σ d ( T ) ⊂ σ p ( T ) . {\displaystyle \sigma _{d}(T)\subset \sigma ...
The formulas provided at § Examples of window functions produce discrete sequences, as if a continuous window function has been "sampled". (See an example at Kaiser window.) Window sequences for spectral analysis are either symmetric or 1-sample short of symmetric (called periodic, [4] [5] DFT-even, or DFT-symmetric [2]: p.52 ).
Energy-dispersive X-ray spectroscopy (EDS, EDX, EDXS or XEDS), sometimes called energy dispersive X-ray analysis (EDXA or EDAX) or energy dispersive X-ray microanalysis (EDXMA), is an analytical technique used for the elemental analysis or chemical characterization of a sample. It relies on an interaction of some source of X-ray excitation and ...
The continuous and discrete spectra of physical systems can be modeled in functional analysis as different parts in the decomposition of the spectrum of a linear operator acting on a function space, such as the Hamiltonian operator. The classical example of a discrete spectrum (for which the term was first used) is the characteristic set of ...
There exist several efficient designs for analyzing an X-ray emission spectrum in the ultra soft X-ray region. The figure of merit for such instruments is the spectral throughput, i.e. the product of detected intensity and spectral resolving power. Usually, it is possible to change these parameters within a certain range while keeping their ...
When the incident x-ray energy matches the binding energy of an electron of an atom within the sample, the number of x-rays absorbed by the sample increases dramatically, causing a drop in the transmitted x-ray intensity. This results in an absorption edge.
The analysis of the energy dependence of the emitted photons is the aim of the X-ray emission spectroscopy. [ 1 ] [ 2 ] [ 3 ] XES is also sometimes referred to as X-ray Fluorescence (XRF) spectroscopy, and while the terms can be used interchangeably, XES more often describes high energy resolution techniques [ 4 ] while XRF studies a wider ...