In the preceding chapters the material necessary for studying photoionization processes in atoms using synchrotron radiation and electron spectrometry was presented. The discussion will now be completed with some examples of current research activities. These include:

1. photon-induced electron emission around the 4d ionization threshold in xenon from which a complete mapping of these spectra can be obtained and many features characteristic of inner- and outer-shell photoprocesses are well visualized;

2. a complete experiment for 2p photoionization in magnesium which also provides a detailed illustration of the role that many-electron effects have on main photolines;

3. an investigation of discrete satellite lines in the outer-shell photoelectron spectrum of argon which demonstrates for a simple case the origin of satellite processes in electron correlations, and also the importance that instrumental resolution has on the determination of satellite structures;

4. a complete experiment for 5p3/2 photoionization in xenon which includes a measurement of the photoelectron's spin polarization;

5. a quantitative study of postcollision interaction (PCI) between 4d5/2 photoelectrons and N5–O2, 3O2, 31S0 Auger electrons in xenon which also serves as an example of energy calibration in accurate experiments;

6. the determination of coincidences between 4d5/2 photoelectrons and N5–O2, 3O2, 31S0 Auger electrons in xenon which allows a spatial view of the angular correlation pattern for this two-electron emission process;

7. a near-threshold study of state-dependent double photoionization in the 3p shell of argon in which the cross section approaches zero and two electrons of extremely low kinetic energy have to be measured in coincidence.

Description of the K–LL Auger spectrum

Inner-shell ionization is accompanied by subsequent radiative and non-radiative decay. In the context of electron spectrometry, the non-radiative or Auger decay is of special interest, because the emitted Auger electron can be detected. After some remarks on the general description and classification of Auger transitions following 1s ionization in neon, the calculation of K–LL Auger transition rates and the formulation of intermediate coupling in the final ionic state of the K–LL Auger transition will be addressed. This information then provides the basis for a detailed analysis of the experimental K–LL Auger spectrum of neon which is organized similarly to the previous discussion of photoelectrons: namely, with respect to line positions, linewidths, line intensities, and angular distributions.

General aspects

In addition to the photoelectron lines, other discrete structures appear in the electron spectrum of neon if the photon energy is higher than the threshold for 1s ionization. These lines are due to radiationless transitions called Auger transitions [Aug25]; the 1s-hole created by photoionization is filled by a subsequent two-electron transition induced by the Coulomb interaction between the electrons. This interaction causes one outer-shell electron to jump down, filling the 1s-hole, simultaneously ejecting another outer-shell electron, the Auger electron, into the continuum. This process has been sketched schematically in Figs. 1.3 and 2.5.

Theoretical background and general aims

In the non-relativistic limit, the electronic structure of an atom is determined by the Coulomb interaction between the electrons and the nucleus and the Coulomb interaction between the electrons themselves. In the relativistic case, other interactions have to be added, of which the spin–orbit interaction represents the largest contribution. The complete and exact description of these forces in the atom follows from quantum electrodynamics which is nowadays a well-established theory. Therefore, structure studies in atoms as compared to other systems (nuclei or elementary particles) have the advantage of involving forces which are known exactly. However, even for an ideal case it is extremely difficult accurately to calculate the atomic parameters for a many-electron system. As an example the structure of the helium atom in its ground state wavefunction will be discussed, first within the model of independent particles and then for two types of wavefunction which take into account electron correlations, i.e., the correlated motions of the electrons. The fundamental features demonstrated for this relatively simple case can then also be applied to the more complicated dynamical process of photoionization. Here the observed effects of electron–electron interactions and their theoretical treatment brought a renaissance of atomic physics with exciting new insight into the structure and dynamics of atoms interacting with photons, and this aspect will appear in many places throughout the book.

Atomic structure

In order to understand atomic structure, some results from quantum mechanics have to be recalled.

Introductory remarks

In this chapter the methodology presented in Chapters 3 and 4 is extended to include processing of images using radial masks. The approach produces higher power (improved detectability) in most image processing operations at a small cost of increase in processing time. Also, the radial processing masks are less sensitive to the degree of correlation of the background noise.

Because of the similarity of some of the mathematical developments, many of the details in describing radial mask operations are omitted. The analysis involves the Markov noise model with the general results easily reduced to the independent noise case by replacing the Markov dependence covariance matrix with a diagonal matrix.

In the first part of the chapter, the potential features (line or edge elements) are extracted using a radial version of the masks for the one-way designs. Next, the symmetrical incomplete block design (SBIB) technique is generalized to include radial processing. This results in improvement in the feature extraction process for a fixed alarm rate.

The contrast function approach is also extended to include radial masking techniques. The algorithm is capable of detecting potential features and their locations simultaneously. The decision threshold is determined by the variance of the contrast function and the correlation coefficient of the noise.

Introductory remarks

The extraction of line features from two-dimensional digital images has been a topic of considerable interest in the past two decades due to its numerous applications in astronomy, remote sensing, and medical fields. For example, typical problems in astronomy are the extraction of streaks corresponding to the trajectory of meteorites or satellites in space. In remote sensing, a major concern is to decipher from satellite images the network of roads and the separation among fields in agriculture. A common problem in both cases is the nature of the scene itself, which is often noisy with a complex background structure.

Among the techniques used in line extraction are those based on the matched filter concept. Under favorable noise conditions, namely, high SNR and i.i.d. Gaussian samples, the matched filter performs well. Unfortunately, typical noise conditions differ from the Gaussian distribution or, even if Gaussian, their variance is unknown. In addition, the SNR is usually not too high and varies unpredictably over the scene under consideration. As a result, a simple thresholding scheme will fail under these conditions.

Finally, the presence of structured backgrounds such as clouds or smoke will often hide parts of the line, and it is important to remove the background interference without affecting the discontinuity of the line.

Introductory remarks

In this chapter, two different classes of image restoration approaches are presented. Though the stress is placed on images corrupted by so-called “salt and pepper” noise, represented by the mixture distribution model, the methodologies presented here are applicable if the background noise deviates significantly from Gaussian. The image restoration is accomplished in two stages. In the first stage, edge detectors introduced in Chapter 4 are used as preprocessors to establish the local orientation of potential edge points. In the second stage, some form of Robbins–Monro type recursive estimator (see Chapter 8) is applied to remove the undesirable corruption of the image. Alternately, the badly corrupted pixels are replaced by estimated values based on the missing value approach. Based on extensive simulation studies in various noise environments, the edge detection preprocessors that were found to be of practical use are 5 x 5 Graeco-Latin squares (GLS) (see Section 4.5.2) and 6 x 7 Youden squares (YS) (see Section 3.7.2).

Many image restoration procedures, such as averaging and median filters, represent a smoothing process and will cause blurring of the restored image. The averaging filter represents a sample mean and is not robust in salt and pepper noise because of the high variance of the latter.