Although almost all quantum mechanics textbooks consider absorption and emission, the discussion is usually limited to hydrogen-like atoms. This gives a somewhat limited view of the process. This book deals with aborption of high-energy X-rays. Let us look at a particular example to demonstrate the concepts that we will be dealing with throughout the book. Figure 1.1 shows a calculation of the L-edge of a divalent cobalt ion in a solid. In X-ray terminology, L-edge stands for the excitation of an electron from a 2p orbital into a 3d one. In fact, the calculated spectrum resembles closely the experimental X-ray absorption on CoO. Simply by looking at this spectrum, a number of salient features are apparent that will hopefully become clearer throughout the book.

First, one can start by asking the very basic question: what is a spectrum? Apparently, it is the absorption intensity as a function of energy. This implies that energy is a good quantum number. Therefore, in an absorption process energy is conserved. We therefore have to understand why certain quantities are conserved. We shall see that this is inherently related to the symmetry properties of the system. It is important to understand these properties since they tell us what quantities are exchanged between the incoming photon field and the material. By studying the changes in the photon field (in this case, how many photons are absorbed by the material), we can learn something about the material. We shall see that energy is not the only quantity that can be exchanged between the photons and the atoms. Linear and angular momentum are other examples of quantities that can be conserved in a spectroscopy experiment.

We already identified the spectrum in Fig. 1.1 as arising from a 2p → 3d transition. This implies that the basic atomic structure is still valid. We shall therefore review some aspects of the hydrogen-like atom in Chapter 2. The absolute energy scale for this transition is of the order of hundreds of electronvolts.