The gamma photons can transfer energy to the orbital electrons. The electron is emitted as a photoelectron of a certain kinetic energy:
where Ek is the kinetic energy of the photoelectron, Eb is the binding energy of the electron, and hv0 is the energy of the gamma photon before the interaction. Because of the great differences between the masses of the atom and the emitted elec­tron, the energy of recoiling can be ignored in Eq. (5.87). The process is called the “photoelectric effect”; it can be observed when the energy of the gamma photon is similar to the binding energy of the electron. For this reason, high-energy gamma photons usually do not induce the photoelectric effect. The low-energy gamma photons have an energy that is closest to the binding energy of the K and L electrons, so the emission of photoelectrons from the K and L orbitals is the most likely.

The emission of the photoelectron results in the formation of an excited electron state because when one electron is missing from the inner shell of the atom, a vacancy is formed. This excited state can relax in two ways. One way is that an electron in outer orbitals moves into the inner orbital to fill the vacancy, emitting the excess energy between the orbitals as a characteristic X-ray photon. The wave number of the X-ray photon (v*) can be calculated by the Moseley law:

(5.88)

where Ry is the Rydberg constant, Z is the atomic number, and n and m are the main quantum numbers of the electron orbitals. This process forms the basis of the X-ray fluorescence analysis.

The other way is the emission of low-energy Auger electrons (as discussed in Section 4.4.3). This process is called the Auger effect (Figure 5.24). For light ele­ments, the emission of Auger electrons is the preferred result, while in the case of heavier elements, the emission of X-ray photons is more preferable. The two pro­cesses, the emission of X-ray photons and Auger electrons, continue until the atom reaches its ground-state energy. All the photoelectrons, Auger electrons, and X-ray photons intensively ionize the atoms of the absorber. This is a secondary ionization effect.

The cross section of the photoelectric effect (of), or the absorption coefficient of the photoelectronic effect (pf), can be given by a rude empirical formula:

(5.89)

where Ey is the energy of the gamma and X-ray photons. Equation (5.89) expresses the fact that the probability of the emission of photoelectrons increases as the atomic number increases and the energy of the gamma photons decreases.

The photoelectric effect produces photoelectrons, characteristic X-ray photons, and Auger electrons. The measurements of the energy and intensity of these radia­tions are used in different analytical techniques. The measurement of the photoelec­trons gives information on the chemical environment of the atoms in a substance (high-resolution beta spectroscopy or photoelectron spectroscopy). The quality and

quantity of the elements of a substance can be determined by the measurement of the characteristic X-ray photons (X-ray fluorescence spectroscopy, as discussed in Section 10.2.3.1). Auger electron spectroscopy (AES) can be used for the analysis of surface layers.