The Basic Phenomenon

Before the geometrical constraints for x-ray(x ray protection) interference are derived the interactions between x-rays and matter have to be considered. There are three different types of interaction in the relevant energy range. In the first, electrons may be liberated from their bound atomic states in the process of photoionization. Since energy and momentum are transferred from the incoming radiation to the excited electron, photoionization falls into the group of inelastic scattering processes. In addition, there exists a second kind of inelastic scattering that the incoming x-ray beams may undergo, which is termed Compton scattering. Also in this process energy is transferred to an electron, which proceeds,however, without releasing the electron from the atom. Finally, x-rays may be scattered elastically by electrons,which is named Thomson scattering. In this latter process the electron oscillates like a Hertz dipole at the frequency ofthe incoming beam and becomes a source of dipole radiation. The wavelength A of x-rays is conserved for Thomson scattering in contrast to the two inelastic scattering processes mentioned above.It is the Thomson component in the scattering ofx-rays that is made use of in structural investigations by x-ray diffraction. Figure 1.1 illustrates the process of elastic scattering for a single free electron of charge e, mass m and at position R0. The incoming beam is accounted for by a plane wave #oexp(-iKKR4), where FO is the electrical field vector and Ko the wave vector. The dependence of the field on time will be neglected throughout. The wave vectors KO and K describe the direction of the incoming and exiting beam and both are of magnitude 2Y/3.. They play an important role in the geometry of the scattering process and the plane defined by them is denoted as the scattering plane. The angle between K and the prolonged direction of Ko is the scattering angle that will be abbreviated by 20 as is general use in x-ray diffraction. We may also define it by the two wave vectors according to
20 = arccos (K,K0}/KK0
The formula is explicitly given here, because the definition of angles by two adjoining vectors will be made use of frequently.The oscillating charge a will emit radiation of the same wavelength A as the primary beam. In fact, a phase shift of 180' occurs with the scattering, but since this shift equally arises for every scattered wave it has no effect on the interference pattern in which we are interested and will be neglected. If the amplitude of the scattered wave E(R)(portable ultrasound machine) is considered at a distance R we may write according to Hertz and Thomson.