The Compton Effect

Here we shall investigate tlu collision b( dween a light quantum and an electron, on tlie assum )ti()iis of the 8])ecial theory of rehitivity. This procedure is approjiriate for our purpose, as it do( s not make the calculations any more eom )li( ,a.t ed, whih on the otluu hand the result obtained is th(ui valid for the scattering even of very liard radiation. 

The calculations a,r( based on th( . th( or(uns of tlu ( ons( rvation of energy and of momentum. TJie (MU rgy of tin, liglit quantum before the collision is hv, its monuMitum hvjc the eorres )onding quantities after the, collision W( shall call hv and Iiv jc. For 

Then if / is the angle of deviation of the light quantum and 0 the angle of deviation of the electron, the theorems of the conservation of energy and of momentum take the following forms (see fig. 4)  

In order to give a strict proof of the relationship U = dvjdr given in the text, we in the first instance consider the most general form of a group of waves it must have the form of a Eourier integral 

We now assume that the group is very narrow, so that in the integral there occur only those waves of finite amplitude whose wave-numbers difl er from the mean wave-mimb( .r Tq by a very small amount. 

---

Spectral Gamma Ray Log. This log makes use of a very efficient tool that records the individual response to the different radioactive minerals. These minerals include potassium-40 and the elements in the uranium family as well as those in the thorium family. The GR spectrum emitted by each element is made up of easily identifiable lines. As the result of the Compton effect, the counter records a continuous spectrum. The presence of potassium, uranium and thorium can be quantitatively evaluated only with the help of a computer that calculates in real time the amounts present. The counter consists of a crystal optically coupled to a photomultiplier. The radiation level is measured in several energy windows. 

In modified scattering, the resulting increase in wavelength (Compton effect) is evidence that the x-ray photon acting as a corpuscle has been scattered by colliding with an electron to which it has lost momentum in the process. The Compton effect is not at present of practical importance in analytical chemistry. 

The Compton effect, in which the photon is scattered with significantly lower energy by a medium electron, which is then ejected with the energy differential. 

The excellent, high-resolution y- and X-ray spectra which can be obtained from semiconductor detectors make the detectors very important in modern instruments. A typical spectrum is shown in Figure 10.11(b) which may be compared with the much broader peaks from a scintillation detector (Figure 10.11(a)). The spectra are not immune from the problem of Compton scattering (p. 461) but a good quality modem detector will have a photopeak to Compton peak ratio of 50 1 or better. Computer-aided spectrum analysis also serves to reduce the interference from the Compton effect. 

Inelastic photon scattering processes are also possible. In 1928, the Indian scientist C. V. Raman (who won the Nobel Prize in 1930) demonstrated a type of inelastic scattering that had already been predicted by A. Smekal in 1923. This type of scattering gave rise to a new type of spectroscopy, Raman spectroscopy, in which the light is inelastically scattered by a substance. This effect is in some ways similar to the Compton effect, which occurs as a result of the inelastic scattering of electromagnetic radiation by free electrons. 

When y radiation hits an electron, it is deviated from its original trajectory and, losing energy, changes its frequency. The increase in frequency consequent upon anelastic scattering is only a function of the angle between incident and deflected rays and does not depend on the energy of the incident radiation. The importance of this fact, known as the Compton effect, increases as the atomic number of the element decreases. 

The Compton effect A photon is characterized not only by its energy, E = Hco but also by a momentum, p. The latter may be evaluated directly by using the relativistic expression for the energy of a particle in terms of its rest mass, m, and momentum, p, namely... 

Fig. 2.4 The scattering of a photon by a stationary electron in the Compton effect.

Now we will briefly indicate the problems that can be usefully treated with the above geometric theory of the hydrogen atom." In many applications, such as the theory of the Compton effect in a bound electron and in the inelastic matter theory of atoms it is a question of determining the norm of the projection of a given function on the subspace of Hilbert space determined by the principal quanmni number nJ This norm is defined by the sum... 

The interpretation given above is simplified, since fluorescence is not the only process that allows the atom to lose its excess energy. Other phenomena such as Rayleigh scattering (elastic scattering) and the Compton effect (inelastic scattering with release of Compton electrons) can complicate the X-ray emission spectrum. 

Quantum mechanics had exploded between 1923 and 1927. A. H. Compton, in 1923, had discovered the change in frequency of X-rays scattered from the electrons (the Compton effect).25 Compton and, independently, Debye had underlined the importance of this discovery in support of the Einstein conception of light-quanta or photon propagation in space.26... 

The primary interaction of gamma rays with matter is the production of ionization or excitation. The three processes of interaction are the photoelectric effect, the Compton effect, and pair production. The predominance of each of these effects is determined by the energy of the gamma ray and the atomic number, Z, of the absorber. The photoelectric effect is favored for low energies, the Compton effect for intermediate energies, and pair production for high energies... 

The relation between the mass (or momentum) of the light quantum and the wave length of the radiation is confirmed experimentally by the observation of the Compton effect. In this effect, the change of the wave length of X-radiation when the latter is scattered by an electron, the experimental result can be calculated simply by treating not only the electron but also the quantum of radiation as material particles colliding with one another. 

---