DSE2T (Nuclear and Particle Physics)
Topic – Interaction of Nuclear Radiation with Matter (Part – 2)
We have already discussed part 1 of this e-report.
Now let us continue part 2 of it.
Cherenkov Radiation:
When a charged particle moves with uniform velocity in free space, it doesn’t emit electromagnetic radiation. However, if it enters a dielectric medium of refractive index , with a speed greater than the speed of light in that medium (i.e. or ), then it emits what is known as Cherenkov radiation. Pavel Cherenkov first observed this effect in 1934 and it was named after him. The direction of the emitted light can be calculated classically using Huygen's wave construction, and can be attributed to the emission of coherent radiation from the excitation of atoms and molecules in the path of the charged particle. The effect is completely analogous to the shock front produced by supersonic aircraft. The emitted light has a spectrum of frequencies, with the most interesting component being in the blue and ultraviolet band of wavelengths. The blue light can be detected with relatively standard photomultiplier tubes, while the ultraviolet light can be converted to electrons using photosensitive molecules that are mixed in with the operating gas in some ionization chamber.
The angle of emission ( ) for Cherenkov light is given by .
The intensity of the produced radiation per unit length of radiator is proportional to . Consequently, for , and light can be emitted, while for , which suggests that is complex and no light can be observed.
The Cherenkov radiation process therefore provides a means for distinguishing two particles of same momentum but different mass. For example, protons, kaons and pions of 1 GeV/ momentum have 0.73, 0.89 and 0.99, respectively. Consequently, to observe Cherenkov light from these particles we require media of different refractive index. In particular, for protons to emit light, we would need a threshold , kaons would require and pion . Now let us suppose that we arrange two Cherenkov counters in series, one filled with water ( ) and the other filled with gas under pressure so that it has . If we pass a mixture of protons, kaons and pions through the two counters, the protons will not provide a signal in either detector, kaons will radiate Cherenkov light only in the water vessel, while pions will register signals in both counters. This can therefore provide a way of discriminating between particles that have different Cherenkov thresholds.
Interaction of Gamma Rays:
Because gamma rays or X-rays (or photons) are electrically neutral, they do not experience the Coulomb force the way charged particles do. We might therefore conclude that they cannot ionize atoms. But that would be erroneous. In fact, photons are the carriers of electromagnetic force and can interact with matter in a three ways that lead to ionization of atoms and to energy deposition in a medium. Those three processes are photoelectric absorption, Compton scattering and pair production. In the photoelectric effect, a photon is absorbed by an atom and one of the atomic electrons, known in this case as a photoelectron, is released. Free electrons cannot absorb a photon and recoil.
Energy and momentum cannot both be conserved in such a process, a heavy atom is necessary to absorb the momentum at little cost in energy. The kinetic energy of the electron is equal to the photon energy less the binding energy of the electron.
We can describe the attenuation of light (photons, X-rays or gamma rays) in a medium in terms of an effective absorption coefficient , which reflects the total cross section for interaction. In general, will depend on the energy or frequency of the incident light. If represents the intensity of photons at any
point in the medium, then the change in intensity in an infinitesimal thickness of material can be written in terms of as
where, as usual, the negative sign indicates that the intensity decreases with traversed distance. We can therefore write . Integrating the above expression from some initial value at to the final intensity at the point , we obtain
or
As in the case of other statistical processes, such as radioactive decay, we can define a half-thickness, denoted as as the thickness of material that photons must traverse in order for their intensity to fall to half of the original or initial value. This can be related to as follows. From the previous equation we write,
or
or
The value of is just the mean free path for absorption or the average distance through which a beam of photons will propagate before their number drops to of the initial value. We will now turn to a brief discussion of the previously mentioned three specific processes that contribute to absorption of photons in any medium.
1. Photoelectric Effect. In this process, a low-energy photon is absorbed by a bound electron, which is subsequently emitted with kinetic energy (from Fig.
1). If we call the energy needed to free the atomic electron (this is the negative of the binding energy) which is basically serves the purpose of work
function for a metal and the frequency of the photon , then energy conservation requires that the Einstein relation holds, namely,
Fig. 1 or
where sets the scale for the appropriate photon energies that are required for the process to take place. The photoelectric effect has a large cross section in the range of X-ray energies (keV) and ignoring the absolute normalization, scales approximately as
for for
Thus the process is particularly important in high- atoms, and is not very significant above the 1 MeV range of photon energies. When the emitted electron originates from an inner shell of the atom, one of the outer electrons drops down to fill the lower (more stable) empty level and the emitted electron is consequently accompanied by an X-ray photon produced in the subsequent atomic transition. Furthermore, there are in the probability for photoelectric absorption discontinuous jumps at energies corresponding to the binding energies of particular electronic shells. That is, the binding energy of a K-shell electron in Pb is 88 keV. Incident photons of energy less than 88 keV cannot
release K-shell photoelectrons (although they can release less tightly bound electrons from higher shells). When the photon energy is increased above 88 keV, the availability of the K-shell electrons to participate in the photoelectric absorption process causes a sudden increase in the absorption probability, known as the K-absorption edge or simply K edge. Fig. 2 shows a sample of the photoelectric absorption cross section.
Fig. 2
2. Compton Scattering. Compton scattering is the process by which a photon scatters from a nearly free atomic electron, resulting in a less energetic photon and a scattered electron carrying the energy lost by the photon. It can be thought of as equivalent to a photoelectric effect on a free electron. In conventional language, one can think of the process as involving the collision of two classical
particles viz. the photon, with energy and momentum and an electron at rest.
Fig. 3
The kinematics for the scattering assumes that the target electron is free. This means that the results are not expected to hold for incident photons of very low energy (much below 100 keV), where effects of atomic binding can be important. Treating the photon as a particle of energy and momentum (zero rest mass) and using fully relativistic momentum-energy expressions for the electron, it is straightforward to show that the kinematic relation between the frequency of the incident and the scattered photon ( ), at a photon scattering angle (shown in Fig. 3) is given by
where is the rest mass of the electron. From the above expression, we see that, for any finite scattering angle, the energy of the scattered photon is smaller than that of the incident one. The incident photon must therefore transfer some of its energy to the electron, which consequently has a recoil energy that depends on the scattering angle.
Relying on special relativity, the quantization of light (that is the particle properties of photons), and quantum theory, the Compton reaction served as one of the early major confirmations of the new ideas of 20th century Physics.
Again, ignoring absolute normalization, the cross section for Compton scattering appears to scale as
where is the atomic number of the medium. Compton scattering dominates energy deposition in the 0.1 to 10 MeV range of photon energies.
3. Pair Production. When a photon has sufficient energy, it can be absorbed in matter and produce a pair of oppositely charged particles. Such conversions can only take place when no known conservation laws are violated in the process. In addition to charge and momentum-energy conservation, other quantum numbers may restrict the possible final states. The best known conversion process, commonly referred to as pair production, involves the creation of a positron- electron (e+ e-) pair through the disappearance of a photon.
However, a massless photon cannot be converted into a pair of massive particles without violating momentum-energy conservation. This is best seen heuristically as follows. Let us suppose that the photon has a very small rest mass (far smaller than the mass of an electron). Now, in the photon’s rest frame, the energy is its rest mass, namely close to zero, while, for the final state, the minimum energy is given by the sum of the rest masses of the two particles, which by assumption is relatively large. It follows therefore that a process such as pair production can only be observed in a medium in which, for example, a recoiling nucleus can absorb any momentum required to assure momentum- energy conservation. Since the mass of the positron equals that of the electron, the threshold for e+ e- pair production is essentially MeV = MeV.
The pair production cross section scales essentially as , where is the atomic number of the medium. It rises rapidly from threshold and dominates all energy- loss mechanisms for photon energies MeV. At very high energies ( MeV), the e+ e- pair cross section saturates and can be characterized by a constant mean free path for conversion (or by a constant absorption coefficient) that essentially equals the electronradiation length of the medium
A natural question to ask is what happens to the positrons that are created in the conversion of photons in matter? Because positrons are the antiparticles of electrons, after production, they traverse matter, much as electrons do, and deposit their energies through ionization or through Bremsstrahlung. Once a positron loses most of its kinetic energy, however, it captures an electron to form a hydrogen-like atom, referred to as positronium, where the proton is replaced by a positron. Unlike hydrogen, positronium atoms are unstable, and decay (annihilate) with lifetimes of about 10-10 sec to form two photons
Fig. 4
The process of annihilation produces photons of equal energy, back-to-back in the laboratory. To conserve momentum-energy, each photon carries away exactly 0.511 MeV. Thus pair annihilation provides a very clean signal for detecting positrons, as well as for calibrating the low-energy response of detectors. The three processes that we have just discussed provide independent contributions to the absorption of photons in any medium. We can therefore write the total absorption coefficient as the sum of the three separate coefficients as
The independent contributions as well as their sum, are shown as a function of photon energy in Fig. 4.
Interaction of Neutrons:
As we have already mentioned, neutrons are in most respects very similar to protons. They are the constituents of nuclei, and have essentially the same mass, same nucleon number and spin as protons. They are, however, electrically neutral, and consequently, just like photons, cannot interact directly through the Coulomb force. Although neutrons have small magnetic dipole moments, these do not provide substantial interactions in media. Neutrons do not sense the nuclear Coulomb forces and as a result even slow neutrons can be scattered or captured by the strong nuclear force. When low-energy neutrons interact inelastically, they can leave nuclei in excited states that can subsequently decay to ground levels through the emission of photons or other particles. Such emitted gamma-rays or other particles can then be detected through their characteristic interactions with matter. Elastically scattered neutrons can transfer some of their kinetic energy to nuclear centres, which in recoiling can also provide signals (e.g. ionization) that can be used to reveal the presence of neutrons. In the elastic scattering of neutrons from nuclei, just as for the case of ionization loss, it is more difficult to transfer a sizable part of a neutron's kinetic energy to a nucleus if the nuclear mass is large.
As we have already mentioned, this is the reason that hydrogen-rich paraffin is often used as a moderator to slow down energetic neutrons. When neutrons are produced in collisions, they can be quite penetrating, especially if their energies are in the range of several MeV, and there are no hydrogen nuclei available for absorbing their kinetic energies. The neutron shine, at accelerators and reactors is often a major source of background to experiments, and can only be reduced through use of appropriate moderators and materials that have large neutron- absorption cross sections.
Reference(s):
Introduction to Nuclear and Particle Physics, A. Das & T. Ferbel, World Scientific
Introductory Nuclear Physics, Kenneth S. Krane, John Wiley & Sons (All the figures have been collected from the above mentioned references)
