INTERACTION OF THE IONIZING RADIATION WITH MATTER

Dr. YaSeen AbdulAzim

Alpha, beta, gamma and X radiations are all ionising radiation with the ability to produce ions in living tissue. It is most important to understand the manner in which radiation interacts with matter and transfers its energy. Energy from radiation is transferred to matter in two ways: Ionisation and Excitation. Ionisation is the process of removal of an electron from an atom leaving the atom with a net positive charge. In excitation, the energy of incoming radiation raises an outer electron to a higher energy state from which it returns very rapidly (10-8s) to its original state emitting a photon of light in the process.

The mechanisms involved in the transfer of energy are dependent on the nature of the ionising radiations involved. Alpha and beta radiations are made up of charged particles and these interact with matter via electrostatic forces. Gamma and X radiations are a type of electromagnetic wave and interact with matter via the Photoelectric Effect, the Compton Effect and the Pair production process. The different mechanisms of the interaction of charged particles with matter are described below.

CHARGED PARTICLES

The charged particles ( and ) interact with matter via electrostatic forces leaving behind an ionised atom or molecule. After each interaction the  or -particle loses energy and with sufficient interactions will eventually be ‘stopped’.

The total energy lost by incident particle per unit length is given by:

(1)

where

ko = 8.99 x 109,

Z – atomic number of heavy particle,

e - electron charge,

n – number of electron per unit volume,

m – electron rest mass,

c – speed of light in vacuum,

β – v/c – speed of the particle relative to c,

I – mean excitation energy of the medium

, ~ 35 eV.

Range

The initial energy of an  or  particle is finite. We find that in traversing matter it continuously loses energy producing ionisations and is finally stopped, thus charged particle radiations have a finite range. This range is calculated as follows:

(2)

The range of an  or  particle is dependent on the number of atoms the particle encounters when it travels through a medium. The best way to estimate the number of atoms in a medium is using the concept of mass per unit area. If the densityof a material is given by  gcm-3, then the mass per unit area of a sheet of thickness t is t gcm-2.

We express the range in a simplified solution of equation (2) and then we find that the formula for the range of  and  particles can be given in terms of the energies of the particles only. Symbolically:

(3) for  particles of energy E (in MeV), and

(4) for  particles of energy E (in MeV).

We can use the concept of range to calculate the thickness of shielding needed to stop any particular beta, in example 1 above the correct shielding for a 32P beta would be  0.7 cm. However, we have to be careful when choosing the type of shielding to use. If we use a high-density material (eg lead) then we will stop the beta very quickly and this can lead to the emission of bremstraahlung radiation. Use of lower-density materials such as perspex requires greater thickness of absorber but produce much less bremstraahlung.

X AND GAMMA RADIATION

The Photoelectric Effect

The photoelectric effect, Fig. 1, is an absorption process and usually occurs for low energy photons (<0.1 MeV) such as X-rays. The energy EX of the X-ray is transferred (absorbed) to an inner electron, normally a K-shell electron, and this gives the electron sufficient energy to escape from the atom. The atom is left positively charged (ie, an ion) and in an excited state due to the vacancy left in the inner shell. This vacancy is quickly filled by another electron dropping down from a higher shell with the subsequent release of a photon of frequency determined by the two shells involved.

The energy of the ejected electron is given by the simple formula;

Ee = EX – BE, (5)

Fig. 1: The Photoelectric Effect.

where

Ee = energy of ejected electron

EX = energy of incoming X or  ray photon

BE = binding energy of ejected electron.

The ejected electron will then travel through the surrounding medium creating ion pairs in the same way as a beta particle of equivalent energy.

The Compton Effect

The Compton Effect, Fig. 2, is essentially an elastic collision process and generally occurs for high-energy photons (>0.1 MeV) such as gamma rays. An incoming photon of high energy (-ray) collides with an electron in the valence band, ejecting the electron from the atom. A photon of lower energy (and hence different frequency) than the original is produced that travels at an angle to the direction of the incident photon, determined by conservation of momentum. The energy of the ejected or Compton electron can be determined by knowledge of the energies of the incoming and scattered photons.

As in the Photoelectric Effect, the ejected electron will then travel through the surrounding medium creating ion pairs in the same way as a beta particle of equivalent energy.

Fig. 2: The Compton Effect

Pair Production

This process cannot happen in free space; it needs the presence of a third body, usually a nucleus, to simultaneously conserve energy and momentum. Since the rest energy of an electron is 0.51 MeV, pair production is energetically impossible for photon energies less than 1.02 MeV. However when pair production becomes possible it soon becomes the dominant interaction process for beams of very high energy photons.

Fig. 3: Pair production
Attenuation of X and Gamma Radiation

X and gamma radiation are types of electromagnetic waves and as such are chargeless and virtually massless. The probability of interaction with the orbital electrons of an atom is much smaller than that of alpha and beta radiation. This accounts for the well-known penetrability of X and gamma radiation.

If the interactions are of the "all-or nothing" type then the attenuation of a beam of particles with identical energies, all traveling in the same direction, is described by an exponential law. If at some distance into the material N0 particles are moving through a slab of material, then after penetrating an extra distance x it is found that the number of particles in the beam is reduced to

N(x) = N0 exp(−μl x) (6)

The quantity μl is known as the linear attenuation coefficient; it is a measure of how rapidly the original photons are removed from the beam. A large value of μl means that the original photons are removed after traveling only a small distance. It is important to remember that the exponential attenuation law does not describe what happens to the energy carried by the photons removed from the beam - it is possible that some of that energy may be carried through the medium by other particles, including some new photons. The linear attenuation coefficient μl is energy dependent.

This exponential attenuation law follows from the fact that, over any short distance, the probability of losing a particle from the beam is proportional to the number of particles left. Where there are many particles many will be lost, but as the number left decreases so does the rate of loss.

Fig. 4: Attenuation of a photon beam - schematic

The original photons interact at random.

Since photons interact with individual atoms, the probability that a photon will interact somewhere within a slab of matter depends on the total number of atoms ahead of it along its path. So the attenuation of radiation depends on the amount of material in the beam's path and not on how it is distributed. It is useful, therefore, to describe the attenuation process in a way that does not depend on the density of material, only on what kind of stuff it is. We can achieve that by defining the mass attenuation coefficient μm which is related to the linear attenuation coefficient by

μl = μmρ (7)

where ρ is the density of the medium.

The total mass attenuation coefficient is just the sum of all the contributions from the different effects:

μm[tot] = μm[pe] +μm[C] +μm[pp] (8)

This total mass attenuation coefficient describes the decrease of the original incident radiation. The total linear attenuation coefficient is given by

μl [tot] =μm[tot]ρ (9)

As the probability of interaction with matter is small we find that a given thickness of absorber produces the same fractional reduction in intensity. We say that the incident radiation is attenuated and the degree of attenuation is dependent on the absorber material and the energy of the radiation. For all absorber materials this attenuation is exponential in character and, unlike the charged particle radiations, there is no thickness of material which will completely ‘stop’ X or gamma radiation (Fig. 5). The distance over which one half the initial beam is absorbed is called the half value layer,x1/2.

Fig. 5: Attenuation of X and Gamma Radiation

You can see from figure 2.3 that this is a similar graph as that for half-life. In place of half-life 1/2 we have half-thickness x1/2. Hence, placing three layers of absorber each of thickness x1/2 would attenuate a beam by x1/2 x1/2 x1/2 = 1/8.

SHIELDING

Alpha

Alpha radiation penetrates less than 4 cm in air and will not penetrate the dead outer layer of skin; consequently most materials can be used for shielding.

Beta

Beta radiation can penetrate several metres in air and up to 0.8 cm in tissue: therefore shielding is required. As a result of the possibility of bremstraahlung radiation, it is best to use low-density materials, such as perspex, for shielding.

Fig. 6: Some examples of suitable shielding, alpha and beta radiation can be completely stopped by shielding, X and gamma radiation can only be attenuated

X Radiation

The energy of an X-ray is generally less than 0.1 MeV, consequently the interaction mechanism is the Photoelectric Effect. It turns out that the Photoelectric Effect is proportional to the fourth power of the atomic number, therefore we need to choose an absorber with a high atomic number – lead (Z = 82) is a good choice and a thickness of about 1 mm should be sufficient.

Gamma Radiation

The interaction mechanism is the Compton Effect. As this depends on the availability of valence electrons, it does not vary greatly with atomic number and subsequently we choose an absorber with a high mass per unit area and, again, lead is a good choice. However, if cost considerations are important, concrete can be used to replace lead but greater thickness will be required.

RADIATION QUANTITIES AND UNITS

There are many measures of radiation that are commonly encounter. These are: Activity, Exposure, Absorbed Dose, Equivalent Dose and Effective Dose. A short summary of these measures and their units will be followed by more in depth information.

Activity

The strength of a radioactive source is called its activity, which is defined as the rate at which the isotope decays. Radioactivity may be thought of as the volume of radiation produced in a given amount of time. The International System (SI) unit for activity is the becquerel (Bq), which is that quantity of radioactive material in which one atom transforms per second. The becquerel is a small unit. In practical situations, radioactivity is often quantified in kilobecquerels (kBq) or megabecquerels (MBq). The curie (Ci) is also commonly used as the unit for activity of a particular source material. The curie is a quantity of radioactive material in which 3.7x1010 atoms disintegrate per second. This is approximately the amount of radioactivity emitted by one gram (1 g) of Radium-226. One curie equals approximately 37,037 MBq.

Flux Ф

It is the number of particles crossing a unit area in a unit time. Considering a source of activity A (Bq), the flux Фat a point distant r (m) from the source is

(particles/m2s) (10)

Exposure

Exposure is a measure of the strength of a radiation field at some point. It is a measure of the ionization of the molecules in a mass of air. It is usually defined as the amount of charge (i.e. the sum of all ions of the same sign) produced in a unit mass of air when the interacting photons are completely absorbed in that mass. The most commonly used unit of exposure is the Roentgen (R). Specifically, a Roentgen is the amount of photon energy required to produce 1.610 x 1012 ion pairs in one cubic centimeter of dry air at 0°C. The main advantage of this unit is that it is easy to directly measure with a survey meter. The main limitation is that it is only valid for deposition in air.

Radiation absorbed dose

Whereas exposure is defined for air, the absorbed dose is the amount of energy that ionizing radiation imparts to a given mass of matter. The most commonly used unit for absorbed dose is the “rad” (Radiation Absorbed Dose). A rad is defined as a dose of 100 ergs of energy per gram of the given material. The SI unit for absorbed dose is the gray (Gy), which is defined as a dose of one joule per kilogram. Since one joule equals 107 ergs, and since one kilogram equals 1000 grams, 1 Gray equals 100 rads.

The size of the absorbed dose is dependent upon the strength (or activity) of the radiation source, the distance from the source to the irradiated material, and the time over which the material is irradiated. The activity of the source will determine the dose rate which can be expressed in rad/hr, mr/hr, mGy/sec, etc.

Equivalent Dose HT

When considering radiation interacting with living tissue, it is important also to consider the type of radiation. Although the biological effects of radiation are dependent upon the absorbed dose, some types of radiation produce greater effects than others for the same amount of energy imparted. For example, for equal absorbed doses, alpha particles may be 20 times as damaging as beta particles. In order to account for these variations when describing human health risks from radiation exposure, the quantity called “equivalent dose in a tissue or organ HT” is used. This is the absorbed dose multiplied by a certain “quality” or “adjustment” factors indicative of the relative biological-damage potential of the particular type of radiation.

The radiation weighting factor (wR) is a factor used in radiation protection to weigh the absorbed dose with regard to its presumed biological effectiveness. Radiation with higher wR factors will cause greater damage to tissue. The rem is a term used to describe a special unit of the equivalent dose. Rem is an abbreviation for roentgen equivalent in man. The SI unit is the Sievert (Sv); one rem is equivalent to 0.01 Sv.

Radiation weighting factor for different types of radiation.

The equivalent dose in tissue T is given by the expression:

(11)

where DT,R is the absorbed dose averaged over the tissue or organ T, due to radiation R.

Effective dose E

The effective dose, E, is the sum of the weighted equivalent doses in all the tissues and organs of the body. It is given by the expression:

(12)

where HTis the equivalent dose in tissue or organ T and wT is the weighting factor for tissue T. The unit of the effective dose E sievert Sv.

ICRP Recommendations for tissue weighting factors in Publication 26 (1977) and Publication 60 (1991).

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