Alpha and Beta Particle Absorption

Posted on Aug 27, 2024 in Physics

Alpha Particle Absorption

Measuring the specific ionization produced in air by alpha particles at various distances, we obtain a curve called the Bragg curve. This curve shows that the specific ionization increases with distance from the source (transmitter of these particles), initially slowly and then quickly, after passing a maximum, it drops abruptly to zero. Ionization specifies the ionization per unit length or per gram. This phenomenon is explained as follows:

The increasing values of specific ionization occur because as the alpha particle moves through its path producing ion pairs, it is constantly losing kinetic energy and therefore speed.
By reducing the speed, the specific ionization increases, therefore it increases with increasing distance from the source.
At the end of its path, the alpha particle moves more slowly, and that is when the ionization peaks. Past a certain point, the particle’s energy has declined as it captures first one electron and then another, becoming a helium atom no longer able to produce ionization.

This explains the sudden drop in the curve. It’s very interesting that this decrease is quite abrupt and not gradual. This implies that since all the alpha particles from a particular source have almost the same energy, they all fail to produce ionization after traveling the same distance. The distance R, at which alpha particles from a particular source stop producing ionization, is called the range of alpha particles in the environment in question.

The range of alpha particles in air or in other material depends on the nature of the source since it depends on the energy of the particles. There is an inverse proportionality between the half-life of a radioisotope and its energy, and therefore, the R (or range) of alpha particles it emits. This means that the shorter the half-life, the greater the energy and range of alpha particles.

The Stopping Power or Absorption of an Absorber

This magnitude is independent of the energy of alpha particles, assuming that capacities are related to one source particle.

Beta Particle Absorption

Beta particles share some common characteristics with alpha particles in their passage through matter, such as ion-pair production in air at a rate of 34 eV per pair. But there are important differences.

The lower mass of beta particles means that the specific ionization is less than that of an alpha particle of the same energy.
Alpha particles from a source are all nearly the same energy or in two or three groups. In contrast, beta particles have a continuous energy distribution, i.e., a continuous energy spectrum up to a maximum value that is characteristic of each source that emits beta particles.
Alpha particles, due to their mass, do not have remarkable changes of direction as they pass through matter. In contrast, beta particles are subject to considerable scattering, causing frequent changes in direction, due to electrostatic interactions with atomic nuclei and electrons.

So, after crossing the thickness of an absorber, beta particles may have different exit points, which means that they traveled paths of different lengths. Beta particles do not present a precise range. But you can determine a thickness which reduces the ionization produced by them almost to zero, except for bremsstrahlung radiation.

Bremsstrahlung Radiation

Bremsstrahlung radiation occurs when electrons (beta particles) lose their high-speed energy as they pass through matter. The fraction of electron kinetic energy that is converted into bremsstrahlung is greater, the higher the energy of the electron and the higher the atomic number of the element with which it interacts. The X-ray energy resulting covers a wide range; the peak is very close to the maximum energy of electrons, but the average energy is much lower.

Considerations in the Stopping or Absorption of Alpha and Beta Particles

We must take into account the range because irradiation is only possible if we are closer than that range.
Beta particles can be stopped or completely absorbed by interposing a material of suitable thickness and density.
Beta radiation shielding is designed to stop even the highest energy levels to achieve total absorption.
The shielding for beta particles can be calculated from the range, the same as for alpha particles.
For the evaluation of adequate shielding for alpha particles, it must be remembered that these do not present a problem of external radiation because their range is very small, but rather it must be considered that the incorporation of a substance that emits these particles means a considerable dose within the body. Therefore, alpha particles do not present a problem of external radiation but rather of internal contamination.
In the case of shielding for beta particles, bremsstrahlung radiation must be borne in mind. This phenomenon depends on the particle energy and the atomic number (Z) of the absorber, which is why in some cases additional shielding must be considered for the radiation generated by this phenomenon.
The maximum energy of beta particles will determine the maximum range and therefore be used to calculate the thickness of the absorber.
This allows us to express the maximum range of a beta particle as the product of density per inch of material (R density) required to stop it completely, independent of the material used. Thus, the density of the material you decide to use will determine the cm. of it (R). The maximum range has units of mg/cm².

Evaluation of Bremsstrahlung

For radiation protection purposes, the total energy of X-rays produced by the stopping of beta particles can be estimated using the following approximation:

f = 3.5 x 10^-4 ZE_max

where Z is the atomic number of the shielding material, E_max is the maximum energy of beta particles, and 3.5 x 10^-4 is a constant. f is the fraction of energy that is transformed into electromagnetic radiation (X-rays) when the beta particle impacts a material. This fraction is directly proportional to Z and the maximum energy of the particle.

Interaction of Electron Beams with the Absorbing Medium

When electrons travel through matter, they interact with atoms through a variety of Coulomb interaction forces, such as:

Inelastic collisions with atomic electrons, resulting in ionization and excitation of atoms.
Inelastic collisions with nuclei, resulting in bremsstrahlung production.
Elastic collisions with atomic electrons.
Elastic collisions with atomic nuclei, resulting in elastic scattering, which is characterized by a change in direction but not in a decrease in energy.

The kinetic energy of the electrons is lost in inelastic collisions, which produce ionization or convert the energy into other forms, such as photon energy or excitation energy. In elastic collisions, the kinetic energy is not lost; however, the direction of the electrons can change, or energy can be redistributed through the particles involved in the collisions.

In therapy, beam energy is lost at a rate of 2 MeV per cm²/g. The rate at which energy is lost in collisions depends on the electron energy and electron density of the medium. The rate of energy loss per cm² per gram (called the mass stopping power) is higher for low atomic number materials. This is because higher atomic number materials have fewer electrons per gram than lower atomic number materials, and in addition, higher atomic number materials have a greater number of tightly bound electrons that are not available for this type of interaction.

The amount of energy lost by radiation interactions (bremsstrahlung) is roughly proportional to the electron energy and the square of the atomic number of the absorbing material. This means that X-ray production through radiation loss is more efficient for higher energy electrons and higher atomic number materials.

When an electron beam passes through a medium, the electrons undergo multiple scattering due to Coulomb interaction forces between the incident electrons and the nuclei, predominantly in the medium. Therefore, the electrons will acquire lateral speed and displacements from their original direction. Therefore, as the electron beam passes through the patient, its energy decreases, and its angular dispersion increases.

Characteristics of Electron Beams

There is an area of more or less uniform dose followed by an abrupt drop, which is an advantage compared to X-rays.
This advantage tends to disappear with increasing energy.
In the higher energy range, X-ray contamination is present.
For a broad beam, the depth in centimeters at which the electrons give a dose of 80-90% is equal to about one-third to one-quarter of the energy of the electrons in MeV. Thus, for electrons of 13 MeV, the useful depth is 3-4 cm.
For therapeutic purposes in which electrons are used, the desired depth reaches 90%.

Range Concept

Electrons can interact with each atom they encounter, and in most of these interactions, they transfer a fraction of their kinetic energy. This energy is transferred gradually and continuously. The total range that a single electron travels is the total distance traveled until it stops, regardless of the direction of motion. The projected range is the sum of individual thicknesses, along the initial direction. The average thickness for an electron of initial energy E₀ is obtained by integrating the reciprocal of the total stopping power.

Maximum Range is defined as the depth that is located by extrapolating from the tail of the depth-dose curve.
Practical Range (R_p) is defined as the depth obtained by projecting the steepest part of the depth-dose curve.

Build-Up Region

(Thickness between Z_max and the surface) The dose build-up for electron beams is much less pronounced than in megavoltage photon beams, and scattering results from the interactions that the electrons experience with atoms of the absorber. At the time they enter the medium, the electron trajectories are approximately parallel; as they travel, the paths become more oblique in relation to the original direction, resulting in an increase in fluence in relation to the central axis of the beam.

In the collision process, it is possible that the kinetic energy gained by the ejected electron is much larger, which causes additional ionization. In this case, these electrons are referred to as secondary electrons, or delta rays, and they contribute to the dose build-up.

Unlike photon beams, the surface dose rate of an electron beam increases with electron energy. This can be explained by the nature of electron scattering. The lower the electron energy, the more easily it is scattered and through greater angles. The dose in the surface build-up region is lower for lower energy beams.