Radiation Physics for Medical Physicists.Interaction of charged Particle with matter

Radiation Physics for Medical Physicists

5 Interaction of charged Particles with Matter

5.1 General Aspects of Stopping Power

5.2 Radiative Stopping Power

5.3 Collision Stopping Power for Heavy Charged Particles
5.3.1 Momentum Transfer from Heavy Charged Particle to Orbital Electron
5.3.2 Linear Collision Stopping Power

5.4 Mass Collision Stopping Power

5.5 Collision Stopping Power for Light Charged Particles

5.6 Total Mass Stopping Power

5.7 Bremsstrahlung (Radiation) Yield

5.8 Range of Charged Particles

5.9 Mean Stopping Power

5.10 Restricted Collision Stopping Power

5.11 Bremsstrahlung Targets

5 Interaction of charged Particles with Matter

In this chapter we discuss interactions of charged particle radiation with matter. A charged particle is surrounded by its Coulomb electric force field that interacts with orbital electrons (collision loss) and the nucleus (radiative loss) of all atoms it encounters as it penetrates into matter.

The energy transfer from the charged particle to matter in each individual atomic interaction is generally small, so that the particle undergoes a large number of interactions before its kinetic energy is spent.

Stopping power is the parameter used to describe the gradual loss of energy of the charged particle as it penetrates into an absorbing medium.

Two classes of stopping powers are known:

• collision (ionization) stopping power that results from charged particle interaction with orbital electrons of the absorber and
• radiative stopping power that results from charged particle interaction with nuclei of the absorber.

Stopping powers play an important role in radiation dosimetry. They depend on the properties of the charged particle such as its mass, charge, velocity and energy as well as on the properties of the absorbing medium such as its density and atomic number.

In addition to stopping powers, other parameters of charged particle interaction with matter, such as the range, energy transfer, mean ionization potential, and radiation yield, are also discussed in this chapter.

5.1 General Aspects of Stopping Power

As a charged particles travels through an absorber, it experiences Coulomb interactions with the nuclei and the orbital electrons of the absorber atoms.

These interaction can be divided into three categories depending on the size of the classical impact parameter b compared to the classical atomic radius a:

1. Coulomb force interaction of the charged particle with the external nuclear field (bremsstrahlung production) for b <<>
2. Coulomb force interaction of the charged particle with the orbital electron for b ≈ a (hard collision).
3. Coulomb force interaction of the charged particle with the charged particle with orbital electron for b >> a (soft collision)

Generally, the charged particle experiences a large number of interactions before its kinetic energy is expended.

In each interaction the charged particle's path may be altered (elastic or inelastic scattering) and it may loss some of its kinetic energy that will be transfered to the medium (collision loss) or to the photons (radiative loss).

Radiative, hard and soft collisions are shown schematically in Fig. 5.1, with b the impact parameter and a the atomic radius.

1. The rate of energy loss per unit of path length by a charged particle in a medium is called the linear stopping power (dE/dx).
2. The stopping power is typically given in units MeV.cm²/g and then referred to as the mass stopping power S equal to the linear stopping power divided by the density ρ of the absorbing medium.
3. The stopping power is a property of the material in which a charged particle propagates.

Two types of stopping powers are known:

1. Radiation stopping power that result from charged particle Coulomb interaction with the nuclei of the absorber. Only light charged particles (electrons and positions) experience appreciable energy losses through these interactions that are usually referred to as bremsstrahlung interactions.
2. Collision (ionization) stopping power that results from charged particle Coulomb interactions with orbital electrons of the absorber. Both heavy and light charged particles experience these interaction that result in energy transfer from the charged particle to orbital electrons, i.e., excitation and ionization of absorber atoms.

The total stopping power Stot for charged particle of energy EK traveling through an absorber of atomic number Z is the sum of the radiative and collision stopping power, i.e.

Stot = Srad + Scol

5.2 Radiative Stopping Power

The rate of bremsstrahlung production by light charged particles (electrons and positrons) traveling through an absorber is expressed by the mass radiative stopping power Srad (in MeV.cm²/g) which is given as follows:

Srad = NaσradEi (5.2)

where

Na is the number of atoms per unit mass: Na = N/m = NA /A

σrad is the total cross section for bremsstrahlung production given for various energy range in Table 5.1

....................................................

Ei is the initial total energy of the light charged particle, i.e., Ei = EKi+mec²

EKi is the initial kinetic energy of the light charged particle.

Inserting σrad for non-relativistic particles from Table 5.1 into (5.2) we obtain the following expression for

(5.3)

Where Brad is a slowly varying function of Z and Ei, also given in Table 5.1 and determined from
. The parameter Brad has a value of 16/3 for light charged particles in the non-relativistic energy range