Nuclear Engineering

Interaction of energetic charged particles with matter

To understand the interaction of charged (alpha, beta, heavy ions etc. ) and neutral particles (photons, neutron, neutrino) with matter is of paramount importance in nuclear detector technology. The energy deposited by these particles in the materials via various physical processes is converted to electrical signals, which eventually gives information about the particles. In this section we will discuss the interaction of charged particles and photons with matter.

*How charge particles loose energy in matter?*

When a charged particle interacts with any atoms of any material medium, it loses its energy via two mechanisms : (i) by collision with the atom and (ii) by exciting and ionizing the target atom. The first process is an elastic collision process and popularly known as nuclear energy loss and the second is an inelastic process and is known as electronic energy loss. In order to understand the nuclear energy loss process, let me first set up basic equations related to a momentum transfer process when two objects collide.
Consider a two body collision process where a particle of mass m ₁ and velocity v, energy E ₀ ( = ½ m ₁v ²) hits another body ( at rest ) of mass m₂ . After collision the projectile scatters at an angle α and the target atom recoils with an angle θ as shown in Fig. m2.4.


FIGURE m2.4: Schematic representation of elastic collision between two bodies of masses m₁ and m₂.

The energy of the projectile becomes E₁ and that of target atom becomes E₂ after scattering and recoiling respectively. Let us now write down the energy-momentum conservation in the parallel and perpendicular to the direction of incidence as per the following mathematical equations:¹
Conservation of energy gives,


Conservation of momentum along incident ion direction gives,


Conservation of momentum perpendicular to the direction of incident ion gives,


Eliminating q and v₂ from the above equations one finds the following relations:


and hence

The energy ratio, called the kinematic factor K =E ₁/E ₀, shows that the energy after scattering is determined only by the masses of the particle and target atom and the scattering angle. For direct backscattering of 180⁰ , the energy ratio has its lowest value given by

And at 90⁰ is given by

In collisions where m ₁ = m ₂, the incident particle is at rest after the collision with all the energy transferred to the target atom. For α =180⁰ , the energy E ₂ transferred to the target atom has its maximum value given by





with general relation given by

Therefore, it is clear from the above analysis that incident particle loses its energy while travelling inside the material by elastic collision process. The energy loss per unit length (dE/dx) by the elastic collision process is known as nuclear energy loss and is denoted by S_n . Similarly, another component of energy loss, i.e. due to inelastic collision with electrons can be determined.^1,2 Let us make a simple picture of this collision process (Fig. m2.5), which was considered by Bohr 1913.


	FIGURE m2.5: Schematic representation of collision of an ion with electrons of an atom


In his picture a particle of charge Z_e, mass M and velocity v passing through an atomic electron of mass m e at a distance p. As the particle passes through the material, it delivers its energy to the electrons of the atoms via Coulomb interaction and consequently loses its energy in the medium. As the excitation and ionization process enhances with increase in incident particle energy, the energy loss per unit path length (dE/dx)_e or S _e increases with increase in incident particle energy. However, at very high energy the probability of excitation and ionization drops down and hence the energy loss. Detailed mathematical formulation can be found in the literature^1,2 . A simulation code based on Monte-Carlo simulation* process and considering the physical processes involved in both nuclear and electronic energy loss, have been developed by Z. F. Ziegler, which is known as transport of ions in matter (TRIM)³ .
In tutorial section you will see how these energy losses change with increase in incident ion energy in various media as per TRIM simulation.
Let me now define the range and straglling of charge particles inside matter, two important physical quantities related to energy loss process. When charged particle passes through a material, due to energy loss by above two processes, it slows down and eventually stops after traversing certain distance inside the material. This distance is known as the range of that particle for that particular particle and material combination. It is obvious that range increases with increase in incident particle’s energy. Now if we fix the energy and increase the density of the material, the range will decrease as the particle receives more atoms inside to interact with. However, as the irradiation is basically by many such charged particles, the energy loss is statistical process, i.e. some particles might stop before the average distance (range) it was supposed to go and some particles stop after this distance.
We can understand this point better from the following experiment:
Monoenergetic alpha particles from a collimated source are collected by a detector after passing through an absorber of variable thickness (Fig. m2.6).



	FIGURE m2.6 Schematic of alpha particle transmission experiment


For small values of absorber thickness, there is no change in the intensity of transmitted particle. With the increase in thickness, as the range is approached the intensity drops, though not as abruptly as expected the range to be a well-defined quantity. Instead the curve slopes down over a certain spread of thickness. This indicates that the energy loss process is a statistical phenomenon, as the two identical particles having same initial energy will not suffer the same number of collisions. This phenomenon is known as range straggling as indicated in Fig. m2.6. This distribution can be considered Gaussian as a first approximation, and the mean value of the distribution is known as the mean range corresponds to the mid point as shown in the figure. Without considering multiple Coulomb scattering, the mean range of a particle of a given energy T₀, can be written by integrating the dE/dx formula,


This is an approximation of straight line range. If the multiple Coulomb scattering is considered, the path will be zigzag and will be slightly longer than the straight line path length¹ .

—————————————————————————————— *Monte-Carlo simulation is a computer based simulation of physical process considering a random number generator. ——————————————————————————————————-

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Interaction of energetic charged particles with matter

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