KAHIBARO
Table of Contents
What collisional energy loss means
When an electron moves through matter, it interacts with the atoms of the material. One important way it loses energy is by colliding electromagnetically with atomic electrons. In these interactions, the moving electron transfers part of its kinetic energy to the electrons in the medium. This process is called collisional energy loss.
For electrons, collisional energy loss mainly produces ionization and excitation of atoms. Ionization means an electron is removed from an atom. Excitation means an atomic electron is pushed to a higher energy state without leaving the atom. Both processes take energy from the incoming electron.
This chapter focuses only on energy loss by collisions with atomic electrons. Another important loss mechanism for electrons, bremsstrahlung, belongs to a separate topic.
Why electrons are special
Heavy charged particles such as alpha particles are much more massive than the electrons in the material. An incident electron is different because it has the same mass as the atomic electrons it interacts with. This has important consequences.
First, in a single collision, the incoming electron can lose a large fraction of its energy. Second, after a collision, it can be difficult to distinguish the original electron from the struck electron, because they are identical particles. Third, electrons are more easily deflected from their original path than heavy particles.
Because of this, electron tracks in matter are usually more tortuous and irregular than the nearly straight tracks of heavy charged particles.
Basic physical picture
As the electron passes near atoms, the Coulomb force acts between the incoming electron and the bound electrons of the material. If the interaction is weak, the atom may only be excited. If the interaction is strong enough, one of the bound electrons may be ejected from the atom.
The ejected atomic electron is often called a secondary electron, or delta ray if it has enough energy to travel a noticeable distance and cause further ionization.
The incoming electron loses energy step by step through many such interactions. Its energy does not decrease smoothly in a perfectly continuous way. Instead, the loss is statistical, with many small transfers and occasional larger ones.
Stopping power for electrons
A useful quantity is the rate at which the electron loses energy per unit path length. This is called the stopping power. For collisional losses, we write it as
$$
-\frac{dE}{dx}
$$
where $E$ is the electron energy and $x$ is distance traveled in the material.
The minus sign shows that the energy decreases as the electron moves forward.
For electrons, the collisional stopping power depends on the electron energy and on the properties of the medium, especially its electron density and mean excitation energy. In general, as the electron moves through matter, it undergoes many inelastic collisions, and the average energy lost per unit distance is described by this stopping power.
The collisional stopping power is the average energy loss rate due to ionization and excitation:
$$
\left( -\frac{dE}{dx} \right)_{\text{coll}}
$$
It is an average quantity. Actual energy loss fluctuates around this average.
Comparison with heavy particles
The general idea of collisional loss is similar for all charged particles, but electrons behave differently from heavy particles.
The most important differences are shown below.
| Feature | Heavy charged particles | Electrons |
|---|---|---|
| Mass compared with atomic electrons | Much larger | Equal |
| Path through matter | Nearly straight | Strongly scattered |
| Energy transfer in one collision | Usually small fraction of total energy | Can be large fraction |
| Identity with target electron | Different particle | Identical particle |
| Importance of radiative losses at high energy | Usually smaller | Often very important |
Because electrons are light, they are easily turned by electric fields inside atoms. Their actual path length can be much longer than the thickness of the material they penetrate.
Energy transfer in a collision
In a collision between an incoming electron and an atomic electron, a significant amount of energy can be transferred. Since both particles have the same mass, the kinematics allow large exchanges of energy.
In some collisions, the struck electron receives enough energy to become a fast secondary electron. Then both electrons may continue through the material, each producing further ionization and excitation.
This is one reason electron energy deposition is spread out in a complicated way. Instead of one straight particle leaving energy along a narrow line, electrons often create branching tracks through many secondary electrons.
Dependence on material
Collisional energy loss depends on how many electrons are available in the medium and how tightly they are bound. Materials with higher electron density generally produce greater collisional losses.
A useful idea is that the stopping power is related to the number of atomic electrons per unit volume. Dense materials tend to cause more frequent interactions over a given distance.
The atomic structure of the medium also matters through its mean excitation energy, often written as $I$. This quantity represents a characteristic energy scale for exciting or ionizing the atoms of the material.
Collisional loss increases when the electron encounters more atomic electrons per unit length of travel. Density and atomic composition of the absorber both matter.
Dependence on electron energy
The collisional stopping power does not stay constant as electron energy changes. At low and moderate energies, collisional losses are often the dominant mechanism. As energy becomes very high, radiative losses can become more important, especially in high atomic number materials.
For the collisional part alone, the dependence on energy is not simple, but the main beginner level idea is clear. The energy loss per unit distance is determined by the probability and strength of ionizing and exciting collisions, and these depend on how fast the electron is moving.
In many practical situations, one studies the total stopping power as
$$
\left( -\frac{dE}{dx} \right)_{\text{total}}
=
\left( -\frac{dE}{dx} \right)_{\text{coll}}
+
\left( -\frac{dE}{dx} \right)_{\text{rad}}
$$
but in this chapter we focus only on the first term.
Secondary electrons and local energy deposition
Not all the energy lost by the incident electron is deposited exactly at the collision point. If a secondary electron is energetic enough, it can travel some distance away before losing its own energy. This spreads the deposited energy over a region.
This is important in radiation physics and detector physics. A single incoming electron may produce many secondary electrons, and these secondaries contribute strongly to the total ionization pattern.
Low energy secondary electrons deposit their energy close to where they are produced. Higher energy delta rays can carry energy farther away.
Average behavior and fluctuations
Although stopping power is defined as an average, real electrons do not all lose energy in exactly the same way. Two electrons with the same initial energy entering the same material can follow different paths and undergo different collisions.
Some may suffer one large energy transfer early. Others may lose energy through many smaller interactions. This statistical variation is part of the nature of radiation transport in matter.
For electrons, fluctuations are especially important because individual collisions can transfer a substantial fraction of the particle's energy.
For electrons, energy loss is not perfectly uniform. It is a statistical process with many small collisions and occasional large energy transfers.
Practical significance
Collisional energy loss is the main reason electrons produce ionization in detectors and in biological tissue. It determines how electrons slow down and how they deposit energy along their path.
This process is central to radiation measurement, shielding, medical physics, and particle detection. Whenever an electron passes through matter and creates ion pairs or excites atoms, collisional energy loss is at work.
A simple summary
An electron moving through matter loses energy by transferring it to atomic electrons. This transfer causes excitation and ionization. Because the incident particle has the same mass as the electrons in the medium, large energy transfers are possible, strong scattering occurs, and many secondary electrons are produced. The average collisional energy loss is described by the stopping power,
$$
\left( -\frac{dE}{dx} \right)_{\text{coll}}
$$
and this quantity depends on both the electron energy and the material through which it moves.
Key idea:
For electrons in matter, collisional energy loss is the loss of kinetic energy due to electromagnetic interactions with atomic electrons, leading mainly to excitation, ionization, and the production of secondary electrons.