Charged Particle Interactions

Charged particles that are of radiobiological concern are electrons (p particles), protons, and a particles. Neutrons are uncharged, of course, but they mostly inter­act by colliding with protons, and the protons then become energetic charged par­ticles. All charged particles interact with the cloud of electrons circulating around the nucleus in atoms by colliding with them and exciting or ionizing the atom, creating what is called an ion pair. The end result of charged particle interactions is to ionize atoms and give energy to electrons, which go on to cause further inter­actions. This is similar to the process shown in Figure 7.1, except that it is due to
a charged particle instead of a photon, and the charged particle continues on its way with slightly less energy.

Each time a charged particle ionizes an atom, the charged particle loses about 34 eV of energy. Frequently a cluster of about three ionizations occurs in a very small volume, so on average an interaction of a charged particle with matter results in the particle giving up about 100 eV of energy to the matter (3). As a result, the charged particle slows down. This transfer of energy from the charged particle to the matter is called the “Stopping Power” (S) or the “Linear Energy Transfer” (LET) of the particle. Specifically, the Stopping Power or LET is the rate of energy loss of a charged particle per unit of distance traveled. Hans Bethe developed an equa­tion to describe the Stopping Power mathematically (4). This equation says that the Stopping Power is proportional to the square of the charge (Z) of the charged particle and inversely proportional to the square of its velocity (v). Mathematically,

Подпись: SZL

V2

The implication of the Bethe-Bloch equation, as it is usually called, is that heavy charged particles, such as protons or a particles, move in a straight line through matter, losing energy to electrons and gradually slowing down. As they slow down, they give up energy at a faster rate, ending up in a very dense cluster of energy deposition called the Bragg peak. Also, because the Z of an a particle is 2 while the Z of a proton is 1, an a particle gives up its energy 4 times faster than a proton. As a result of this pattern of energy deposition, heavy charged particles move a defi­nite distance in matter and then come to a complete stop. This is called the range of the particle. Beyond that range, no energy can be given to the matter, so there are no further effects from the radiation. This property of heavy charged particle interactions is the basis for cancer therapies using heavy ions such as protons or carbon nuclei. The radiation penetrates into the tumor but cannot pass completely through it into surrounding normal tissue because its range is very well defined. This allows a very high dose to be given to the tumor but little to the normal tissue.

Electrons have charged particle interactions and also follow the Bethe-Bloch equation, but there is a critical difference. Since they are very light, when they knock an electron out of its orbit to ionize an atom, they are deflected like pool balls collid­ing. As a result, electrons have a zig-zag path as they move through matter and scat­ter their energy over a broader path than a heavy charge particle. They also do not have a well-defined range but gradually taper off as they move deeper into matter.

These interactions of photons and charged particles explain why different types of radiation have different abilities to penetrate into matter. Photons such as у and X-rays are the most penetrating, being able to go through several centime­ters or meters of tissue, depending on their energy. Electrons can penetrate a few microns (millionths of a meter) up to a centimeter in tissue, depending on their energy. Alpha particles can only penetrate a few microns in tissue and are easily stopped by a piece of paper or the outer layer of skin cells.

Neutron Interactions

There is one other type of radiation that we have not yet considered, namely neutrons. Since many neutrons are produced in a nuclear reactor and are funda­mental to its operation, it is important to also understand their interactions with matter. Neutrons do not have a charge so they cannot directly interact with elec­trons. Instead, neutrons crash into the nucleus and can bounce off while giving up part of their energy in what are known as elastic collisions. When a neutron hits a hydrogen nucleus, which is just a single proton, it bounces off, just like pool ball collisions, and gives energy to the proton. When it hits a heavier nucleus, it is more like a pool ball hitting a bowling ball, so the neutron bounces off but the heavy nucleus does not move much and the neutron does not lose much energy. The best way to slow down neutrons is to use material that has a lot of hydrogen nuclei. This is the reason that Fermi got a high rate of fission when he put paraffin between his source of neutrons and uranium, since paraffin has a lot of hydrogen to slow neutrons down, and slow neutrons are essential for fission to occur (see Chapter 6). It is also why water is used as a moderator in most nuclear reactors, since water (H2O) also has a lot of hydrogen. As the neutron gives up energy to a proton, the proton then becomes an energetic charged particle and gives up its energy according to the Bethe-Bloch equation, as discussed above. Since our cells are about 85% water (5) and our bodies are about 60% water, we are also good absorbers of neutrons, so shielding of neutrons is extremely important around nuclear reactors.

Neutrons can interact by another method known as inelastic collisions. Since the neutron has no charge, it can actually penetrate the nucleus and is sometimes captured by the nucleus to form a new isotope. Hydrogen can capture a slow neutron to become deuterium (hydrogen with 1 proton and 1 neutron or 2 H) and deuterium can capture a slow neutron to become tritium (hydrogen with 1 proton and 2 neutrons or 3H). This is also the process that produces transuranic elements when uranium captures a neutron and, instead of fissioning, becomes a new element, as described in Chapter 6. Sometimes neutrons can knock a proton out of a nucleus and change it into a new element. The carbon isotope ^C that is important for radiocarbon dating is produced in the upper atmosphere by neutrons from outer space that crash into nitrogen (^N) and are absorbed while knocking out a proton. And, of course, under the right circumstances, neutrons can be absorbed by uranium or plutonium isotopes and cause fission.

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