Nuclear radiation

Atomic nuclei can store far more energy than chemical bonds. When a high energy nucleus becomes a low energy nucleus, it needs to shed that excess energy somehow. It does this by emitting particles or waves that carry away most of that energy. These particles or waves move away from the nuclear material in all directions – they radiate away, and hence this phenomenon is called nuclear radiation.

A similar process can occur with sub-atomic particles. Some varieties of these can react to distribute their energy among various other kinds of particles or waves that radiate away. Because these particles or waves are also highly energetic, they behave in a very similar fashion to nuclear radiation and can largely be handled in the same way.

(By quantum mechanics, all particles are also waves and all waves can be represented as particles. Consequently, from here on out, we'll just use "particle" to refer to both particle and wave radiation behavior.)

Radioactivity

Nuclei with stored energy can be unstable. Given time, they can spontaneously decay, releasing their energy as radiation. These unstable nuclei are called radioactive, and the process of their decay is radioactivity. Note that, despite having similar sounding names, radioactivity is separate from radiation – if you protect yourself from one, you are not necessarily protecting yourself from the other. Penetrating radiation emerging from radioactivity can get through barriers that will keep the radioactive material out, and all the shielding in the world will not help you if the radioactive material can get to your side of the shielding.

Radioactive material where you do not want it is called radioactive contamination.

The original radioactive nucleus is called the parent nucleus, and the nucleus it decays into is called the daughter nucleus.

Sub-atomic particles behave in the same way, with unstable particles decaying to more stable particles by emitting radiation. They are also radioactive. However, sub-atomic radioactivity tends to occur at a much faster rate than nuclear radioactivity, such that it is essentially instant from a human time scale.

Radiactive decay

In any given span of time, a given fraction of the radioactive material in any sample (as measured from that present at the start of that span of time) will decay. It is convenient to find the time it takes for exactly half of the radioactive material to decay, this is called the half-life and is commonly denoted with $t_{1/2}$ in equations. In another half-life after the first, half of the remaining material will decay and thus you will be left with one-half of one-half of the original sample, or one quarter of the original amount. Similarly, after three half-lives, you will have $1/8$^th of the original material; after four half-lives, $1/16$^th of the original material, and so on. In general, after $n$ half-lives, $1/2^{n}$ of the original sample will still be present. After many half-lives, a sample will have decayed away to the point where it is negligible.

When doing calculations, the half-life can be inconvenient to use. It is more convenient to define a characteristic decay time $\tau$ which is related to the half-life by

$\tau ={\frac {t_{1/2}}{\ln[2]}}.$

After any arbitrary amount of time $t$ when starting with an amount $N_{0}$ of radioactive material, the amount of remaining material will be

$N(t)=N_{0}\exp[-t/\tau ].$

If $N$ is measured in number of atoms, the rate at which the decays occur is

$A=N/\tau .$

This rate is called the activity of the sample. Note that while a long half-life means that you need to deal with the radioactivity for a long time, the overall activity will be low. Meanwhile, an isotope with a short half life may go away quickly but will have a high activity during that time.

It is also occasionally useful to note that $\tau$ is the average life span of any given radioactive particle.

Decay chains

You can often find yourself in a situation where a parent nucleus decays into a daughter which is itself unstable. You can get a whole sequence of decays between unstable nuclei before you settle down into a stable state. This is called a decay chain.

It is important to keep decay chains in mind; just because a parent has gone through so many half-lives that essentially none is remaining it does not necessarily mean that all the radioactivity is gone if there are daughter products with longer half-lives that were produced by the sample.

Further, just because the parent to daughter decay might produce a relatively benign form of radiation does not mean that you don't get nastier radiation from decays further down the decay chain.

An example of a decay chain from one of the most common naturally occurring radioactive isotopes on our planet is

$\,^{238}{\rm {U}}\to \,^{234}{\rm {Th}}\to \,^{234}{\rm {Pa}}\to \,^{234}{\rm {U}}\to \,^{230}{\rm {Th}}\to \,^{226}{\rm {Ra}}\to \,^{222}{\rm {Rn}}\to \,^{218}{\rm {Po}}\to \,^{214}{\rm {Pb}}\to \,^{214}{\rm {Bi}}\to \,^{214}{\rm {Po}}\to \,^{210}{\rm {Pb}}\to \,^{210}{\rm {Bi}}\to \,^{210}{\rm {Po}}\to \,^{206}{\rm {Pb}}.$

The final daughter product, $\,^{206}{\rm {Pb}}$ is stable.

If you have a chain of daughters with half-lives that are much shorter than that of the parent, any initial excess of the daughter products in your sample will quickly decay away on the scale of a parent half-life to the point where the only daughter products present are those produced by the parent decay. Any initial deficit will build up over a similar time scale until the rate of production of the daughter products equals their rate of decay – and when you follow the chain back to the parent, the rate of production is the same as the rate of parental decay. Thus, all the daughter products in such a chain will have the same activity as the parent, until you reach a daughter product with a longer half-life. This is called secular equilibrium.

Kinds of radiation

Alpha

Alpha radiation what you get when an energetic nucleus sheds its energy by throwing off a helium-4 nucleus (often called an alpha particle when it is emitted as radiation). Helium-4 is very stable and tightly bound, thus favoring is emission over other nuclear particles such as protons. Alpha particles are short ranged in matter, as the massive alpha particles are slow-moving and highly charged, and thus leave tracks of very high levels of ionization that quickly sap off the kinetic energy and bring the particle to a stop. Alpha particles travel a few centimeters through air, and are stopped by a sheet of paper or the outer (dead) layer of your skin. Alpha radiation is mainly dangerous when it happens inside your body (see the sections on radioactivity and radioactive contamination, which despite the similar name are separate concepts from radiation). The high concentration of ionization from the alpha particles can cause serious biological effects on living cells.

Beta

Beta- radiation happens when a nucleus turns a neutron into a proton via the weak nuclear force; a process that emits an electron (the beta particle) and an electron anti-neutrino as radiation. The resulting proton stays inside the nucleus, but the electron and anti-neutrino escape. Neutrinos almost never interact with matter, so it can be ignored from here on out. However, the electron is charged so it will leave behind an ionization track. Because the electron moves much faster than an alpha particle (nearly the speed of light), it leaves a much sparser ionization track and thus has a significantly longer range through matter. Electrons from nuclear radiation can travel on the order of a meter through air, and can reach the living tissues of the skin, causing sunburn-like radiation burns. They can be stopped by a thin sheet of aluminum foil or a stack of several sheets of paper. If beta emission occurs inside an organism (likely because of internal radioactive contamination), it can cause whole body radiation exposure although the sparse ionization tracks are less damaging than those from alpha radiation of equal energy.

Beta+ radiation is a rarer process that happens when a proton turns into a neutron and emits an electron neutrino and a positron (the beta particle) as radiation. Again, the resulting neutron stays in the nucleus, but the neutrino and positron escape. The positron behaves almost the same way as the electron from beta- decay, except that at the end of the radiation track when it is slowed to a near stop it will encounter an electron and annihilate. This produces a pair of gamma rays (see below) of a very characteristic energy that can be used to identify beta+ activity.

Electron capture is a process that competes with beta+ activity. In this case, a proton turns into a neutron not by emitting a positron but by capturing one of the electrons orbiting the nucleus. This produces only the electron neutrino as radiation, although there may be some shake-up of the electron shell leading to x-rays and auger electrons.

Gamma

When a nucleus is in an energetic state that has the same number of protons and neutrons as a nucleus in a less energetic state, it can transition to the lower energy nucleus by emitting a gamma ray to conserve energy. A gamma ray is a quanta of oscillation of electromagnetic radiation with very high frequency. Essentially, as the electric charges in the nucleus re-arrange themselves into a more stable state with a rapid collapse of their configuration, some of the electric field they created is left behind in the process. This left-over field creates an oscillating electromagnetic wave that is called the gamma ray.

Nuclei with the same number of protons and neutrons but different internal configurations are called isomers of each other.

Gamma rays are extremely penetrating compared to alpha and beta radiation. They can be mostly stopped by several centimeters of lead, or on the order of a meter of concrete, water, or biological material. However, unlike charged alpha and beta radiation, gamma rays are uncharged. Hence, they do not have a fixed range in matter like alpha or beta particles. Instead, the probabilistic nature of their capture results in a situation similar to radioactive decay, were a fixed fraction of the incident gamma rays will be attenuated by any given thickness of a particular material. This leads to attenuation, with the intensity falling off as the Beer-Lambert law. There are three main processes by which gamma rays are attenuated:

Photoabsorption

When a gamma ray encounters an atom, its electromagnetic field can accelerate an electron away from the rest of the atom, giving all of the gamma ray's energy to the ejected electron. This is called photoabsorption, and the process is the photoelectric effect. The high energy electron produced behaves in all respects like the energetic electrons from beta decay; the main difference is that the highly penetrating nature of the gamma rays can act to produce the photoelectrons deep inside of a person or object even if no radioactive contamination is there.

Photoabsorption is the most important form of gamma ray attenuation at low energies and for lighter elements.

Compton scatter

A gamma ray that encounters an electron can scatter off the electron, imparting some of its energy to the electron and leaving in a different direction. The resulting energetic electron, again, behaves identically to the electrons produced by beta decay but, again, can be produced deep inside of a person or object. Although the incident gamma ray flux is decreased by the Beer-Lambert law, you get a build-up of scattered gamma rays in your system so the total gamma flux does not strictly follow the Beer-Lambert relationship. The scattered gamma rays can then go on to further interact with the environment until they either escape or are stopped through photoabsorption or pair production (the latter of which, of course, also tends to produce additional gamma rays).

Compton scatter can be the dominant form of gamma ray attenuation at intermediate gamma ray energies and is more important for heavy elements than light elements.

Pair production

When a gamma ray has enough energy, it can produce an electron and its antimatter counterpart (a positron) out of empty vacuum when it interacts with the electric field of a nearby atomic nucleus. These electrons and positrons then go on to act like the electrons and positrons from beta radiation, including the production of annihilation gamma rays at the end of the positron's track.

Pair production is the most important method of attenuation at high gamma ray energies. Although it can occur for any gamma ray at more than the energy threshold for producing an electron-positron pair, it only becomes significant at several times this threshold.

Photo-nuclear interactions

It is possible for gamma rays to directly interact with a nucleus. This is not usually an issue for gamma rays produced by nuclear radioactivity, but it can be significant for some applications when considering very high energy gamma rays from more exotic processes.

One method of nuclear-gamma interaction is when a gamma ray excites an otherwise stable nucleus to one of its more energetic isomers, getting absorbed in the process. This requires a gamma ray of very nearly exactly the same energy as the isomeric transition. In most cases, the isomer is so short lived that it immediately decays, producing gamma radiation of nearly the same energy as the incident gamma ray going in a random direction. This is called nuclear resonance fluorescence, or NRF. However, a small portion of the energy of the interaction goes into the recoil of the absorbing and emitting nucleus, so that the re-radiated gamma ray no longer has the right energy to further participate in nuclear resonance fluorescence. NRF might be useful in the future for scanning materials for elements or isotopes of interest, but has little relevance to the off-resonance gamma rays emitted by nuclear radioactivity or positron annihilation or the broad spectrum Compton scatter gamma rays and this is generally of little significance.

At gamma ray energies well above that of most nuclear decays, in the range of 8 to 15 MeV, you can get a process where the electric field of the gamma pulls on the charged protons of a nucleus, tugging them all in one direction. The neutrons, being uncharged, are not pulled by the gamma ray's field and are left behind. The nuclear force of the neutrons then pulls the protons back. If the protons respond in about the same amount of time it takes for the fluctuating electric field of the gamma ray to change direction, the gamma ray will now be pushing on the protons in the same direction that the neutrons are tugging on them, causing them to overshoot so that they are again pulled back by the neutrons and pushed back by the gamma's fields. In the same way that small periodic pushes of a child on a playground swing at just the right time can build up a high amplitude motion, a gamma ray at this resonance energy can put all of its energy into an excited nuclear state of the protons sloshing around in the opposite direction of the neutrons, called a giant dipole resonance. Giant dipole resonances usually decay by ejecting nuclear particles – neutrons, protons, or light ions such as alpha particles, deuterons, tritons, or helions – although for very heavy atoms you can induce fission instead. This latter effect is called photofission.

Internal conversion

Instead of creating a gamma ray, it is occasionally possible for an isomer to decay to a less energetic isomer by giving up its excess energy to one of the electrons orbiting the nucleus. This is called internal conversion. The electron that receives the energy gets kicked out of the nucleus and, again, acts like a beta electron as far as material interactions. Internal conversion competes with gamma ray emission for transitions between isomers.

Ions

Fission products