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 radiation is very common after alpha or beta decay, as the earlier decay very often leaves the daughter nucleus in an excited isomeric state. Usually, this happens so quickly afterward that the gamma emission seems essentially coincident with the alpha or beta decay. However, there are some decays that can leave a nucleus in a long-lived isomer which can persist for some time under the usual behavior of radioactive materials. Often, an excited isomer will decay to another, albeit lower energy, excited isomer which can itself decay. This leads to a gamma cascade, where the nucleus emits many gamma rays as it decays (usually with most of them within so short a time period that they seem to be simultaneous).

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.

Neutron

Neutrons are not usually emitted by radioactive decay (although some very short lived isotopes that undergo beta decay can also emit a neutron in the process). However, neutrons are emitted in copious amounts by fission and (especially) fusion reactions. They are also produced by various high energy processes that can knock off bits of atomic nuclei or even make the nuclei disintegrate into fragments, such as high energy particle beams or antimatter annihilation.

Neutrons make for very penetrating radiation, on the same order of penetration as gamma rays. However, while gamma rays are best stopped by heavy elements the best ways to stop neutrons is with light elements. Neutrons, being uncharged, do not leave behind ionization tracks. Instead, they lose their energy by interacting directly with nuclei.

Elastic collisions

The most straightforward kind of interaction is one where the neutron simply strikes and then bounces off a nucleus. The struck nucleus will recoil when the neutron rebounds, and the energy of the original neutron is now distributed between the recoil energy of the nucleus and the kinetic energy of the scattered neutron. The closer in mass the nucleus is to the neutron, on average the more of the neutron's energy will be transferred to the nucleus. For a neutron bouncing off an individual proton with nearly the same mass, the effect is analogous to billiard balls striking each other with, on average, the neutron losing half of its energy to the proton with each bounce. For heavier nuclei, the effect would be more analogous to a billiard ball striking a bowling ball, with the billiard ball rebounding with most of its original energy and little energy going into the bowling ball. Thus hydrogen (with its nucleus of just a single proton) is the best shielding material against energetic neutrons. It will usually take repeated collisions for a fast neutron to be slowed down to the point that it can be absorbed.

The recoil nucleus becomes an energetic ion, and thus will leave behind a dense ionization track that is particularly effective at causing biological damage.

Neutron capture

Sometimes, when a neutron hits a nucleus, instead of bouncing off it might stick. This adds the neutron's energy to that of the new nucleus, giving an excited isomer that usually decays by producing a gamma ray. Occasionally, however, the isomer can decay by spitting off charged particles instead. Neutron capture is more likely for lower energy neutrons, so high energy neutrons entering a material may need to bounce around for many collisions before they are slow enough to be absorbed in this fashion.

Nearly any isotope can absorb a free neutron, but some isotopes are better at this than others. Some are much better. $\,{157}{\rm {Gd}}$ has the best neutron capture cross section of any stable isotope, and $\,{155}{\rm {Gd}}$ is also a spectacularly good neutron capture isotope. So spiking a material with gadolinium can help it sop up excess neutrons. Similarly, $\,{10}{\rm {B}}$, $\,{6}{\rm {Li}}$, and $\,{113}{\rm {Cd}}$ have an exceptionally high neutron capture cross sections. The former two even lose their capture energy by emitting alpha particles (although $\,{10}{\rm {B}}$ also emits a gamma ray) so pose less of a gamma hazard.

In any event, neutrons present in a material will produce gamma rays, so once the neutrons are stopped you will then need to worry about the gammas.

Inelastic collisions

If a neutron slams into a nucleus hard enough, it can knock off bits of it. These bits can be other neutrons, protons, deuterons, tritons, helions, alpha particles, or occasionally even heavier nuclei. It can also happen that the neutron collision just excites the nucleus to a higher energy isomer before it bounces off, which will gamma decay. All of these inelastic collisions take away more energy from the incident neutron than elastic collisions where the neutron just bounces off while leaving the nucleus in its original state. Thus, for very high energy neutrons you can get by with fewer collisions to bring the neutron down to energies low enough for capture than you would by elastic collisions alone. At the price, of course, of producing additional radiation you need to shield against.

Fission

When a neutron hits a very heavy nucleus, it can impart enough energy to make it deform and elongate. Because the two ends of the elongated nucleus are both very highly positively charged, they strongly electrically repel each other. Normally, this is countered by the strong nuclear force gluing the nuclear particles together, but if the nucleus elongates it gives a lower cross sectional area for the nuclear force to stick the nucleus together. This leads to a runaway process, with the two ends pushing each other apart as the center thins out, forms a neck, and finally snaps. Which leaves two now separate new nuclei where once there was one; usually with one nucleus a bit heavier than the other. This process is called fission.

The fission process typically flings off some excess neutrons that are not needed in either of the two new nuclei. The rapidly changing charge configuration also usually throws off several gamma rays. In addition, the two halves of the original nucleus are thrown apart violently by their mutual electric repulsion, giving two heavy ions to go careening through the material. The exact energy and particle distribution will vary from fission to fission, but "typical" values might be

• Ions: 165 MeV distributed between the two ions, of which the light ion has about 2/3 the energy of the heavy ion.
• Neutrons: 5 MeV; split among an average of about 2.5 neutrons with approximately 2 MeV each.
• Prompt gamma rays: 8 MeV, typically 1-2 MeV each
• Delayed gamma rays from subsequent beta decay of the fission fragments: 7 MeV, typically 1-2 MeV each
• Delayed beta particles from subsequent beta decay of the fission fragments: 7 MeV, typically 1-2 MeV each
• Delayed neutrinos from subsequent beta decay of the fission fragments: 12 MeV (one for each beta particle produced)

For some heavy nuclei, the energy of neutron capture is enough to do kick-start this process and thus will readily fission in the presence of thermal neutrons. These isotopes are called fissile. Other isotopes can fission but which usually do not do so unless hit hard enough by a fast neutron (or which can photofission by having a high energy gamma ray excite their giant dipole resonance). Any isotope that can undergo fission, fissile or not, is called fissionable.

Neutron energy

Neutrons are often characterized by their energy. Those released by nuclear processes initially have enough energy that they are classified as fast neutrons. Fast neutrons scatter via elastic and inelastic collisions until they lose enough energy to fall below the inelastic thresholds. They then enter an epithermal energy regime. Epithermal neutrons are still moving fast enough that neutron capture is unlikely, so they go through the long, slow (for atomic scale processes, still instant on human time scales) process of losing energy by elastic scatters. Finally, the neutrons lose so much energy that they have nearly the same kinetic energy as the nuclei around them. These are called thermal neutrons, and they can no longer lose energy (on average) by colliding with the nuclei of the material. It is thermal energy neutrons that are most susceptible to neutron capture and removal from the system.

Ions

A fast moving nucleus careening through a material will leave extensive ionization tracks. These ions can come from fission, from particle accelerators, … and the alpha particles from alpha decay are also ions. Ions thus behave much like alpha particles, although heavier ions will be even more highly charged and leave even denser ion tracks. The way ions slow down in matter is discussed extensively in the particle accelerator page. For rough purposes, they can often be considered as extra damaging alpha particles.