# Decay Schemes

All radioactive decays involve an unstable atom releasing particles and/or energy to reach a more stable state. The energy released in the transition is equal to the difference in mass between the original atom and the resulting atom and particles, and is known as the disintegration energy - denoted by the symbol Q.
The radioactive decay can be represented as a decay scheme. This is a diagram which displays the parent and daughter nuclide, arranged according to:

• Their atomic numbers
• The difference in energy between them

For radioactive decays, the daughter nuclide is drawn lower than the parent as there is a loss of energy during the decay. If the nucleus of the daughter nucleus has energy levels, these are drawn above the stable state.
Lines drawn between the parent nuclide, the daughter nuclide and any of its energy levels indicate the type of decay that occurs.

• Electron emission (beta minus) will increase the atomic number of the material and is denoted by a green arrow.
• Electron capture is a red arrow.
• Positron emission (beta positive) is a pink arrow
• Alpha decay is a double purple arrow
• Photon emission is a blue arrow

## Fate of Disintegration Energy

The disintegration energy may be given to particles as kinetic energy, released from the nucleus as a photon or through a combination of these mechanisms.

### Kinetic Energy

Example: The radioactive atom tritium (3H) decays through emission of an electron to stable helium-3 (3He). The disintegration energy - the difference in mass between the tritium and the helium-3 - is shared between the electron and the 3He nucleus as kinetic energy. Therefore, the electron may have a kinetic energy of between 0 keV to 18.6 keV. The mean energy of the electron is 5.7 keV.

This is a straightforward beta decay with no further emissions of gamma photons. The most important feature of this decay is that the released particles possess a spectrum of energies up to the maximum energy possible.

### Photon Emission

Example: The radioactive atom 99mTc mostly decays through emission of a single photon with energy of 143 keV to its ground state of 99Tc. Unlike the release of an alpha or beta particle, the gamma photon always has an energy of 143 keV - there is no spectrum of energies in this scenario.

This decay scheme is not entirely accurate, as there is a 0.003 chance of beta decay to 99Ru.
When the nucleus has several energy levels, a series of photons may be released. Each photon has discrete energies related to the energy levels of the nucleus. The best example is 60Co - see below.

### Combination

Example: The radioactive atom 192Ir is commonly used in brachytherapy applications. It may decay through electron emission (95%) or electron capture (5%), and then releases a spectrum of photons with discrete energies.

192Ir decays through numerous processes and its daughter nuclei have multiple energy levels. However, all the electrons will be released with a spectrum of energies ranging from 0 keV to the maximum energy; and all gamma photons will be released at discrete energies depending on the nuclear energy levels.

## Alpha decay

Alpha particle decay occurs in unstable atoms with an atomic number of 82. The theory is that when the number of protons climbs over this number, the repulsive Coulomb forces (charge) are able to overcome the attractive strong nuclear forces. Alpha decay involves the ejection of two protons and two neutrons.

(1)
\begin{align} ^A_Z\text{X} \rightarrow ^{A-4}_{Z-2}\text{Y}+ ^4_2\text{He} + Q \end{align}

In the above equation, element X is the original atom with an atomic number of Z and an atomic mass of A. Element Y is the daughter nucleus after the release of the helium atom/alpha particle, and Q refers to the distintegration energy which is given to the two nuclei as kinetic energy.

The most important alpha decay process in radiation oncology is that of radium 226 to radon 222.

(2)
\begin{align} ^{226}_{88}\text{Ra} \rightarrow ^{222}_{86}\text{Rn}+ ^4_2\text{He} + 4.87 \text{MeV} \end{align}

## Beta Decay

Beta decay occurs when an atom possesses an excess of neutrons relative to protons, or protons relative to neutron.

### Beta negative decay / electron generation

In the former, a neutron is converted to a proton, releasing an electron and antineutrino in the process. This is beta negative decay.

(3)
\begin{align} ^A_Z\text{X} \rightarrow ^{A}_{Z+1}\text{Y}+ ^{-1}\beta^- + \tilde{\nu}+ Q \end{align}

There are numerous radionuclides that decay through beta negative decay, but the most relevant for radiation oncology is:

(4)
\begin{align} ^{60}_{27}\text{Co} \rightarrow ^{60}_{28}\text{Ni}+ \beta^- + \tilde{\nu}+ Q \end{align}

### Beta positive decay / position generation

When the number of protons exceed the number of neutrons, the atom may achieve stability by converting a proton into a neutron and releasing a positron and a neutrino.

(5)
\begin{align} ^A_Z\text{X} \rightarrow ^{A}_{Z-1}\text{Y}+ \beta^+ + \nu+ Q \end{align}

An important reaction in nuclear medicine is that seen in PET Scanning:

(6)
\begin{align} ^{18}_9\text{F} \rightarrow ^{18}_{8}\text{O}+ \beta^+ + \nu+ Q \end{align}

The positron released in the above reaction will annihalate with an electron, releasing annihalation energy (0.51 MeV) which is then detected in the patient.

## Electron Capture

Electron capture is a special form of beta decay, where instead of converting a proton into a neutron and releasing a positron, the nucleus consumes an orbital electron and releases disintegration energy and a neutrino.

(7)
\begin{align} ^A_Z\text{X} + ^0_{-1}\text{e} \rightarrow ^{A}_{Z-1}\text{Y}+ \nu+ Q \end{align}

This reaction occurs in some brachytherapy sources, including iodine-125.

(8)
\begin{align} ^{125}_{53}\text{I} + ^0_{-1}\text{e} \rightarrow ^{125}_{52}\text{Te}+ \nu+ Q \end{align}

## Gamma Decay

Gamma decay is the release of high energy photons from an excited nucleus. After undergoing decay through one of the methods above, the nucleus may be in a higher energy state (similar to an excited electron existing in a higher energy shell). The nucleus releases this energy is a gamma ray.

(9)
\begin{align} ^{Am}_Z\text{Y} \rightarrow ^{A}_{Z}\text{Y} + \gamma \end{align}

This is a very common occurence, although the 'm' (standing for metastable state) is only used when the nucleus remains in the excited state for some period of time. A commonly cited example is that of the isotope frequently used in nuclear medicine, 99mTechnetium

(10)
\begin{align} ^{99m}_{43}\text{Te} \rightarrow ^{99}_{43}\text{Te} + \gamma^{140 keV} \end{align}

Many brachytherapy sources decay through electron capture or beta decay, leaving the daughter nucleus in an excited state. This is released as a gamma photon. This gamma photon is the clinically desired part of the radioactive decay process, and shielding is used to filter out the less penetrating electrons.

## Internal Conversion

Internal coversion is related to gamma decay. Instead of releasing a gamma photon, the energy may be transferred to an orbital electron (this may be considered to be some type of short range photoelectric effect). The electron is ejected from the atom as an Auger electron. When another electrons falls into the hole left by the Auger electron, characteristic x-rays may result (depending on the K-Shell energy).