KAHIBARO
Table of Contents
Basic idea
Electron capture is a type of beta decay in which a nucleus absorbs one of its own atomic electrons. This usually happens with an electron from an inner shell, most often the $K$ shell, because those electrons spend the most time close to the nucleus.
In this process, a proton inside the nucleus changes into a neutron. At the same time, an electron neutrino is emitted. The reaction is
$$
p + e^- \rightarrow n + \nu_e
$$
Inside an atom, we often write electron capture as
$$
{}^{A}_{Z}X + e^- \rightarrow {}^{A}_{Z-1}Y + \nu_e
$$
The mass number $A$ stays the same, because the total number of nucleons does not change. The atomic number $Z$ decreases by 1, because one proton becomes a neutron.
What changes in the atom
When the nucleus captures an inner electron, it leaves a vacancy in the electron shell. Electrons from higher shells then fall down to fill the empty place. As they do, the atom releases energy, usually in the form of characteristic X rays or sometimes Auger electrons.
So electron capture has two parts to notice. The nuclear part is the conversion of a proton into a neutron. The atomic part is the rearrangement of the remaining electrons.
In electron capture, the nucleus emits a neutrino, not an electron.
$$
{}^{A}_{Z}X + e^- \rightarrow {}^{A}_{Z-1}Y + \nu_e
$$
Important results:
$A$ is unchanged, $Z$ decreases by 1.
Comparison with beta-plus decay
Electron capture is closely related to beta-plus decay. In both processes, a proton turns into a neutron. The difference is how this happens.
In beta-plus decay,
$$
p \rightarrow n + e^+ + \nu_e
$$
In electron capture,
$$
p + e^- \rightarrow n + \nu_e
$$
Both processes move the nucleus toward a more stable neutron to proton ratio. Electron capture is often possible when beta-plus decay is not energetically allowed. Beta-plus decay must create a positron, and creating a positron requires extra energy. Electron capture does not need to create that positron.
Why inner electrons are captured
The nucleus is extremely small, and only electrons with significant probability density near the nucleus are likely to be captured. Inner-shell electrons, especially $s$ electrons, have the greatest chance because their wave functions are nonzero at the nucleus.
This is why $K$ capture is the most common form. Sometimes capture can also occur from the $L$ shell or higher shells, but it is less probable.
Energy considerations
For electron capture to occur spontaneously, the initial atom must have more energy than the final atom. The energy difference appears mainly as kinetic energy of the neutrino and as atomic radiation from shell rearrangement.
A simple way to express the reaction energy is through the $Q$ value. Using atomic masses, electron capture is energetically allowed when
$$
Q = \left[M(X) - M(Y)\right]c^2 > 0
$$
Here $M(X)$ and $M(Y)$ are the atomic masses of the parent and daughter neutral atoms.
Because no positron has to be created, electron capture can occur for some nuclei that cannot undergo beta-plus decay.
Using atomic masses, electron capture is allowed if
$$
Q = \left[M(X) - M(Y)\right]c^2 > 0
$$
This is less restrictive than beta-plus decay, which needs additional energy to create a positron.
Example of electron capture
A classic example is beryllium 7:
$$
{}^{7}_{4}\mathrm{Be} + e^- \rightarrow {}^{7}_{3}\mathrm{Li} + \nu_e
$$
The beryllium nucleus has 4 protons and 3 neutrons. After capture, one proton becomes a neutron, so the lithium nucleus has 3 protons and 4 neutrons. The mass number remains 7.
Another well known example is potassium 40, which can decay in more than one way, including electron capture.
Observable signals
Electron capture can be harder to detect directly than beta-minus or beta-plus decay because no energetic charged beta particle has to emerge from the nucleus. Instead, experiments often detect the secondary effects:
| Signal | Origin |
|---|---|
| Characteristic X rays | Electrons fall into the inner-shell vacancy |
| Auger electrons | Atomic shell rearrangement transfers energy to another electron |
| Gamma rays | Daughter nucleus may be formed in an excited state |
| Neutrino | Emitted in the nuclear reaction, but very hard to detect |
If the daughter nucleus is left in an excited nuclear state, it may later emit a gamma ray. That gamma ray is from the nucleus, while X rays are from the electron cloud.
Change in nuclear composition
It is useful to track the nuclear numbers carefully.
| Quantity | Before capture | After capture |
|---|---|---|
| Protons | $Z$ | $Z-1$ |
| Neutrons | $A-Z$ | $A-Z+1$ |
| Mass number | $A$ | $A$ |
This shows clearly that one proton turns into a neutron, while the total number of nucleons stays fixed.
Simple schematic
A note about the atomic electron
The captured electron usually belongs to the atom itself, not to an outside beam of electrons. Since the process depends on the presence of inner electrons, the decay rate can be affected slightly by the chemical environment, because chemical bonding changes the electron distribution a little. This effect is usually small, but it is more noticeable for electron capture than for many other nuclear decay modes.
Summary
Electron capture is a decay mode in which a nucleus absorbs an inner atomic electron, converting a proton into a neutron and emitting an electron neutrino. The nuclear charge decreases by 1, the mass number stays the same, and the atom often emits X rays or Auger electrons afterward because of the empty inner-shell vacancy.
Core facts of electron capture:
$$
{}^{A}_{Z}X + e^- \rightarrow {}^{A}_{Z-1}Y + \nu_e
$$
One proton becomes one neutron.
Atomic number changes as
$$
Z \to Z-1
$$
Mass number stays
$$
A \to A
$$