KAHIBARO
Table of Contents
What Internal Conversion Is
Internal conversion is a way an excited nucleus can lose energy without emitting a gamma ray. Instead of sending the energy out as a photon, the nucleus transfers its excitation energy directly to one of the atom's own electrons. That electron is then ejected from the atom.
So the process starts with an excited nucleus, written schematically as
$$
{}^{A}_{Z}X^* \to {}^{A}_{Z}X + e^-
$$
Here the star means the nucleus is in an excited state. The emitted electron is called a conversion electron.
This is called internal conversion because the nuclear energy is converted internally into the kinetic energy of an atomic electron.
Internal conversion is not the same as gamma emission.
In gamma decay, the nucleus emits a photon.
In internal conversion, the nucleus gives its energy directly to an orbital electron, which is expelled from the atom.
How the Process Happens
The nucleus and the atomic electrons are very close to each other. Because of this, an excited nucleus can interact with an inner-shell electron, especially one in the K shell or L shell. If the nuclear transition energy is large enough, that electron can be knocked out of the atom.
The energy balance is simple. The excited nucleus has transition energy $E_\gamma$, which is the energy that would have been carried by a gamma photon if gamma emission had occurred. In internal conversion, part of that energy is used to remove the electron from the atom, and the rest becomes the electron's kinetic energy.
If the electron comes from a shell with binding energy $E_b$, then approximately
$$
K_e = E_\gamma - E_b
$$
where $K_e$ is the kinetic energy of the emitted conversion electron.
This means conversion electrons have discrete energies, because atomic binding energies are discrete.
For internal conversion to occur, the nuclear transition energy must exceed the binding energy of the electron being ejected.
$$
E_\gamma > E_b
$$
Internal Conversion Compared with Gamma Emission
An excited nucleus often has more than one possible way to de-excite. It may emit a gamma ray, or it may undergo internal conversion. These are competing processes.
Internal conversion is more likely when the transition energy is relatively low and when the nucleus strongly interacts with inner electrons. Heavy atoms often show stronger internal conversion because their inner electrons are more tightly bound and spend more time close to the nucleus.
The nucleus changes from a higher energy state to a lower one in both gamma emission and internal conversion. The difference is only in how the energy leaves the atom.
| Process | What leaves the atom | Source of emitted energy |
|---|---|---|
| Gamma decay | Gamma photon | Nuclear transition energy |
| Internal conversion | Atomic electron | Nuclear transition energy transferred to electron |
The Conversion Electron and the Atom Afterward
When the conversion electron is ejected, it leaves a vacancy in an inner atomic shell. The atom is then ionized and in an excited atomic state. Electrons from higher shells can fall down to fill the vacancy.
That atomic rearrangement can produce characteristic X rays or Auger electrons. Those secondary effects come from the electron cloud, not directly from the nucleus.
So internal conversion is a nuclear process that often triggers later atomic processes.
Energy of Conversion Electrons
Because different electron shells have different binding energies, internal conversion can produce several possible electron energies for the same nuclear transition.
For example, if the nucleus transfers energy to a K-shell electron, the kinetic energy is approximately
$$
K_K = E_\gamma - E_K
$$
If instead an L-shell electron is ejected,
$$
K_L = E_\gamma - E_L
$$
Since usually $E_K > E_L$, the K-shell conversion electron has less kinetic energy than the L-shell conversion electron for the same transition.
| Electron shell | Binding energy | Conversion electron kinetic energy |
|---|---|---|
| K shell | Larger | Smaller |
| L shell | Smaller | Larger |
| M shell | Even smaller | Even larger |
This discrete set of electron energies is an important experimental signature of internal conversion.
Internal Conversion Coefficient
To describe how important internal conversion is compared with gamma emission, physicists use the internal conversion coefficient, usually written as $\alpha$.
It is defined as
$$
\alpha = \frac{\text{number of internal conversion electrons}}{\text{number of gamma rays}}
$$
If $\alpha$ is large, internal conversion is more probable than gamma emission for that transition. If $\alpha$ is small, gamma emission is more common.
There can also be shell-specific coefficients such as $\alpha_K$, $\alpha_L$, and so on, depending on which shell the electron came from.
The internal conversion coefficient measures the competition between two de-excitation modes:
$$
\alpha = \frac{N_{\mathrm{IC}}}{N_\gamma}
$$
A larger $\alpha$ means internal conversion is more favored.
Why Internal Conversion Matters
Internal conversion is important because it shows that nuclear transitions can interact directly with atomic electrons. It also helps explain why some excited nuclei emit fewer gamma rays than expected.
In experiments, conversion electrons provide useful information about nuclear energy levels and transition types. By measuring their energies and intensities, physicists can learn about the structure of the nucleus.
Internal conversion is especially significant in heavy nuclei and in low-energy nuclear transitions, where gamma emission can be less favorable.
Internal Conversion and Pair Production
It is useful to avoid confusion with another nuclear de-excitation process, internal pair production. In internal conversion, an already existing orbital electron is expelled. In pair production, the nuclear energy creates an electron and a positron.
These are different processes with different conditions.
| Process | What happens | Requires orbital electron? |
|---|---|---|
| Internal conversion | Bound electron is ejected | Yes |
| Internal pair production | Electron-positron pair is created | No |
A Simple Picture
You can think of the excited nucleus as holding extra energy. Usually that energy may leave as a gamma photon. But sometimes the nucleus gives the energy directly to a nearby electron. The electron escapes, carrying away most of the transition energy after the binding energy has been paid.
That is the central idea of internal conversion.
Key idea of internal conversion:
An excited nucleus de-excites by transferring energy directly to an atomic electron, ejecting it with kinetic energy approximately
$$
K_e = E_\gamma - E_b
$$
No gamma photon is emitted in that event.