KAHIBARO
Table of Contents
What the photopeak is
In a gamma ray spectrum, the photopeak is the peak that appears at an energy equal, or very close, to the full energy of the incoming gamma photon. It is also called the full-energy peak. It represents events in which the detector ultimately collects the entire gamma ray energy.
If a gamma ray has energy $E_\gamma$, then the photopeak appears at channel or calibrated energy corresponding to
$$
E_{\text{measured}} \approx E_\gamma
$$
This is one of the most important features in gamma spectroscopy because it allows us to identify radioactive isotopes by their characteristic gamma energies.
The photopeak corresponds to full energy absorption of the incident gamma ray in the detector.
If a gamma ray of energy $E_\gamma$ deposits all its energy, the detected event contributes to the photopeak at
$$
E = E_\gamma
$$
Why full energy can be recorded
A gamma ray usually does not lose all its energy in a single simple step. Instead, it may interact one or more times inside the detector. The key idea is that the total deposited energy must equal the original gamma energy.
For example, a gamma ray may first undergo Compton scattering, giving part of its energy to an electron, and then the scattered photon may interact again and again until no energy escapes. The detector then sums all deposited energies from those interactions, and the final recorded pulse corresponds to the full gamma energy.
Another common route is photoelectric absorption, where the gamma ray transfers essentially all its energy to an electron in one interaction, apart from small atomic rearrangement processes that also remain inside the detector.
If every secondary particle and X ray created in the interaction is stopped inside the detector, the event contributes to the photopeak.
Physical meaning in the spectrum
A gamma spectrum is a plot of the number of detected events versus detected energy. The photopeak stands out as a distinct peak because many events cluster around the full gamma energy.
For a monoenergetic gamma source, the ideal detector would produce a very narrow line at one energy. Real detectors do not give a perfectly sharp line. Instead, the photopeak has a finite width because of statistical fluctuations in signal creation and electronic noise.
So the photopeak tells us two things. Its position tells us the gamma energy, and its width tells us something about the detector resolution.
Example of a photopeak
Suppose a radioactive source emits gamma rays of energy $662 \,\text{keV}$, such as cesium 137. In the measured spectrum, one important feature is a photopeak near $662 \,\text{keV}$. Events in that peak are those in which the detector collected the full energy of the gamma ray.
A simplified interpretation is shown below.
Processes that create the photopeak
The exact mechanism depends on gamma energy and detector material. Several interaction histories can end in full energy absorption.
| Interaction path | What happens | Contributes to photopeak? |
|---|---|---|
| Photoelectric absorption | Gamma transfers all energy to an electron, secondary energy remains in detector | Yes |
| Multiple Compton interactions | Gamma loses energy in steps, final scattered photon is absorbed | Yes, if nothing escapes |
| Pair production, then full containment | Gamma creates electron positron pair, annihilation photons also absorbed | Yes |
The detector does not care how the energy was shared internally. It records the total deposited energy.
Different interaction mechanisms can lead to the same photopeak, as long as the detector retains all the energy released by the original gamma ray.
Why the photopeak is useful
The photopeak is central to gamma-ray identification. Each nucleus emits gamma rays with specific energies, so locating photopeaks allows us to determine which radionuclides are present.
If the energy calibration of the detector is known, the measured photopeak energy can be compared with tabulated gamma energies. This is the basis of qualitative gamma spectroscopy.
The area under the photopeak is also important. It is related to how many full-energy events were detected, which can be used to estimate source activity when detector efficiency and measurement time are known.
In a simple form,
$$
N_{\text{peak}} \propto A \, \epsilon_{\text{peak}} \, t
$$
where $N_{\text{peak}}$ is the number of counts in the photopeak, $A$ is the source activity, $\epsilon_{\text{peak}}$ is the full-energy peak efficiency, and $t$ is the counting time.
Peak shape and width
A real photopeak is not infinitely narrow. It has a spread in energy. In many cases, its central part is approximately Gaussian in shape.
A common measure of the width is the full width at half maximum, abbreviated FWHM. A smaller FWHM means better energy resolution.
If the peak center is at energy $E_0$, the relative resolution is often written as
$$
R = \frac{\text{FWHM}}{E_0}
$$
A good detector has a small value of $R$.
Photopeak efficiency
Not every incoming gamma ray produces a photopeak event. Some gammas pass through the detector without interacting, and others interact only partially, with some energy escaping. The probability that an emitted gamma ray produces a count in the full-energy peak is called the photopeak efficiency or full-energy peak efficiency.
This efficiency depends strongly on detector size, geometry, gamma energy, and detector material. Larger and denser detectors usually have a greater chance of fully absorbing the gamma ray.
Photopeak efficiency is not the same as total detection efficiency.
Total efficiency counts all detected interactions, but photopeak efficiency counts only full-energy events.
Relation to other spectral features
A photopeak is only one part of a gamma spectrum. Other structures, such as the Compton continuum, Compton edge, and escape peaks, arise when only part of the gamma energy is recorded or when secondary photons leave the detector. Those features belong to separate topics, but they are easiest to understand by comparing them with the photopeak.
The photopeak is the reference feature because it marks the full gamma energy, while other features usually appear at lower recorded energies.
Practical interpretation
When analyzing a measured spectrum, the photopeak is usually found by looking for a local maximum and fitting it mathematically. The centroid of the peak gives the best estimate of the gamma energy, and the integrated counts under the peak give the number of full-energy detections.
In practice, one often subtracts background and then integrates the net peak area. If the channel number is $C$ and the detector has been energy calibrated, the energy can often be written approximately as
$$
E = aC + b
$$
where $a$ and $b$ are calibration constants.
Then the photopeak position in channels can be converted into physical energy units such as keV or MeV.
Summary idea
The photopeak is the signature of complete energy capture from a gamma ray inside the detector. It appears at the gamma's full energy, helps identify the emitting nucleus, and provides a basis for quantitative analysis.
Key idea: the photopeak is produced when the detector records the entire energy of the incoming gamma photon.
Its position gives the gamma energy, and its area reflects the number of full-energy absorption events.