# Interaction of Radiation with Matter

## Photon Interactions with Matter

### Photoelectric Effect

In the photoelectric effect, an incident photon is completely absorbed by an inner-shell electron, which is then ejected from the atom with kinetic energy equal to the photon energy minus the electron's binding energy. The probability of this interaction is proportional to Z^3 / E^3, meaning it is strongly favored in high atomic number materials and at low photon energies. This is why lead is an excellent shielding material, why iodinated contrast enhances CT images, and why bone appears bright on radiographs. After the electron is ejected, the resulting shell vacancy is filled by outer electrons, producing characteristic X-rays and Auger electrons. Crucially, no scattered photon is produced in the photoelectric effect, which means it contributes no scatter noise to the image.

### Compton Scattering

Compton scattering occurs when an incident photon interacts with a loosely bound outer-shell electron. The photon is deflected from its original path with reduced energy, while the electron recoils with the transferred kinetic energy. The probability of Compton scattering depends primarily on electron density (roughly proportional to physical density) and is nearly independent of atomic number. This interaction dominates at intermediate photon energies, from about 100 keV to several MeV, which encompasses the energy range of most nuclear medicine photons. At 140 keV (the Tc-99m photopeak), Compton scattering is the dominant interaction in soft tissue, making it the primary source of scatter that degrades image quality in both SPECT and PET. The energy of the scattered photon varies with the scattering angle according to the Compton formula.

### Pair Production

Pair production occurs when a photon interacts within the electric field of a nucleus and converts into an electron-positron pair. This process requires a minimum photon energy of 1.022 MeV, which corresponds to twice the rest mass energy of an electron (2 x 511 keV). The probability increases with both atomic number and photon energy above this threshold. Pair production is not significant at the energies used in diagnostic nuclear medicine, but it becomes relevant in high-energy therapy settings and is fundamental to the annihilation physics underlying PET.

### Coherent (Rayleigh) Scattering

Coherent or Rayleigh scattering is an elastic process in which a photon changes direction without losing energy and without ionizing the atom. It makes only a minor contribution in the diagnostic energy range and is not clinically significant in nuclear medicine practice.

## Charged Particle Interactions

### Beta Particle Interactions

Beta particles -- whether electrons from beta-minus decay or positrons from beta-plus decay -- lose energy through two primary mechanisms as they traverse matter. Collisional losses involve ionization and excitation of atoms along the particle's path. Radiative losses occur when the charged particle decelerates in the electric field of a nucleus, producing X-rays known as bremsstrahlung. The probability of bremsstrahlung production is proportional to Z^2 of the absorbing material and to the energy of the electron. This phenomenon is clinically exploited in bremsstrahlung imaging of Y-90, which is a pure beta emitter with no gamma emissions, allowing post-therapy verification of microsphere distribution. Beta particles are emitted with a continuous energy spectrum, each radionuclide characterized by a maximum energy.

### Alpha Particle Interactions

Alpha particles have extremely high linear energy transfer, approximately 80 keV per micrometer, and a very short range in tissue of 50 to 80 micrometers -- just a few cell diameters. They deposit their energy through dense ionization along a nearly straight track, causing predominantly double-strand DNA breaks that are highly cytotoxic and difficult for the cell to repair. Despite their destructive power, alpha particles are easily shielded; a sheet of paper or even the dead layer of skin is sufficient to stop them.

### Positron Range and Annihilation

After emission, a positron travels a short distance through tissue, losing kinetic energy through interactions with surrounding atoms, before annihilating with an electron. This positron range sets a fundamental limit on PET spatial resolution. F-18 has the shortest positron range among common PET isotopes (approximately 1 mm), yielding the best intrinsic resolution. Ga-68 has an intermediate range of about 3.5 mm, while Rb-82 has the longest range at roughly 5 to 7 mm, producing inherently lower resolution images. At annihilation, two 511 keV photons are emitted at approximately 180 degrees. A small angular deviation of about 0.5 degrees from perfect collinearity, due to residual momentum in the positron-electron system, contributes additional spatial resolution degradation in PET.

| PET Isotope | Max Positron Energy (MeV) | Mean Range in Tissue (mm) | Impact on Spatial Resolution |
|---|---|---|---|
| F-18 | 0.63 | ~1.0 | Best intrinsic resolution |
| C-11 | 0.96 | ~1.2 | Very good resolution |
| Ga-68 | 1.90 | ~3.5 | Intermediate resolution |
| Rb-82 | 3.35 | ~5–7 | Lowest resolution |

## Attenuation and Transmission

### Linear and Mass Attenuation Coefficients

When a beam of photons passes through matter, some fraction is removed (attenuated) through photoelectric absorption, Compton scattering, or other interactions. The linear attenuation coefficient (mu) quantifies the fraction of photons removed per unit thickness of material, expressed in cm^-1. The mass attenuation coefficient (mu/rho) normalizes for density, expressed in cm^2/g. For a monoenergetic beam passing through a uniform material, the transmitted intensity follows the exponential relationship I = I_0 x e^(-mu x t). The half-value layer (HVL) is the thickness of material that reduces beam intensity by 50% and equals 0.693/mu. The tenth-value layer (TVL) reduces intensity by 90%.

### Attenuation in Nuclear Medicine

Attenuation causes significant count loss from deeper structures within the body, producing artifacts that can mimic or obscure pathology. The effect is more pronounced for lower-energy photons. For Tc-99m at 140 keV, the half-value layer in soft tissue is approximately 4.5 cm, meaning substantial attenuation occurs across the chest or abdomen. For F-18 at 511 keV, the HVL is about 7.2 cm, offering somewhat better penetration. Attenuation correction is therefore essential for accurate quantification in both SPECT and PET.

### Shielding Considerations

Lead (Z = 82) is the primary shielding material in nuclear medicine due to its high atomic number and density, which favor photoelectric absorption. For Tc-99m, just 0.3 mm of lead provides greater than 90% attenuation. I-131 at 364 keV requires substantially thicker lead shielding. For PET energies (511 keV), lead is less efficient; tungsten or thick lead barriers are used instead. Standard protective equipment includes syringe shields, L-shaped benchtop shields, and lead aprons, though for high-energy photons, maximizing distance from the source is often more practical than relying on portable shielding alone.

| Radionuclide | Energy (keV) | HVL in Lead (mm) | HVL in Soft Tissue (cm) | Shielding Strategy |
|---|---|---|---|---|
| Tc-99m | 140 | 0.3 | 4.5 | Thin lead syringe shields |
| I-131 | 364 | 2.4 | 6.3 | Thick lead barriers |
| F-18 / PET | 511 | 4.1 | 7.2 | Tungsten shields, distance |

## Clinical Relevance to Image Quality

### Scatter and Energy Windows

Compton scatter adds unwanted background counts to nuclear medicine images, reducing contrast and degrading image quality. Energy discrimination using photopeak windows -- typically set at 15 to 20% of the photopeak energy -- helps reject scattered photons that have lost energy. Various scatter correction methods exist, including dual-energy window subtraction, triple-energy window (TEW) estimation, and model-based approaches. There is always a trade-off: narrower energy windows reject more scatter but also reduce sensitivity by excluding some valid photopeak events.

### Tissue Composition Effects

Different tissue types affect photon attenuation in ways that create predictable artifacts. Bone, with its high atomic number and density, causes increased photoelectric absorption that can produce cold artifacts in adjacent structures. Lung tissue, with its low density, attenuates fewer photons and appears relatively "hot" on images without attenuation correction. In cardiac SPECT, breast tissue causes significant anterior attenuation that can simulate an anterior wall perfusion defect, while the diaphragm causes inferior wall attenuation artifacts. Recognizing these tissue-specific effects is essential for accurate image interpretation.

<image>A medical physics illustration showing the three major photon interactions with matter side by side: photoelectric effect (photon completely absorbed, electron ejected, characteristic X-ray emitted), Compton scattering (photon deflected at angle theta with reduced energy, electron recoils), and pair production (photon converts to electron-positron pair near nucleus). Each panel should show the incident photon, the target atom, and all products with energy labels. Include a graph below showing the dominant interaction regions as a function of photon energy (x-axis) and atomic number Z (y-axis).</image>

<image>A cross-sectional diagram of a patient's thorax showing how photon attenuation affects nuclear medicine image quality. Illustrate gamma rays originating from a cardiac source, with some photons being attenuated by overlying breast tissue (anterior) and diaphragm (inferior), while lateral photons pass through less tissue. Show the resulting artifactual perfusion defect pattern on a bull's-eye polar map display, with labels indicating breast attenuation artifact (anterior wall) and diaphragmatic attenuation artifact (inferior wall).</image>

<image>A comparative diagram showing positron range for three common PET isotopes: F-18 (short range, ~1 mm), Ga-68 (intermediate range, ~3.5 mm), and Rb-82 (long range, ~5-7 mm). Show each positron path as a tortuous track from the parent nucleus to the annihilation point, with the two 511 keV photons emitted at 180 degrees. Include a small PET image resolution comparison panel showing how spatial resolution degrades with increasing positron range.</image>

## Clinical Pearls

At 140 keV, the energy of Tc-99m emissions, Compton scattering is the dominant interaction in soft tissue. This is precisely why scatter correction is so critical for quantitative SPECT -- without it, scattered photons add noise and degrade contrast.

The photoelectric effect dominates in high-Z materials and at low energies, which explains both why lead is such an effective shield and why iodinated contrast produces such strong enhancement on CT images.

Positron range fundamentally limits PET spatial resolution in a radionuclide-specific way. F-18 offers the best resolution with a range of about 1 mm, while Rb-82 has the worst at 5 to 7 mm. This is why cardiac Rb-82 PET images appear inherently "smoother" than F-18 FDG images.

Bremsstrahlung imaging is used clinically for post-therapy verification of Y-90 microsphere distribution. Because Y-90 is a pure beta emitter with no gamma emissions, the bremsstrahlung X-rays produced as beta particles decelerate in tissue provide the only imageable signal.

Breast and diaphragmatic attenuation artifacts are the most common cause of false-positive myocardial perfusion defects on SPECT imaging. CT-based attenuation correction has largely eliminated these artifacts, though readers must remain vigilant for CT-related artifacts introduced by the correction process itself.

For PET radionuclides at 511 keV, lead shielding is substantially less effective than at Tc-99m energies. Tungsten syringe shields and increased working distance are the primary protective strategies for PET radiopharmaceuticals.

The half-value layer concept is essential for radiation safety calculations and is frequently tested on board examinations.

## References

- Cherry SR, Sorenson JA, Phelps ME. *Physics in Nuclear Medicine*. 4th ed. Elsevier; 2012. Chapters 6-7.
- Bushberg JT, et al. *The Essential Physics of Medical Imaging*. 4th ed. Lippincott Williams & Wilkins; 2020. Chapters 3-4.
- Fahey FH. Data acquisition in PET imaging. *J Nucl Med Technol*. 2002;30(2):39-49.