Shielding Design Simulator: Gamma & Neutron Attenuation

simulator intermediate ~10 min
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Attenuation ≈ 1.2×10⁻³ — 20 cm of concrete reduces 1 MeV gamma intensity by ~800×

20 cm of ordinary concrete attenuates 1 MeV gamma rays by a factor of approximately 800 (including buildup). The dose rate behind the shield from a 1000 Ci source at 1 meter drops from a lethal ~540 mSv/h to about 0.7 mSv/h.

Formula

I = B(μx, E) · I₀ · Math.pow(e, -μ·x) (attenuated intensity with buildup)
HVL = ln(2) / μ = 0.693 / μ (half-value layer)
μ(E) = ρ · (μ/ρ)_mass (linear attenuation from mass attenuation coefficient)

Stopping Invisible Energy

Gamma rays and neutrons carry enough energy to ionize atoms and damage biological tissue, but they are invisible, odorless, and penetrating. A 1 MeV gamma ray can traverse 10 cm of lead. A fast neutron can pass through a meter of steel. Shielding design is the engineering discipline of placing enough material between radiation sources and people to reduce dose rates to acceptable levels — typically below 1 mSv per year for the public and 20 mSv per year for radiation workers.

Exponential Attenuation

Gamma-ray intensity decreases exponentially with shield thickness: each additional centimeter removes the same fraction of the remaining beam. This is characterized by the linear attenuation coefficient μ, which depends on photon energy and shield material. At 1 MeV, μ is about 0.15/cm for concrete and 0.77/cm for lead — meaning lead is roughly five times more effective per centimeter, though concrete is far cheaper per unit area.

The Buildup Problem

Simple exponential attenuation underestimates actual dose because Compton-scattered photons can still reach a person behind the shield. The buildup factor corrects for this scattered radiation and depends on shield material, thickness in mean free paths, and photon energy. For thick concrete shields, the buildup factor can exceed 10 — meaning scattered photons deliver ten times more dose than the direct, unscattered beam alone.

Designing the Shield

This simulation calculates gamma-ray attenuation through four common shield materials using the buildup factor method. Adjust gamma energy, shield thickness, material type, and source strength to explore how each parameter affects the transmitted dose rate. Compare the half-value layers of different materials and notice how higher gamma energies require dramatically thicker shields due to reduced photoelectric absorption.

FAQ

How does gamma-ray shielding work?

Gamma rays interact with matter through three mechanisms: photoelectric absorption (dominant at low energy, high Z), Compton scattering (dominant at medium energy), and pair production (above 1.022 MeV). Each interaction removes or redirects a photon from the beam, causing exponential attenuation I = I₀ · e^(-μx) where μ is the linear attenuation coefficient.

What is a buildup factor?

The simple exponential attenuation formula I = I₀·e^(-μx) only counts uncollided photons. In reality, Compton-scattered photons can still reach the detector. The buildup factor B corrects for this: I = B · I₀ · e^(-μx). For broad beams in thick shields, B can be 5–20×, meaning the actual dose is much higher than the uncollided calculation suggests.

What is the best material for gamma shielding?

Lead and depleted uranium provide the most compact gamma shielding due to high density and atomic number. Concrete is preferred for large structures due to low cost. Water is used in spent fuel pools. The choice depends on the application — a portable medical source shield uses lead, while a reactor biological shield uses reinforced concrete 1–3 meters thick.

How do you shield against neutrons?

Neutrons are best stopped by hydrogen-rich materials (water, polyethylene, concrete) that thermalize fast neutrons through elastic scattering, followed by materials with high neutron capture cross-sections (boron, cadmium, gadolinium) to absorb the thermalized neutrons. A complete shield often combines hydrogenous moderator, thermal neutron absorber, and gamma shield (for capture gammas).

Sources

Embed

<iframe src="https://homo-deus.com/lab/nuclear-engineering/shielding-design/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub