Radiation Shielding & Dose

Gamma μ values are at 1.25 MeV (Co-60) from the vault shielding notes. Analytical attenuation + Taylor buildup is a first-order estimate — for mixed fields and real geometry use MCNP/OpenMC (per 07_Radiation_Shielding_Overview).

Gamma Attenuation & Shield Thickness

I=I₀·e^(−μx); with buildup Ḣ∝B·e^(−μx), Taylor B=1+A₁μx·e^(A₂μx). Curve shows transmission with HVL/TVL marks.

Shield material

μ (cm⁻¹) @1.25 MeV

Thickness x (cm)

apply Taylor buildup

Target attenuation factor (e.g. 1000 = TVL×3)

Dose Rate & Required Shield

Ḣ=Γ·A/r²·B·e^(−μx); solve x for a dose limit.

Isotope (Γ in µSv·m²/GBq·h)

Γ (µSv·m²/GBq·h)

Activity (GBq)

Standoff r (m)

μ shield (cm⁻¹)

Dose limit (µSv/h)

Radioactive Decay

N=N₀e^(−λt), t½=ln2/λ, A=λN.

Isotope

Half-life

Units

Initial activity A₀ (GBq)

Elapsed time

Activity from Mass

A₀=(ln2/t½)·(m·N_A/M).

Mass (g)

Molar mass (g/mol)

Half-life

Units

Fast-Neutron Removal

φ=φ₀·e^(−Σ_R x); hydrogenous moderators.

Moderator

Σ_R (cm⁻¹)

Thickness (cm)

Formula reference & material data

Attenuation I=I₀e^(−μx); HVL=ln2/μ, TVL=ln10/μ. Buildup (Taylor) B=1+A₁μx·e^(A₂μx).

Dose Ḣ=ΓA B e^(−μx)/r²; required x=(1/μ)ln(ΓAB/(r²Ḣ_lim)). Decay N=N₀e^(−λt), λ=ln2/t½, A=λN.

Neutron φ=φ₀e^(−Σ_R x). μ@1.25 MeV (cm⁻¹): W 1.17, Pb 0.77, Fe 0.42, heavy concrete 0.16, Al 0.15, ord. concrete 0.10, water 0.062, HDPE 0.056. Limits: occupational 50 mSv/yr; public 1 mSv/yr.