What the result means
The calculator gives the share of gamma rays in a narrow, perpendicular beam that interact at least once in the crystal, including Compton scattering. It is a first estimate for choosing crystal thickness. It is not the full-energy peak efficiency of a finished detector: some photons scatter and escape, so the photopeak fraction is lower, especially at high energy and in small crystals.
The relation used is P = 1 − exp(−μ · t), where μ is the linear attenuation coefficient and t is the thickness along the beam.
How the values are calculated
Mass attenuation coefficients (total, with coherent scattering) are taken from the NIST X-ray mass attenuation coefficient tables for each element and combined by weight fraction. Compositions are NaI, CsI, Lu1.8Y0.2SiO5 (LYSO), Gd3Al2Ga3O12 (GAGG), Bi4Ge3O12 (BGO) and vinyltoluene plastic (8.5% H, 91.5% C by weight). Dopants are ignored. Densities are the values listed on our product pages: NaI(Tl) 3.67, CsI(Tl) 4.51, LYSO(Ce) 7.1, GAGG(Ce) 6.6, BGO 7.13 and plastic 1.023 g/cm³.
Checked against published values
The calculator agrees with values published by Saint-Gobain Crystals (now Luxium Solutions).
| Check | Calculator | Published | Source |
|---|---|---|---|
| LYSO, attenuation length at 511 keV | 1.22 cm | 1.2 cm | PreLude 420 data sheet |
| BGO, attenuation length at 511 keV | 1.04 cm | 1.0 cm | PreLude 420 data sheet |
| NaI(Tl), thickness to stop 50% at 662 keV | 2.46 cm | 2.5 cm | Scintillation properties chart |
| CsI(Tl), thickness to stop 50% at 662 keV | 1.97 cm | 2 cm | Scintillation properties chart |
| BGO, thickness to stop 50% at 662 keV | 0.97 cm | 1 cm | Scintillation properties chart |
Choosing a crystal
Stopping power is only one factor. Light yield, decay time, energy resolution, intrinsic background (Lu-176 in LYSO) and the need for hermetic encapsulation (NaI and CsI(Na) are hygroscopic) also decide the choice. Compare materials in our scintillation crystal selection guide, GAGG vs LYSO and LYSO vs BGO. For gamma spectroscopy with a photomultiplier, see encapsulated NaI(Tl) scintillators.
Frequently asked questions
How thick should a NaI(Tl) crystal be for Cs-137 (662 keV)?
About 51% of a narrow 662 keV beam interacts in 1 inch (25.4 mm) of NaI(Tl), about 76% in 2 inches and about 88% in 3 inches. A 2″x2″ or 3″x3″ crystal is common for laboratory gamma spectroscopy.
What LYSO thickness is used for 511 keV PET detectors?
About 56% of 511 keV photons interact in 10 mm of LYSO and about 81% in 20 mm. PET pixels are often 15 to 20 mm long; shorter pixels improve timing and depth-of-interaction behaviour but stop fewer photons.
Why does plastic scintillator show a low value?
Plastic scintillator contains only hydrogen and carbon, so gamma rays interact mainly by Compton scattering and the density is about 1 g/cm³. It is used for counting, timing and large-area detectors such as muon panels, rather than for gamma-ray energy spectroscopy.
Can I use these values as detector efficiency?
Use them to compare materials and choose a starting thickness. For a final design, confirm the efficiency with Monte Carlo simulation, for example Geant4, or by measurement with your source geometry.