A halide scintillator crystal (NaI, CsI, CaF₂ doped with a small amount of Tl or Eu "activator" ions) absorbs an incoming gamma photon by the photoelectric effect. The absorbed energy kicks electrons into the conduction band; they migrate through the lattice and recombine at activator sites, each recombination emitting one visible-light photon. The number of scintillation photons is proportional to the deposited energy:
N = LY × E_deposited
LY = light yield (photons/MeV), material-dependent
QE ≈ 0.25 = photomultiplier quantum efficiency
N_detected ≈ N × QE
Because photon counting is a Poisson process, the pulse height fluctuates event to event. The statistical (Poisson-limited) energy resolution is:
R (FWHM, %) = 2.35 / √N_detected × 100
Repeating many events at the same energy builds a photopeak in the pulse-height spectrum whose width matches this resolution — exactly how a real gamma-ray spectrometer (NaI(Tl) probe, CsI(Tl) detector in a PET/CT scanner) identifies an isotope by its characteristic gamma-line energy and estimates dose from the peak area.
- Material — sets the light yield, so higher-yield crystals (CsI(Tl)) give sharper peaks than lower-yield ones (CaF₂(Eu)) at the same energy.
- Gamma energy — more deposited energy means more scintillation photons and a narrower relative resolution (√N grows faster than the peak shifts).
- Fire gamma photon — sends one photon into the lattice at a random entry point and interaction depth (deeper penetration on average at higher energy), spawning the visible cascade and adding one count to the spectrum.