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Germanium gamma spectrometer

A γ ray crosses the crystal without a trace until it interacts: it is absorbed (photoelectric), scatters off an electron (Compton) or, above keV (2m_ec²), makes an e⁺e⁻ pair. Only the energy left in the germanium is measured, so one line becomes a peak, a continuum and an edge.

Source

distance

Crystal (illustrative size)

diameter

length

Resolution (user setting)

@ 122 keV

@ 1332 keV

Gaussian, FWHM(E) = √(a² + bE) through these two values (FWHM, keV). With a² ≥ 0 and b ≥ 0 the FWHM can neither fall with energy nor grow faster than √E, so moving one slider pushes the other along when it would leave that range (the 1332 keV value stays between 1 and √(1332/122) times the 122 keV value). Illustrative settings, not a detector's datasheet.

Rendering

To scale: crystal, core hole, source distance and lead block (the breadboard holes are 2.5 cm apart). Drawn but not in the simulation: the end cap, cold finger, dewar, source disc and stand; their sizes are illustrative. The end cap is drawn see-through. Photons move at a display speed of about 30 cm/s; the drawn ones are chosen to show the crystal (most aim at it), the spectrum counts every photon with its proper weight.

The Monte Carlo (assets/hpge.js, runs in this page): attenuation of Ge and Pb from NIST XCOM (M.J. Berger, J.H. Hubbell, S.M. Seltzer, J. Chang, J.S. Coursey, R. Sukumar, D.S. Zucker, K. Olsen, NIST Standard Reference Database 8 (XGAM), doi:10.18434/T48G6X), photoelectric, incoherent and pair (nuclear and electron field), log-log interpolation; densities from NIST X-ray mass attenuation Table 1. Coherent (Rayleigh) scattering omitted. Compton angle and energy from Klein-Nishina for a free electron at rest (no Doppler broadening, no binding effect on the angle; XCOM's incoherent cross section, which includes binding, sets how often). Photoelectric: the full energy stays at the point, no fluorescence (no Ge or Pb X-ray escape, no Pb X-ray lines). Pair: E − 2m_ec² stays at the point, the positron annihilates there at rest into two photons of m_ec² back to back in a random direction (positron range neglected). Every electron deposits its energy where it is made (no bremsstrahlung, no escape). Bare crystal in vacuum: no dead layer, no end cap, no holder; the point source sits on the axis. Each photon of the source is an independent event: no true-coincidence summing (the ⁶⁰Co sum peak at keV is absent, and so is the summing of the two annihilation photons). m_ec² from CODATA 2018.
Lines: DDEP/LNHB recommended data (Laraweb tables), every γ ray, K X-ray and annihilation line of at least % per decay above keV; the ²²⁸Th chain in transient equilibrium (the long-time Bateman limit with the DDEP branchings and half-lives: ²²⁴Ra and everything below it run 0.5 to 0.6 % above the ²²⁸Th activity times the branching; no ²²⁰Rn loss). Checked against an independent Julia Monte Carlo (tests/check_hpge.jl).

Ge crystal

source

lead

end cap (drawn only)

LN₂ dewar (drawn only)

drag to orbit · scroll to zoom · drag on the spectrum to zoom it