Radiation Detectors and Nuclear Spectroscopy

A radiation detector turns the energy an incident particle or photon deposits into an electrical pulse. The chain is the same in every device: the radiation ionizes or excites the detector material, the resulting charge carriers or light photons are collected, and the collected signal is proportional to the deposited energy. The three detector families differ in the medium and in how they amplify the signal: gas counters collect ions directly, scintillators emit light that a photomultiplier converts and amplifies, and semiconductors collect electron-hole pairs in a solid. The quality of a spectrometer is set by how many independent carriers one event produces, which fixes the statistical spread of the signal.¹

Ionization and the number of carriers

When radiation deposits energy $E$ in a detector medium, the average number of primary charge carriers (ion pairs, or electron-hole pairs) is

where $W$ is the mean energy expended per carrier, a property of the medium. In a gas $W\approx 30\mathrm{eV}$; in silicon it is $3.6\mathrm{eV}$ and in germanium $2.96\mathrm{eV}$. A solid produces roughly ten times as many carriers per unit energy as a gas, and a scintillator followed by a photomultiplier produces far fewer photoelectrons per unit energy than either. Because the signal is the sum of $\bar{N}$ independent contributions, its statistical fluctuation drives the energy resolution.

The Fano factor $F$ is about $0.1$ in semiconductors and near unity for the photoelectron statistics of a scintillator; the small $W$ and small $F$ of germanium together give it a resolution one to two orders of magnitude finer than a sodium-iodide scintillator.

Gas-filled counters

A gas counter is a chamber of gas with a central wire anode at positive voltage. Radiation ionizes the gas; the electrons drift to the wire and the ions to the wall. The pulse height as a function of the applied voltage passes through three distinct operating regions.

• Ionization chamber (low voltage): the field is just enough to collect the primary ion pairs before they recombine, with no multiplication. The pulse is small but strictly proportional to the deposited energy.
• Proportional counter (intermediate voltage): near the thin anode wire the field is strong enough that drifting electrons gain enough energy between collisions to ionize further, producing a Townsend avalanche. The collected charge is the primary ionization times a gas gain of $10^3$ to $10^6$, and it remains proportional to the deposited energy, so the counter measures energy.
• Geiger-Mueller region (high voltage): the avalanche propagates along the whole wire and saturates. Every event, regardless of its initial energy, gives the same large pulse. A Geiger counter counts particles efficiently but carries no energy information, and its avalanche must be quenched before the next count, giving a dead time.

Scintillation detectors

A scintillator is a material that emits a brief flash of visible or ultraviolet light when radiation deposits energy in it. Inorganic crystals such as thallium-doped sodium iodide, $\mathrm{NaI}(\mathrm{Tl})$, are dense and high-$Z$, so they absorb gamma rays efficiently through the photoelectric effect; the light output is proportional to the deposited energy. The flash is faint, and the amplification is supplied by a photomultiplier tube (PMT): the light strikes a photocathode, which ejects photoelectrons; these are accelerated onto a chain of dynodes, each releasing several secondary electrons, so a single photoelectron becomes an avalanche of $10^6$ to $10^7$ electrons at the anode.

Scintillators are fast and efficient and can be made large, but their energy resolution is modest: the number of photoelectrons produced per keV is small, and the Poisson spread on that number dominates. A $\mathrm{NaI}(\mathrm{Tl})$ detector resolves the $662\mathrm{keV}$ line of ${}^{137}\mathrm{Cs}$ to about $7\%$.

Semiconductor detectors

A semiconductor detector is a reverse-biased diode in which the radiation creates electron-hole pairs that the field sweeps to the electrodes. Because $W$ is only a few eV, a given energy makes far more carriers than in a gas or scintillator, and the resolution is correspondingly finer. Silicon detectors are standard for charged particles and low-energy photons; high-purity germanium (HPGe), with its higher atomic number, is the workhorse for gamma spectroscopy, resolving the same $662\mathrm{keV}$ line to better than $0.2\%$. Germanium's small band gap means it must be cooled, usually to liquid-nitrogen temperature, to suppress thermally generated leakage current.

The gamma pulse-height spectrum

A monoenergetic gamma line does not give a single peak, because the photon can deposit its energy in the detector through more than one process. The pulse-height spectrum shows several features:

• Full-energy (photo)peak. The photon is fully absorbed, by a photoelectric event or a Compton scatter followed by absorption of the scattered photon; the deposited energy equals $E_{\gamma }$. This is the peak used to identify the line.
• Compton continuum. A single Compton scatter followed by escape of the scattered photon deposits only the recoil-electron energy, which ranges continuously from zero up to the maximum at $180^{\circ }$ backscatter.
• Compton edge. The upper end of the continuum, at the maximum electron energy $E_{\gamma }-E_{\gamma }^{\prime }(180^{\circ })$, appears as a shoulder below the photopeak.
• Backscatter peak. Photons that Compton-scatter in surrounding material and then enter the detector deposit the low scattered energy, giving a small peak.
• Escape peaks. For $E_{\gamma }>1.022\mathrm{MeV}$, pair production followed by escape of one or both $0.511\mathrm{MeV}$ annihilation photons gives single- and double-escape peaks at $E_{\gamma }-0.511$ and $E_{\gamma }-1.022\mathrm{MeV}$.

Coincidence and timing

Two detectors registering events within a short resolving time $\tau$ are in coincidence, and requiring coincidence selects correlated events. A positron-annihilation pair fires two opposed detectors simultaneously, the basis of positron emission tomography; a gamma-gamma cascade from a single nucleus fires two detectors within nanoseconds, isolating the cascade from background. The rate of accidental coincidences between uncorrelated singles rates $r_1$ and $r_2$ is $r_{\mathrm{acc}}=2\tau r_1{r}_2$, so a short resolving time suppresses the random background. Fast timing also measures short nuclear lifetimes directly: the delay between a populating event and the subsequent decay gamma, recorded by a time-to-amplitude converter, gives the mean life of a level down to the picosecond range.