---
title: Radiation Detectors and Nuclear Spectroscopy
module: Radiation and Applications
moduleNumber: 11
lessonNumber: 3
order: 1103
summary: >
  Every detector converts the energy a radiation deposits into a measurable
  electrical signal. Gas counters read the ionization directly, in three operating
  regions set by the applied voltage; scintillators convert the energy to light
  read out by a photomultiplier; semiconductor detectors collect electron-hole
  pairs and give the best energy resolution because so many carriers are made per
  event. The resolution is governed by the number of independent charge carriers,
  and the pulse-height spectrum of a gamma line shows a full-energy photopeak, a
  Compton continuum with its edge, and escape peaks.
topics: [Radiation and Applications]
sources:
  - book: Krane
    ref: "Ch. 7 — Detecting Nuclear Radiations; §7.2 Gas-Filled Counters, §7.3 Scintillation Detectors, §7.4 Semiconductor Detectors"
  - book: Wong
    ref: "Ch. 4 — Nuclear Collective Motion; §4-4 Radiation Detectors"
draft: false
---

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.[^krane-detectors]

## 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

$$
\bar N = \frac{E}{W},
$$

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.

> **Definition (Energy resolution).** The energy resolution of a spectrometer is
> the full width at half maximum of a monoenergetic line divided by its centroid,
> $R = \Delta E_\mathrm{FWHM}/E$. If the carrier number fluctuated as an independent
> Poisson process it would give $R = 2.35/\sqrt{\bar N}$; correlations among carriers
> reduce this by the Fano factor $F < 1$, so
> $$
> R = 2.35\,\sqrt{\frac{F\,W}{E}}.
> $$
> The resolution improves as $1/\sqrt E$ and is best for the medium with the smallest
> $W$, which is why germanium far outperforms a scintillator.

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.

$$
% caption: Pulse height versus applied voltage passes through the recombination
% region, the ionization-chamber plateau, the proportional region where gas gain
% rises with voltage, and the Geiger region where every event gives the same
% saturated pulse.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  \draw[->, black] (0,0) -- (8.4,0) node[right, black!70] {applied voltage};
  \draw[->, black] (0,0) -- (0,4.6) node[above, black!70] {pulse height (log)};
  % recombination rise
  \draw[acc, very thick] (0.3,0.15) .. controls (0.8,0.9) and (1.1,1.15) .. (1.5,1.2);
  % ionization plateau
  \draw[acc, very thick] (1.5,1.2) -- (3.0,1.2);
  % proportional rise
  \draw[acc, very thick] (3.0,1.2) .. controls (3.8,1.7) and (4.5,2.6) .. (5.2,3.2);
  % limited proportional bend
  \draw[acc, very thick] (5.2,3.2) .. controls (5.7,3.6) and (6.0,3.85) .. (6.4,3.9);
  % geiger plateau
  \draw[acc, very thick] (6.4,3.9) -- (7.9,3.9);
  % region dividers
  \foreach \x in {1.5,3.0,6.4} \draw[black, dashed] (\x,0) -- (\x,4.2);
  \node[black, font=\scriptsize, anchor=south, align=center] at (2.25,1.3) {ion\\chamber};
  \node[black, font=\scriptsize, anchor=south, align=center] at (4.4,3.0) {proportional};
  \node[black, font=\scriptsize, anchor=south, align=center] at (7.1,3.95) {Geiger};
\end{tikzpicture}
$$

## 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, $\mathrm{NaI(Tl)}$, 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.

$$
% caption: The scintillation signal chain: a gamma flashes the crystal, the light
% ejects photoelectrons at the photocathode, and a dynode chain multiplies them
% into a measurable pulse whose height is proportional to the deposited energy.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  % incoming gamma
  \draw[->, black, thick] (0.2,2.4) -- (1.3,2.4);
  \node[black!70, font=\scriptsize, anchor=south] at (0.7,2.45) {gamma};
  % crystal
  \draw[thick] (1.35,1.6) rectangle (2.7,3.2);
  \node[black, font=\scriptsize, align=center] at (2.02,2.4) {scint.\\crystal};
  % light photons
  \draw[->, black] (2.75,2.4) -- (3.5,2.4);
  \node[black, font=\scriptsize, anchor=south] at (3.12,2.55) {light};
  % photocathode
  \draw[black, thick] (3.55,1.55) -- (3.55,3.1);
  \node[black, font=\scriptsize, anchor=north] at (3.5,1.5) {cathode};
  % dynode chain (zig-zag of short plates)
  \foreach \x/\y in {4.1/1.9, 4.7/2.9, 5.3/1.9, 5.9/2.9, 6.5/1.9} {
    \draw[black, thick] (\x,\y) -- ++(0.35,0);
  }
  \draw[->, black] (3.6,2.4) -- (4.1,2.0);
  \draw[->, black] (4.45,2.0) -- (4.7,2.85);
  \draw[->, black] (5.05,2.9) -- (5.3,2.05);
  \draw[->, black] (5.65,2.0) -- (5.9,2.85);
  \draw[->, black] (6.25,2.9) -- (6.5,2.05);
  \node[black, font=\scriptsize, anchor=north] at (5.3,1.55) {dynodes};
  % anode output
  \draw[->, thick] (6.9,2.0) -- (7.7,2.0);
  \node[black, font=\scriptsize, anchor=west] at (7.75,2.0) {pulse};
\end{tikzpicture}
$$

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 $\mathrm{NaI(Tl)}$ 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.

$$
% caption: The same two gamma lines recorded by a scintillator and by high-purity
% germanium: the scintillator peaks are broad and may merge, while the germanium
% peaks are sharp and cleanly separated, the difference set by the number of
% carriers per event.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  \draw[->, black] (0,0) -- (8.2,0) node[right, black!70] {energy};
  \draw[->, black] (0,0) -- (0,4.4) node[above, black!70] {counts};
  % broad scintillator peaks (dashed)
  \draw[black, very thick, densely dashed]
    (0.6,0.2)
    .. controls (2.0,0.4) and (2.7,2.2) .. (3.4,2.2)
    .. controls (4.1,2.2) and (4.6,0.5) .. (5.2,0.45)
    .. controls (5.6,0.9) and (6.0,1.5) .. (6.4,1.5)
    .. controls (6.8,1.5) and (7.2,0.4) .. (7.9,0.3);
  \node[black, font=\scriptsize, anchor=south] at (2.3,1.3) {scintillator};
  % sharp HPGe peaks (solid accent)
  \draw[acc, very thick]
    (0.6,0.15) -- (3.28,0.15) -- (3.35,3.9) -- (3.42,0.15)
    -- (6.28,0.15) -- (6.35,2.9) -- (6.42,0.15) -- (7.9,0.15);
  \node[acc, font=\scriptsize, anchor=south west] at (3.5,3.4) {HPGe};
\end{tikzpicture}
$$

## 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
  $E_\gamma - E'_\gamma(180^\circ)$, 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 $E_\gamma - 1.022\ \mathrm{MeV}$.

$$
% caption: The pulse-height spectrum of a single gamma line: the full-energy
% photopeak, a continuous Compton distribution ending at the Compton edge, and a
% low-energy backscatter peak; the sharp photopeak is the identifying feature.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  \draw[->, black] (0,0) -- (8.2,0) node[right, black!70] {deposited energy};
  \draw[->, black] (0,0) -- (0,4.6) node[above, black!70] {counts};
  % backscatter peak (small bump low)
  \draw[very thick]
    (0.5,0.2) .. controls (1.0,1.0) and (1.4,1.0) .. (1.8,0.55);
  % compton continuum (flat-ish) then edge
  \draw[very thick]
    (1.8,0.55) .. controls (2.6,0.75) and (3.6,0.8) .. (4.4,0.9)
    .. controls (4.9,0.95) and (5.1,1.55) .. (5.2,1.55);
  % drop after compton edge
  \draw[very thick] (5.2,1.55) .. controls (5.4,0.9) and (5.6,0.35) .. (5.9,0.3);
  % photopeak
  \draw[acc, very thick] (5.9,0.3) -- (6.5,0.3)
    .. controls (6.75,0.3) and (6.8,4.1) .. (6.95,4.1)
    .. controls (7.1,4.1) and (7.15,0.3) .. (7.4,0.3) -- (7.9,0.28);
  \node[acc, font=\scriptsize, anchor=south] at (6.95,4.1) {photopeak};
  \node[black, font=\scriptsize, anchor=south] at (5.2,1.6) {Compton edge};
  \node[black, font=\scriptsize, anchor=south] at (1.15,1.0) {backscatter};
  \node[black, font=\scriptsize, anchor=north] at (3.4,0.85) {Compton continuum};
\end{tikzpicture}
$$

## 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.

> **Result.** A detector's energy resolution scales as $\sqrt{F W/E}$, so the
> medium with the smallest energy per carrier resolves the finest structure:
> germanium far outperforms sodium iodide, which outperforms a gas counter used as
> a spectrometer. A single gamma line produces a photopeak plus a Compton continuum
> and escape peaks, and coincidence timing selects correlated events and measures
> level lifetimes. These are the instruments that turn the interaction cross
> sections of the previous lessons into the measured spectra of nuclear
> spectroscopy, and into the dose quantities taken up
> [next](/nuclear-physics/radiation-matter-applications/dosimetry-radiation-biology).

[^krane-detectors]: **Krane**, _Introductory Nuclear Physics_, §7.2–7.4, and
**Wong**, _Introductory Nuclear Physics_, §4-4. Gas-counter operating regions and
the Townsend avalanche; scintillator light output and photomultiplier gain;
semiconductor electron-hole collection and the small $W$; the resolution
$R = 2.35\sqrt{FW/E}$ with the Fano factor; the photopeak, Compton continuum and
edge, and escape peaks; and coincidence and timing methods. Detector-response and
attenuation data are maintained by NIST, [https://physics.nist.gov/](https://physics.nist.gov/).