The Ultimate Guide to Choosing Introduction To Radiation Detectors

Author: Morgan

Aug. 06, 2024

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Introduction to Radiation Detectors

For those who work with or around radiation, one of the most important factors is an awareness of the levels of radiation around them. This is primarily accomplished through the use of radiation detectors of varying types. A basic understanding of the different types of detectors out there and how they work can go a long way both to finding the best detector for the required task and also for maximizing the benefits of operating that detector.

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A NOTE: &#;GEIGER COUNTERS&#;

Many people, thinking of radiation detection, tend to group them all together under the term &#;Geiger counters,&#; a misconception heartily encouraged by popular TV shows and movies. While one of the most common types of radiation detector is in fact called a &#;Geiger Mueller (G-M) tube,&#; the catchall phrase &#;Geiger Counter&#; isn&#;t always the most appropriate. It applies to a very specific type of detector, and generally to a specific application of that detector. Radiation detection devices are typically categorized by either the type of detector element employed, or by the application involved. People will refer to instruments as an Ion Chamber, or a Survey Meter, or a Contamination Meter, or a Frisker Probe. Popular culture has so thoroughly subverted the proper usage of &#;Geiger Counter&#; that using the phrase doesn&#;t generally provide enough information about the device in question.

FIRST RADIATION DETECTORS

Since the early days of radiation testing by Roentgen and Becquerel, scientists have sought ways to measure and observe the radiation given off by the materials they worked with. One of the earliest means of capturing any sort of data from radioactivity was a photographic plate. A photographic plate would be placed in the path/vicinity of a radioactive beam or material. When the plate was developed, it would have spots or be fogged from the exposure to the radiation. Henri Becquerel used a method similar to this to demonstrate the existence of radiation in .

Another common early detector was the electroscope. These used a pair of gold leaves that would become charged by the ionization caused by radiation and repel each other. This provided a means of measuring radiation with a better level of sensitivity than was reliably possible using photographic plates. Depending on the arrangement of the device, they could be configured to measure alpha or beta particles, and were a valuable tool for early experiments involving radioactivity.

An interesting early device, borne out of a desire to measure the actual individual particles or rays being emitted by a radioactive substance, as opposed to a more gross measurement of a radioactive field, was the spinthariscope. Developed by William Crookes, who had also invented the Crookes Tube used by Wilhelm Roentgen to discover X-Rays, it used a zinc sulfide screen at the end of a tube, with a lens at the other end, with a small amount of a radioactive substance near the zinc sulfide screen. The zinc sulfide would react with the alpha particles emitted, and each interaction would result in a tiny flash of light. This was one of the first means of counting a rate of decay, albeit a very tedious one, as it meant scientists had to work in shifts watching and literally counting the flashes of light. The spinthariscope wasn&#;t very practical as a long term solution for radiation detection, though it did undergo a revival later in the 20th century as an educational tool. This tendency of certain materials to give off light when exposed to radiation would also prove valuable in future radiation detection technologies.

These early devices, and many others, such as cloud chambers, were valuable in developing an understanding of the basic principles of radiation and conducting important experiments that set the stage for later developments. This included development of new types of radiation detectors, many of which are still in use today, such as G-M Tubes, Ion Chambers, and Scintillators.

WHERE/WHEN YOU&#;D NEED RADIATION DETECTORS

An important part of knowing what type of detector to use is to have an idea of how and where it will be used. Different applications and settings call for different types of detectors, as each detector type has various ways it can be specialized to fit a role. The applications for radiation detection instruments can be broadly categorized into a few different core tasks: measurement, protection, and search.

Radiation measurement tasks are for situations where there is a known presence of radioactive materials which need to be monitored. The goal with this type of detection is awareness. Awareness of the strength of an established radioactive field, the boundaries of a radioactive area, or simply of the spread of radioactive contamination. These are settings where the presence of radiation is expected, or at least considered likely. The requirements for detectors involved in these settings are unique, often with relatively higher measurement ranges or with modifications needed to specifically look for one type of radiation.

Radiation protection is similar to radiation measurement applications in the sense that it is usually in a setting where radiation is expected to be found. However, the goals are different. With radiation measurement settings, the goal is to monitor the radioactivity itself, to be aware of fluctuations, boundaries, etc. With radiation protection, the goal is monitoring people. Radiation dosimetry is the most common example of this, with radiation badges being worn by medical personnel, nuclear industry workers, and many other occupationally exposed workers all over the world. The importance of this is that it provides protection from the most harmful effects of radiation exposure through awareness, in that a wearer can keep informed of how much radiation they&#;ve been exposed to, and how that corresponds to potential health effects, and alter their behavior or position or schedule accordingly.

Radiation search differs from the other two basic categories of radiation detection applications in that it is predicated both on the fact that radiation is not expected in the area, and the desire to keep things that way. Primarily the goal of radiation security personnel, first responders, or groups such as customs & border inspectors, radiation search has a different set of requirements to mirror the significantly different circumstances in which it takes place. Detectors need to be highly sensitive, with the concern being more about smaller, concealed radioactive sources or materials. Spectroscopy is often very helpful as well, since it is typically a small subset of radioactive isotopes that are of concern, and being able to filter those out that are present due to legitimate reasons such as medical treatment or just an accumulation of a naturally occurring radioactive substance is important.

These three categories, and the varying tasks that fit inside them, help determine what the best type of instrument or detector is best suited for the task.

TYPES

When talking about radiation detection instruments, there are three types of detectors that are most commonly used, depending on the specific needs of the device. These are: Gas-Filled Detectors, Scintillators, and Solid State detectors. Each has various strengths and weaknesses that recommend them to their own specific roles.

GAS FILLED

The first type of radiation detector, gas-filled detectors, are amongst the most commonly used. There are several types of gas-filled detector, and while they have various differences in how they work, they all are based on similar principles. When the gas in the detector comes in contact with radiation, it reacts, with the gas becoming ionized and the resulting electronic charge being measured by a meter.

The different types of gas-filled detectors are: ionization chambers, proportional counters, and Geiger-Mueller (G-M) tubes. The major differentiating factor between these different types is the applied voltage across the detector, which determines the type of response that the detector will register from an ionization event.

ION CHAMBER

At the lower end of the voltage scale for gas-filled detectors are Ionization Chambers, or Ion Chambers. They operate at a low voltage, meaning that the detector only registers a measurement from the &#;primary&#; ions (in actuality pair of ions created: a positively charged ion and a free electron) caused by an interaction with a radioactive photon in the reaction chamber. Thus the measurement that the detector records is directly proportional to the number of ion pairs created. This is particularly useful as a measure of absorbed dose over time. They are also valuable for the measurement of high-energy gamma rays, as they don&#;t have any of the issues with dead time that other detector types can have.

However, ion chambers are unable to discriminate between different types of radiation, meaning they cannot be used for spectroscopy. They can also tend towards being more expensive than other solution. Despite this, they are valuable detectors for survey meters. They are also widely used in laboratories to establish reference standards for calibrations.

PROPORTIONAL

The next step up on the voltage scale for gas-filled detectors is the proportional (or gas-proportional) counter. They are generally devised so that for much of the area inside the chamber, they perform similarly to an ion chamber, in that interactions with radiation create ion pairs. However, they have a strong enough voltage that the ions &#;drift&#; towards the detector anode. As the ions approach the detector anode, the voltage increases, until they reach a point where a &#;gas amplification&#; effect occurs.

Gas amplification means that the original ions created by the reaction with a photon of radiation causes further ionization reactions, which multiply the strength of the output pulse measured across the detector. The resulting pulse is proportional to the number of original ion pairs formed, which correlates to the energy of the radioactive field that it is interacting with.

The makes proportional counters very useful for some spectroscopy applications, since they react differently to different energies, and thus are able to tell the difference between different types of radiation that they come into contact with. They are also highly sensitive, which coupled with their effectiveness at alpha and beta detection and discrimination, makes this type of detector very valuable as a contamination screening detector.

GM TUBE

The last major class of gas-filled detectors is the Geiger-Mueller tube, the origin of the name &#;Geiger Counter.&#; Operating at a much higher voltage than other detector types, they differ from other detector types in that each ionization reaction, regardless of whether it is a single particle interaction or a stronger field, causes a gas-amplification effect across the entire length of the detector anode. Thus they can only really function as simple counting devices, used to measure count rates or, with the correct algorithms applied, dose rates.

After each pulse, a G-M has to be &#;reset&#; to its original state. This is accomplished by quenching. This can be accomplished electronically by temporarily lowering the anode voltage on the detector after each pulse, which allows the ions to recombine back to their inert state. This can also be accomplished chemically with a quenching gas such as halogen which absorbs the additional photons created by an ionization avalanche without becoming ionized itself.

Due to the extensive reaction G-M tubes experience with each pulse of radiation, they can experience something called &#;dead time&#; at higher exposure rates, meaning that there is a lag between the pulse cascade and when the gas is able to revert to its original state and be ready to detect another pulse. This can be accommodated for with calibration, or with algorithms in the detection instruments themselves to &#;calculate&#; what the additional pulses would be based on the existing measurement data.

SCINTILLATORS

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The second major type of detectors utilized in radiation detection instruments are Scintillation Detectors. Scintillation is the act of giving off light, and for radiation detection it is the ability of some material to scintillate when exposed to radiation that makes them useful as detectors. Each photon of radiation that interacts with the scintillator material will result in a distinct flash of light, meaning that in addition to being highly sensitive, scintillation detectors are able to capture specific spectroscopic profiles for the measured radioactive materials.

Scintillation detectors work through the connection of a scintillator material with a photomultiplier (PM) tube. The PM tube uses a photocathode material to convert each pulse of light into an electron, and then amplifies that signal significantly in order to generate a voltage pulse that can then be read and interpreted. The number of these pulses that are measured over time indicated the strength of the radioactive source being measured, whereas the information on the specific energy of the radiation, as indicated by the number of photons of light being captured in each pulse, gives information on the type of radioactive material present.

Due to their high sensitivity and their potential ability to &#;identify&#; radioactive sources, scintillation detectors are particularly useful for radiation security applications. These can take many forms, from handheld devices used to screen containers for hidden or shielded radioactive material, to monitors set up to screen large areas or populations, able to differentiate between natural or medical sources of radiation and sources of more immediate concern, such as Special Nuclear Material (SNM).

SOLID STATE

The last major detector technology used in radiation detection instruments are solid state detectors. Generally using a semiconductor material such as silicon, they operate much like an ion chamber, simply at a much smaller scale, and at a much lower voltage. Semiconductors are materials that have a high resistance to electronic current, but not as high a resistance as an insulator. They are composed of a lattice of atoms that contain &#;charge carriers,&#; these being either electrons available to attach to another atom, or electron &#;holes,&#; or atoms with an empty place where an electron would/could be.

Silicon solid state detectors are composed of two layers of silicon semiconductor material, one &#;n-type,&#; which means it contains a greater number of electrons compared to holes, and one &#;p-type,&#; meaning it has a greater number of holes than electrons. Electrons from the n-type migrate across the junction between the two layers to fill the holes in the p-type, creating what&#;s called a depletion zone.

This depletion zone acts like the detection area of an ion chamber. Radiation interacting with the atoms inside the depletion zone causes them to re-ionize, and create an electronic pulse which can be measured. The small scale of the detector and of the depletion zone itself means that the ion pairs can be collected quickly, meaning that the instruments utilizing this type of detector can have a particularly quick response time. This, when coupled with their small size, makes this type of solid state detector very useful for electronic dosimetry applications. They are also able to withstand a much higher amount of radiation over their lifetime than other detectors types such as G-M Tubes, meaning that they are also useful for instruments operating in areas with particularly strong radiation fields.

Gamma and X-Ray Detection

DETECTOR OVERVIEW
The kinds of detectors commonly used can be categorized as:

  1. Gas-filled Detectors
  2. Scintillation Detectors
  3. Semiconductor Detectors

The choice of a particular detector type for an application depends upon the X-ray or gamma energy range of interest and the application&#;s resolution and efficiency requirements. Additional considerations include count rate performance, the suitability of the detector for timing experiments, and of course, price.

DETECTOR EFFICIENCY
The efficiency of a detector is a measure of how many pulses occur for a given number of gamma rays. Various kinds of efficiency definitions are in common use for gamma ray detectors:

  1. Absolute Efficiency: The ratio of the number of counts produced by the detector to the number of gamma rays emitted by the source (in all directions).
  2. Intrinsic Efficiency: The ratio of the number of pulses produced by the detector to the number of gamma rays striking the detector.
  3. Relative Efficiency: Efficiency of one detector relative to another; commonly that of a germanium detector relative to a 3 in. diameter by 3 in. long NaI crystal, each at 25 cm from a point source, and specified at 1.33 MeV only.
  4. Full-Energy Peak (or Photopeak) Efficiency: The efficiency for producing full-energy peak pulses only, rather than a pulse of any size for the gamma ray.

Clearly, to be useful, the detector must be capable of absorbing a large fraction of the gamma ray energy. This is accomplished by using a detector of suitable size, or by choosing a detector material of suitable high Z. An example of a full-energy peak efficiency curve for a germanium detector is shown in Figure 1.1.

Figure 1.1 - Efficiency Calibration

DETECTOR RESOLUTION
Resolution is a measure of the width (full width half max) of a single energy peak at a specific energy, either expressed in absolute keV (as with Germanium Detectors), or as a percentage of the energy at that point (Sodium Iodide Detectors). Better (lower FWHM value) resolution enables the system to more clearly separate the peaks within a spectrum. Figure 1.2 shows two spectra collected from the same source, one using a sodium iodide (NaI(TI)) detector and one using germanium (HPGe). Even though this is a rather simple spectrum, the peaks presented by the sodium iodide detector are overlapping to some degree, while those from the germanium detector are clearly separated. In a complex spectrum, with peaks numbering in the hundreds, the use of a germanium detector becomes mandatory for analysis.

Figure 1.2

GAS-FILLED DETECTORS
A gas-filled detector is basically a metal chamber filled with gas and containing a positively biased anode wire. A photon passing through the gas produces free electrons and positive ions. The electrons are attracted to the anode, producing an electric pulse.

At low anode voltages, the electrons may recombine with the ions. Recombination may also occur for a high density of ions. At a sufficiently high voltage nearly all electrons are collected, and the detector is known as an ionization chamber. At higher voltages the electrons are accelerated toward the anode at energies high enough to ionize other atoms, thus creating a larger number of electrons. This detector is known as a proportional counter. At higher voltages the electron multiplication is even greater, and the number of electrons collected is independent of the initial ionization. This detector is the Geiger-Mueller counter, in which the large output pulse is the same for all photons. At still higher voltages continuous discharge occurs.

The different voltage regions are indicated schematically in Figure 1.3. The actual voltages can vary widely from one detector to the next, depending upon the detector geometry and the gas type and pressure.

Figure 1.3 - Gas Detector Output vs. Anode Voltage

IONIZATION CHAMBER
The very low signal output for the ionization chamber makes this detector difficult to use for detecting individual gamma rays. It finds use in high radiation fluxes in which the total current produced can be very large. Many radiation monitoring instruments use ionization chambers. Absolute ionization measurements can be made, using an electrometer for recording the output.1

PROPORTIONAL COUNTER
Proportional counters are frequently used for X-ray measurements where moderate energy resolution is required. A spectrum of 57Co is shown in Figure 1.5 in which 14.4 keV gamma rays are wellseparated from the 6.4 keV X rays from iron.

Proportional counters can be purchased in different sizes and shapes, ranging from cylindrical with end or side windows to &#;pancake&#; flat cylinders. They may be sealed detectors or operate with gas flow, and may have thin beryllium windows or be windowless. A detector is typically specified in terms of its physical size, effective window size and gas path length, operating voltage range and resolution for the 5.9 keV X ray from a 55Fe source (Mn X ray). Typical resolutions are about 16 to 20% full-width at half maximum (FWHM).

Operating voltages depend upon the fill gas as well as the geometry. For X rays, noble gases are often used, with xenon, krypton, neon and argon common choices. Xenon and krypton are selected for higher energy X rays or to get higher efficiencies, while neon is selected when it is desired to detect low energy X rays in the presence of unwanted higher energy X rays. Sometimes gas mixtures are used, such as P-10 gas, which is a mixture of 90% argon and 10% methane. Gas pressures are typically one atmosphere. The preamplifier available for proportional counters is shown in Figure 1.4.

Figure 1.4 - Proportional Counter and Preamplifier

GEIGER-MUELLER COUNTER
The Geiger-Mueller counter produces a large voltage pulse that is easily counted without further amplification. No energy measurements are possible since the output pulse height is independent of initial ionization. Geiger-Mueller counters are available in a wide variety of sizes, generally with a thin mica window. The operating voltage is in the plateau region (see Figure 1.3), which can be relatively flat over a range of bias voltage. The plateau is determined by measuring the counting rate as a function of the anode voltage.

The discharge produced by an ionization must be quenched in order for the detector to be returned to a neutral ionization state for the next pulse. This is accomplished by using a fill gas that contains a small amount of halogen in addition to a noble gas. The voltage drop across a large resistor between the anode and bias supply will also serve to quench the discharge since the operating voltage will be reduced below the plateau.

The Geiger-Mueller counter is inactive or &#;dead&#; after each pulse until the quenching is complete. This dead time can be hundreds of microseconds long, which limits the counter to low count rate applications.

SCINTILLATION DETECTORS
A gamma ray interacting with a scintillator produces a pulse of light, which is converted to an electric pulse by a photomultiplier tube. The photomultiplier consists of a photocathode, a focusing electrode and 10 or more dynodes that multiply the number of electrons striking them several times each. The anode and dynodes are biased by a chain of resistors typically located in a plug-on tube base assembly. Complete assemblies including scintillator and photomultiplier tube are commercially available from Mirion.

The properties of scintillation material required for good detectors are transparency, availability in large size, and large light output proportional to gamma ray energy. Relatively few materials have good properties for detectors. Thallium activated NaI and CsI crystals are commonly used, as well as a wide variety of plastics. LaBr3 (Ce) crystals are a newer type of scintillation detector material offering better resolution, but otherwise, similar characteristics to NaI detector crystals. NaI is still the dominant material for gamma detection because it provides good gamma ray resolution and is economical. However, plastics have much faster pulse light decay and find use in timing applications, even though they often offer little or no energy resolution.

Figure 1.5 - 57Co Spectrum from Counter

NaI(Tl) SCINTILLATION DETECTORS
The high Z of iodine in NaI gives good efficiency for gamma ray detection. A small amount of Tl is added in order to activate the crystal, so that the designation is usually NaI(Tl) for the crystal. The best resolution achievable ranges from 7.5%-8.5% for the 662 keV gamma ray from 137Cs for 3 in. diameter by 3 in. long crystal, and is slightly worse for smaller and larger sizes. Figure 1.7 shows, respectively, the absorption efficiencies of various thicknesses of NaI crystals and the transmission coefficient through the most commonly used entrance windows. Many configurations of NaI detectors are commercially available, ranging from crystals for X-ray measurements in which the detector is relatively thin (to optimize resolution at the expense of efficiency at higher energies), to large crystals with multiple phototubes. Crystals built with a well to allow nearly spherical 4π geometry counting of weak samples are also a widely-used configuration. A typical preamplifier and amplifier combination is shown in Figure 1.6.

Figure 1.6 - NaI(Tl) Detector Electronics

The light decay time constant in NaI is about 0.25 microseconds, and typical charge sensitive preamplifiers translate this into an output pulse rise time of about 0.5 microseconds. For this reason, NaI detectors are not as well-suited as plastic detectors for fast coincidence measurements, where very short resolving times are required. LaBr3 (Ce) detectors have a light decay time constant of 0.03 microseconds making them another possible solution for coincidence measurements.

SEMICONDUCTOR DETECTORS
A semiconductor is a material that can act as an insulator or as a conductor. In electronics the term &#;solid state&#; is often used interchangeably with semiconductor, but in the detector field the term can obviously be applied to solid scintillators. Therefore, semiconductor is the preferred term for those detectors which are fabricated from either elemental or compound single crystal materials having a band gap in the range of approximately 1 to 5 eV. The group IV elements silicon and germanium are by far the most widely-used semiconductors, although some compound semiconductor materials are finding use in special applications as development work on them continues.

Table 1.1 shows some of the key characteristics of various semiconductors as detector materials:

Semiconductor detectors have a p-i-n diode structure in which the intrinsic (i) region is created by depletion of charge carriers when a reverse bias is applied across the diode. When photons interact within the depletion region, charge carriers (holes and electrons) are freed and are swept to their respective collecting electrode by the electric field. The resultant charge is integrated by a charge sensitive preamplifier and converted to a voltage pulse with an amplitude proportional to the original photon energy.

Since the depletion depth is inversely proportional to net electrical impurity concentration, and since counting efficiency is also dependent on the purity of the material, large volumes of very pure material are needed to ensure high counting efficiency for high energy photons.

Figure 1.7

Prior to the mid-&#;s the required purity levels of Si and Ge could be achieved only by counter-doping p-type crystals with the n-type impurity, lithium, in a process known as lithium-ion drifting. Although this process is still widely used in the production of Si(Li) X-ray detectors, it is no longer required for germanium detectors since sufficiently pure crystals have been available since .

The band gap figures in Table 1.1 signify the temperature sensitivity of the materials and the practical ways in which these materials can be used as detectors. Just as Ge transistors have much lower maximum operating temperatures than Si devices, so do Ge detectors. As a practical matter both Ge and Si photon detectors must be cooled in order to reduce the thermal charge carrier generation (noise) to an acceptable level. This requirement is quite aside from the lithium precipitation problem which made the old Ge(Li), and to some degree Si(Li) detectors, perishable at room temperature.

The most common medium for detector cooling is liquid nitrogen, however, recent advances in electrical cooling systems have made electrically refrigerated cryostats a viable alternative for many detector applications.

In liquid nitrogen (LN2) cooled detectors, the detector element (and in some cases preamplifier components), are housed in a clean vacuum chamber which is attached to or inserted in a LN2 Dewar. The detector is in thermal contact with the liquid nitrogen which cools it to around 77 °K or &#;200 °C. At these temperatures, reverse leakage currents are in the range of 10-9 to 10-12 amperes.

In electrically refrigerated detectors, both closed-cycle mixed refrigerant and helium refrigeration systems have been developed to eliminate the need for liquid nitrogen. Besides the obvious advantage of being able to operate where liquid nitrogen is unavailable or supply is uncertain, refrigerated detectors are ideal for applications requiring long-term unattended operation, or applications such as undersea operation, where it is impractical to vent LN2 gas from a conventional cryostat to its surroundings.

A cross-sectional view of a typical liquid nitrogen cryostat is shown in Figure 1.8.

Figure 1.8 - Model SL Vertical Dipstick Cryostat

DETECTOR STRUCTURE
The first semiconductor photon detectors had a simple planar structure similar to their predecessor, the Silicon Surface Barrier (SSB) detector. Soon the grooved planar Si(Li) detector evolved from attempts to reduce leakage currents and thus improve resolution.

The coaxial Ge(Li) detector was developed in order to increase overall detector volume, and thus detection efficiency, while keeping depletion (drift) depths reasonable and minimizing capacitance. Other variations on these structures have come, and some have gone away, but there are several currently in use. These are illustrated in Figure 1.9 with their salient features and approximate energy ranges.

Figure 1.9 - Detector Structures and Energy Ranges

DETECTOR PERFORMANCE
Semiconductor detectors provide greatly improved energy resolution over other types of radiation detectors for many reasons. Fundamentally, the resolution advantage can be attributed to the small amount of energy required to produce a charge carrier and the consequent large &#;output signal&#; relative to other detector types for the same incident photon energy. At 3 eV/e-h pair (see Table 1.1) the number of charge carriers produced in Ge is about one and two orders of magnitude higher than in gas and scintillation detectors respectively. The charge multiplication that takes place in proportional counters and in the electron multipliers associated with scintillation detectors, resulting in large output signals, does nothing to improve the fundamental statistics of charge production.

The resultant energy reduction in keV (FWHM) vs. energy for various detector types is illustrated in Table 1.2.

At low energies, detector efficiency is a function of cross-sectional area and window thickness while at high energies total active detector volume more or less determines counting efficiency. Detectors having thin contacts, e.g. Si(Li), Low-Energy Ge and Reverse Electrode Ge detectors, are usually equipped with a Be or composite carbon cryostat window to take full advantage of their intrinsic energy response.

Coaxial Ge detectors are specified in terms of their relative fullenergy peak efficiency compared to that of a 3 in. x 3 in. NaI(Tl) Scintillation detector at a detector to source distance of 25 cm. Detectors of greater than 100% relative efficiency have been fabricated from germanium crystals ranging up to about 75 mm in diameter. About two kg of germanium is required for such a detector.

Curves of detector efficiency vs. energy for various types of Ge detectors can be found in the Detector Product Section of this catalog.

1. A.C. Melissinos, Experiments in Modern Physics, Academic Press, New York (), p. 178.

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