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Gamma rays
Electromagnetic radiation emitted from excited atomic nuclei as an integral part of the process whereby the nucleus rearranges itself into a state of lower excitation (that is, energy content). For the theory of gamma emission
Nature of gamma rays
The gamma ray is an electromagnetic radiation pulse—a photon—of very short wavelength. The electric (E) and magnetic (H) fields associated with the individual radiations oscillate in planes mutually perpendicular to each other and also the direction of propagation with a frequency ν which characterizes the energy of the radiation. The E and H fields exhibit various specified phase-and-amplitude relations, which define the character of the radiation as either electric (EL) or magnetic (ML). The second term in the designation indicates the order of the radiation as 2L-pole, where the orders are monopole (20), dipole (21), quadrupole (22), and so on. The most common radiations are dipole and quadrupole. Gamma rays range in energy from a few kiloelectronvolts to 100 MeV, although most radiations are in the range 50–6000 keV. As such, they lie at the very upper high- frequency end of the family of electromagnetic radiations, which include also radio waves, light rays, and x-rays.
Wave-particle duality
Wave-particle duality
The dual nature of gamma rays is well understood in terms of the wavelike and particlelike behavior of the radiations. For a gamma ray of intrinsic frequency ν, the wavelength is λ = c/ν, where c is the velocity of light; energy is E = hν, where h is Planck's constant. The photon has no rest mass or electric charge but, following the concept of mass-energy equivalence set forth by Einstein, has associated with it a momentum given by p = hν/c = E/c.
While gamma rays and x-rays are usually labeled by their energies (in kiloelectronvolts or megaelectronvolts), an equivalent useful specification in terms of either wavelength or frequency is easily obtained from the relationships given above. For less energetic members of the electromagnetic family, it is customary to classify radio waves in terms of wavelength (in meters) or frequency (in hertz). Photons in the visible and near-visible regime are labeled alternately by energy (in electronvolts) or wavelength (in nanometers). However, the general considerations on propagation, polarization, and Doppler shifts are quite similar for all. One of the early techniques for precise measurements of low-energy nuclear gamma rays utilized a bent-crystal spectrometer, which measures wavelength; the corresponding energies were subsequently obtained from the equivalence relations given above.
Origin
Origin
From a historical perspective, the term “gamma ray” was introduced to label the electromagnetic radiations emanating from nuclear de-excitations (as distinct from alpha, beta, and x-rays). Early observations of nuclear giant-dipole resonance phenomena dealt with gamma rays in the range up to about 30 MeV. High-energy radiations are also observed in cosmic events; for example, the pi-zero meson (π0) annihilates by the simultaneous emission of two gamma rays with total energies in the 100-MeV range.
Other sources of very high energy electromagnetic radiations (or gamma rays) have become of increasing interest. Electron beams in the gigaelectronvolt range can produce gamma rays in the range of hundreds of megaelectronvolts via brehmsstrahlung from a fixed target, or alternatively from a collision between high-energy beam electrons and an opposing photon beam from a simple laser (all carried out in vacuum).
For example, if an argon laser [wavelength (λ) ≈ 350 nm; energy (E) ≈ 3.5 eV] is focused opposite to the electron beam direction, low-energy photons backscattered from the electrons (in Compton scattering) will achieve an energy boost proportional to the electron momentum, resulting in scattered photons with energies of around 500 MeV. With this technique, simultaneous observation of the scattered electron (direction and momentum) also defines the precise gamma-ray energy. Since the Compton scattering process conserves polarization, the polarization of the gamma-ray flux is also known. This production process has been used to map out the region of the nuclear delta resonance (at around 300 MeV), which lies well above the giant dipole resonance.
Nuclear gamma rays
Nuclear gamma rays
One of the most frequently utilized sources of nuclear gamma rays is 60Co (that is, the cobalt isotope of N = 33 neutrons, Z = 27 protons, and thus of atomic mass number A = N + Z = 60). The decay process (Fig. 1) begins when 60Co (in its ground state, or state of lowest possible excitation) decays to 60Ni (N = 32, Z = 28) by the emission of a β− particle. More than 99% of these decays lead to the 2506-keV level of 60Ni; this level subsequently deexcites by an 1173-keV gamma transition to the 1332-keV level, which in turn emits a 1332-keV gamma ray leading to the 60Ni ground state.
Fig. 1 Energy-level diagram illustrating the gamma decay of levels of 60Ni resulting from beta decay of 60Co.
The gamma rays from 60Ni carry information not only on the relative excitation of the 60Ni levels, but also on the quantum-mechanical nature of the individual levels involved in the gamma decay. From the standpoint of nuclear physics, the levels of a given nucleus can be described most simply in terms of their excitation energies (Ex) relative to the ground state, and in terms of the total angular momentum (J) and parity (π) quantum numbers given as Jπ. For a gamma-ray transition from initial state i to final state f, one obtains Eix − Efx = E′γ is the measured gamma energy after small (second-order) corrections for nuclear recoil and relativistic effects. Nuclear selection rules restrict the multipole character of the radiation according to the change in the quantum numbers Jπ of the initial and final states. In Fig. 1, for example, the transitions must be electric quadrupole (E2), since they connect states of similar parity (π = +) by radiation of order L ≥ Ji − Jf = 2.
Use as nuclear labels
Various nuclear species exhibit distinctly different nuclear configurations: the excited states, and thus the gamma rays which they produce, are also different. Precise measurements of the gamma-ray energies resulting from nuclear decays may therefore be used to identify the gamma-emitting nucleus, that is, not only the atomic number Z but also the specific isotope as designated by A. This has ramifications for nuclear research and also for a wide variety of more
practical applications
The two most widely used detectors for such studies are the NaI(Tl) detector and the Ge(Li) detector. Figure 2 shows typical gamma spectra measured for sources of 60Co and 54Mn. Full-energy peaks are labeled by the gamma-ray energy, given in kiloelectronvolts. The figure of merit for these detectors, defined for a given gamma energy as the full-width-at-half-maximum (FWHM) for the full energy peak, is indicated. Although the more efficient NaI(Tl) detector can clearly distinguish the 60Co and 54Mn gamma rays, it is evident that the Ge(Li) detector, having a line width of only 1.8 keV, is more appropriate for complex nuclei, or for studies involving a greater number of source components.
The two most widely used detectors for such studies are the NaI(Tl) detector and the Ge(Li) detector. Figure 2 shows typical gamma spectra measured for sources of 60Co and 54Mn. Full-energy peaks are labeled by the gamma-ray energy, given in kiloelectronvolts. The figure of merit for these detectors, defined for a given gamma energy as the full-width-at-half-maximum (FWHM) for the full energy peak, is indicated. Although the more efficient NaI(Tl) detector can clearly distinguish the 60Co and 54Mn gamma rays, it is evident that the Ge(Li) detector, having a line width of only 1.8 keV, is more appropriate for complex nuclei, or for studies involving a greater number of source components.
Fig. 2 Gamma-ray spectra from radioactive sources as measured with both Nal(TI) and Ge(Li) detectors. Inset shows the components of detector apparatus. (a) 54Mn source. (b) 60Co sources.
Applications to nuclear research
One of the most useful studies of the nucleus involves the bombardment of target nuclei by energetic nuclear projectiles, to form final nuclei in various excited states. For example, 48Ca bombarded by 16O makes 60Ni strongly via the 48Ca(16O, 4n)60Ni reaction, as well as numerous other final species. Ge(Li) measurements of the decay gamma rays are routinely used to identify the various final nuclei according to their characteristic gamma rays, that is, the 1332- and 1173-keV gamma rays of 60Ni, for example.Precise measurements of the gamma energies, together with intensity and time-coincidence measurements, are then used to establish the sequence of gamma-ray decay, and thus construct from experimental evidence the nuclear level scheme. Angular correlation and linear polarization measurements determine the radiation character (as M1, E1, E2, or M2 or mixed) and thus the spin-parity of the nuclear levels. These studies provide a very useful tool for investigations of nuclear structure and classification of nuclear level schemes.
Practical applications
Practical applications
In these applications, the presence of gamma rays is used to detect the location or presence of radioactive atoms which have been deliberately introduced into the sample. In irradiation studies, for example, the sample is activated by placing it in the neutron flux from a reactor. The resultant gamma rays are identified according to isotope by Ge(Li) spectroscopy, and thus the composition of the original sample can be inferred. Such studies have been used to identify trace elements found as impurities in industrial production, or in ecological studies of the environment, such as minute quantities of tin or arsenic in plant and animal tissue. In tracer studies, a small quantity of radioactive atoms is introduced into fluid systems (such as the human bloodstream), and the flow rate and diffusion can be mapped out by following the radioactivity. Local concentrations, as in tumors, can also be determined.
Doppler shift
If Eγ0 = hν0 is the gamma ray energy emitted by a nucleus at rest, then the energy Eγ = hν emitted from a nucleus moving with velocity v at angle θ (with respect to the direction of motion) is given by Eq. (1)
(1) where c is the velocity of light. In terms of the frequency ν, this expression is entirely analogous to the well-known Doppler shift of sound waves. Experimental measurements of the Doppler shift are used to determine the velocity of the nucleus and, more importantly, to shed light on the lifetime of the nuclear gamma-emitting state. A major advantage of this technique is that the same nuclear reaction which produces the excited nuclear states can also be employed to impart a large velocity to the nucleus.For example, the velocity of 60Ni nuclei produced via the 48Ca(16O,4n)60Ni reaction at E(16O) = 50 MeV is v/c = 0.00204, and instead of Eγ = 1332 keV one should observe Eγ = 1359 keV. The extent of the shift is clearly within the resolving power of the Ge(Li) detector, which may therefore be used to measure Eγ and thus infer v. In most nuclear reactions, v is a known function of time t [that is, v = v(t)], and one therefore obtains a distribution of Eγ's whose precise shape may be related to the lifetime of the nuclear state.Doppler-shift measurements of gamma rays from recoil nuclei produced in nuclear reactions have been routinely used since the mid-1960s to measure nuclear lifetimes of 10−9 to 10−14 s, a range previously considered inaccessible to study.
Interaction with matter
Interaction with matter
For the three types of interaction with matter which together are responsible for the observable absorption of gamma rays, namely, Compton scattering, the photoelectric effect, and pair production,
The energy of a photon may be absorbed totally or partially in interaction with matter; in the latter case the energy of the photon is reduced and its direction of motion is changed. Photons are thus absorbed not gradually, but in discrete events, and one interaction is sufficient to remove a photon from a collimated beam of gamma rays. The intensity I of a beam decreases exponentially, as in Eq. (2), where x is the
The energy of a photon may be absorbed totally or partially in interaction with matter; in the latter case the energy of the photon is reduced and its direction of motion is changed. Photons are thus absorbed not gradually, but in discrete events, and one interaction is sufficient to remove a photon from a collimated beam of gamma rays. The intensity I of a beam decreases exponentially, as in Eq. (2), where x is the
(2) path length, I0 is the initial intensity, and μ is the linear attenuation coefficient, which is characteristic of the material and the gamma energy.
The dependence of the attenuation coefficient on gamma-ray energy is shown in Fig. 3 for a lead absorber. For different absorbers, the attenuation is greater for the more dense materials. Most attenuation coefficients are tabulated as mass attenuation coefficients μ/ρ where ρ is the material or elemental density.
The dependence of the attenuation coefficient on gamma-ray energy is shown in Fig. 3 for a lead absorber. For different absorbers, the attenuation is greater for the more dense materials. Most attenuation coefficients are tabulated as mass attenuation coefficients μ/ρ where ρ is the material or elemental density.
Fig. 3 Graphic representation of partial and total attenuation coefficients for lead as a function of gamma energy. (National Institute of Standards and Technology
Gamma-ray detectors
Instruments that register the presence of gamma (γ) radiation. Such detectors convert some or all of the energy of gamma radiation into an electrical signal. Most instruments are capable of detecting individual gamma-ray photons (or quanta), each of which produces a short (0.1–5-microsecond) current pulse at the detector output. The output pulses may be made visible on an oscilloscope, made audible through a speaker (such as the familiar Geiger counter), or be electronically processed further, depending on the application.
Fig. 1 Domains in photon energy versus atomic number (Z) of an absorber. Each of the three mechanisms by which gamma rays lose energy to ionization is of dominant importance in its domain. (After R. D. Evans, The Atomic Nucleus, McGraw-Hill, 1955)
Gamma-ray detectors range from hand-held devices capable of giving some indication of the intensity of a radiation field, to devices that accurately measure the energy and event time of individual photons reaching detectors assembled into a single complex instrument. These diverse detectors are widely used in industry, medicine, and research.
Response to gamma radiation
In common with most radiation detectors, gamma-ray detectors respond not to the radiation but to its secondary effects, in this case energetic electrons. Photons have neither mass nor charge and pass through matter rather easily. In so doing, they lose energy by (1) elastic scattering of electrons (Compton effect), (2) electron-positron (β+β-) pair production, and (3) at lower energies by photoabsorption. In these processes the energy of the photon is converted to the kinetic energy of the few electrons with which it interacts. Since electrons are much less penetrating than gamma-ray photons, their energy is largely trapped within the detector, where their ionizing effect creates a response convertible to an electrical output. In a gas-ionization device, such as Geiger counter, this occurs by the production of ion–electron pairs and in a solid-state device, such as a germanium detector, by production of electron-hole pairs. In a scintillation device, for example, a sodium iodide (NaI) detector, the response is caused by the emission of optical photons from atoms excited by the passage of energetic electrons.
In accurate instruments the magnitude of the current pulse created by a single gamma-ray photon is closely proportional to the energy within the detector volume. However, gamma radiation is so penetrating that any particular event may involve only partial absorption of the photon. For example, a single Compton scattering may be followed by the escape of the scattered photon (now reduced in energy) from the detector, leaving behind only the energy of the scattered electron.
Photon interactions in matter
The three principal interactions of gamma rays with matter depend on the photon energy and the atomic number (Z) of the absorber. In photoabsorption, a photon is absorbed by collision with an atom, its energy and momentum being conserved by the ejection of an electron. This mechanism is important to gamma-ray detection since it is the only one of these interactions in which the photon energy is completely captured by ionization. This mechanism dominates at low photon energies and for absorbers of high Z; for high-energy photons, pair production dominates Fig. 1. This process cannot occur unless the photon energy exceeds twice the rest-mass of an electron (2 × 511 keV), the minimum requirement for creating an electron-positron pair (β+ β-). Although this positron loses energy rapidly in a solid, it ultimately annihilates an electron to liberate two new gamma photons, each of energy 511 keV. To register the full energy, both photons must be contained within the detector.Desirable detector characteristics are therefore (1) high Z, enhancing the domain of photoabsorption, (2) reasonable size, giving photons a chance to convert energy to ionization in more than one encounter, and (3) high density, maximizing the number of electrons encountered in the distance traveled.
Gamma-ray spectra and detector characteristics
An experiment may be imagined in which a detector is placed adjacent to a point source such as a cobalt-60 source that emits gamma rays of energies 1173 and 1332 keV. The output current pulses (one per photon detected) are amplified electronically and digitized. The resulting stream of data is stored in the form of a histogram showing numbers of events on the ordinate and output pulse amplitude on the abscissa, and called a spectrum by analogy with optical spectra. Since the source has only two photon energies (or wavelengths, photon energy E being related to wavelength λ by λ = hc/E, where h is Planck's constant and c is the speed of light), two lines are found in the spectrum Fig. 2.
Fig. 2 Gamma-ray spectra of a cobalt-60 radiation source. (a) Spectrum from a high-purity germanium detector of 25% efficiency. The two peaks represent events in which the original photon energy (1173 and 1332 keV) was completely contained within the crystal. The platform at lower energies corresponds to events in which a photon lost some energy to the crystal but eventually escaped. (b) Spectrum that results from activating a bismuth germanate scintillation detector surrounding the high-purity germanium crystal so that the event is not recorded if both detectors give an output. The platform of degraded events seen in the high-purity germanium detector is substantially suppressed.
For events at the peak energy (or photopeak), all the photon energy is trapped within the sensitive volume. The background of partial-energy events is called the Compton platform. Such spectra help to define the three characteristic parameters of gamma-ray detectors: (1) resolution, the width of a peak at its half-height point, which measures the minimum energy separation at which two different photon peaks of comparable intensity are distinguishable; (2) total detection efficiency, the number of events registered in the spectrum versus the number of photons known to have struck the detector (by calculation from the source emission rate); and (3) peak-to-total ratio, the number of events in the photopeak versus the total number detected at that and all lower energies. These characteristics vary with photon energy, which must therefore be specified with the performance figures.
For events at the peak energy (or photopeak), all the photon energy is trapped within the sensitive volume. The background of partial-energy events is called the Compton platform. Such spectra help to define the three characteristic parameters of gamma-ray detectors: (1) resolution, the width of a peak at its half-height point, which measures the minimum energy separation at which two different photon peaks of comparable intensity are distinguishable; (2) total detection efficiency, the number of events registered in the spectrum versus the number of photons known to have struck the detector (by calculation from the source emission rate); and (3) peak-to-total ratio, the number of events in the photopeak versus the total number detected at that and all lower energies. These characteristics vary with photon energy, which must therefore be specified with the performance figures.
Gas-ionization detectors
These detectors are simple, cheap, and reliable but have very low efficiency because of the low density of their sensitive volume. Their principal application is in monitoring strong radiation fields for industry and radiation protection. The individual output pulses are electronically integrated; the instrument gives a reading of count rate or field intensity, often calibrated directly in dose rate. The amplification occurs in the gas itself as a discharge develops under the intense electric field surrounding the anode wire. This process is virtually noise-free and results in a gain of about 106 on the original number of electrons liberated.
Scintillation detectors
These detectors employ certain materials which are nearly transparent and convert a significant amount of ionization energy into light emitted in the visible or near-visible region. The material is viewed by one or more photomultiplier tubes, which collect the light and convert it into an electrical pulse with very low noise and a typical gain of 108. The most common scintillator for gamma-ray application is sodium iodide with a thallium doping, NaI(Tl). Crystals can be produced in virtually any shape or size up to 15 × 15 in. (38 × 38 cm) cylinders; the most common laboratory detector is 3 × 3 in. (7.6 × 7.6 cm). For small crystals, the resolution is typically 6.5% at 662 keV (cesium-137 radiation) and increases approximately with the inverse square root of the energy.
Other alkali halide scintillators in common laboratory use are barium fluoride (BaF2) and cesium iodide (CsI). These have a higher density and average atomic number than sodium iodide, and for a given detector size give a higher efficiency and higher peak-to-total ratio, although their resolution is slightly poorer. The barium fluoride scintillator is used where a fast response is important, as with very high counting rates or fast electronic timing.Another class of scintillator used for gamma-ray detection comprises the heavy-metal complex oxides, especially bismuth germanate (Bi4Ge3O12). It has a very high density and offers the strongest gamma-radiation absorption of any known practical scintillator. In resolution it is appreciably poorer than sodium iodide; a good performance for a 3 × 3 in. (7.6 × 7.6 cm) crystal is 11.5% at 662 keV.
Solid-state detectors
For general application, the germanium detector is the most useful. The first successful ones, called Ge(Li) detectors, depended on lithium compensation of crystal imperfections. Manufacturing techniques have been improved, and detectors based on high-purity intrinsic germanium (HPGe), are now readily available. Germanium detectors function at liquid-nitrogen temperature. High-purity germanium detectors have the following advantages over Ge(Li) detectors: they may be thermally cycled, and radiation damage, such as that caused by neutrons, can be annealed cheaply and easily.
Germanium detectors have better resolution than most other gamma-ray detectors, which scales differently with energy than the resolution of scintillation detectors: a typical performance is 1 keV resolution at 100 keV, 2 keV at 1300 keV, and 3 keV at 2000 keV. Historically, the photopeak efficiency of germanium detectors has been defined in terms of a 3 × 3 in. (7.6 × 7.6 cm) NaI(Tl) detector at the same distance from a radiation source, usually cobalt-60. On this standard, an efficiency of 25% is typical for high-purity germanium, but detectors of up to 70% are routinely available, and a 100% detector has been demonstrated.Silicon detectors have less general applicability. They must also be cooled to liquid-nitrogen temperature, and have significantly better resolution than germanium detectors but are less efficient. These detectors are useful in the spectroscopy of very low-energy radiation (below 50 keV) where the efficiency is equal but the resolution (typically 0.6 keV) nearly two times better than that of germanium.
Detector systems
Powerful instrumentation has been created by assembling separate gamma-ray detectors into a single unit. For example, Fig. 2b shows the performance gained by suppressing escaped radiation from a high-purity germanium detector. In this case the active crystal was surrounded by a bismuth germanate scintillator detector except in the direction of the radiation source. Electronic circuits processed the output pulses from both detectors so that if they were simultaneous (within 5 × 10-8 s) the event was rejected. In some instruments a spherical shell of scintillation detectors (typically 100 elements) surrounds the radiation source. In one application the outputs of all the detectors are summed whenever an event occurs. In this way the instrument acts as a gamma-ray calorimeter, registering an output proportional to the energy of gamma radiation emitted in the event. For example, the fusion of two heavy nuclei is typically accompanied by a burst of up to 30 gamma rays with a total energy of perhaps 30 MeV. Photon energies exceeding 100 MeV are associated with the decay of subnuclear systems such as the J/ψ particle