Notes on Scintillation

Detectors for Particle Radiation by Konrad Kleinknecht-

Detection of Charged Particles

2 If a charged particle traverses a layer of material, three processes can occur: atoms can be ionized, the particle can emit Cherenkov radiation, or the particle can cause the emission of transition radiation. (8)

2 At photon energies below the excitation energies of the material, the emission of real photons is possible ("Cherenkov Effect") if the velocity of the particle is larger than the phase velocity ^c/_ÖE of light in the material (Cherenkov Threshold"). (8-9)

2 At photon energies from 2eV through 5keV, e=e₁+ie₂ (complex dielectric constant) is complex with e₂>0 and e₁<1. In this case, only virtual photons are exchanged between the particle and the atoms of the material, resulting in excitation or ionization of the atoms and a corresponding energy loss of the particle. (9)

2 In the X-ray domain, at photon energies above 5keV, the absorption coefficient becomes small (e₂×1), and still e₁<1. The threshold velocity for the Cherenkov effect is then larger than the light velocity in a vacuum (in vacuo). In spite of this, radiation is emitted below this threshold if there are discontinuities in the material traversed by the particle. This is called transition radiation. (9)

2 The exact calculation in the photo-absorption model gives the differential cross-section per electron and per energy loss dE of the charged particle:

Here a=e²/(4pe₀ħc)=¹/₁₃₇ is the fine structure constant; e=e₁+ie₂ is the complex dielectric constant; q is the phase of the complex expression 1-e₁b²+ie₂b²; s_g is the cross-section for absorption of a photon of energy E by the atoms of the medium; and N=N₀r/A is the atomic density. (10-11)

2 For photon energies below the excitation energy of the atoms, in the optical region where s_g vanishes, the only remaining term is the 4^th one. It describes the production of Cherenkov radiation. In this region e₂=0 and e=e₁, such that the phase q of the expression 1-e₁b² vanishes below the Cherenkov threshold (b²=1/e₁) and jumps to p above the threshold. (11)

2 The 1^st three terms are responsible for the energy loss of a charged particle by ionization. The third one describes the probability for generating an energetic knock-on electron ("d-ray"). From the other 2 terms the differential average energy loss dE/dx per path dx can be obtained. This is done by integrating the transferred energy E from a value corresponding to the average ionization potential I of the atom up to maximum energy of a struck electron (2m_ec²b²g²). This approximation is the Bethe-Bloch formula:

where N₀ is Avogadro's number; Z and A are the atomic number and mass number of the material transversed; ze and v=bc are the charge and velocity of the ionizing particle; m_e=electron mass; r_e=2.8 fm; and I is the effective ionization potential. (12)

2 The equation gives the average loss of a particle. However, the differential distribution of energy losses isn't, in general, a Gaussian distribution. (14)

2 The average energy lost per ion pair produced (W_i) in gases lies between 41eV in helium and 22eV in xenon. In semiconductors this energy amounts only to 3.5eV in silicon and 2.85eV in germanium; the number of ions created is much larger for the same energy deposit. On the other hand, the fabrication of large silicon or germanium crystals of the purity required meets technical difficulty, and therefore the use of such semiconductor counters is restricted to nuclear physics applications. (16-17)

2 In liquid noble gases the values of W_i are near to those for the gaseous phase: L Ar=23.6eV and L Xe=16eV. Again, the collection of charges in such materials requires a very high degree of purity. (17)

2 A particle will be detected in a measuring instrument by the charge Q liberated during the passage of the particle at t=0 in one of the processes mentioned above or by light quanta. If the precise time of passage is irrelevant for the purpose of the measurement, the simplest way of recording the detector output is a measurement of the average dc current delivered by the detector. (36-37)

Photomultiplier Tubes

2 One of the most common instruments used for measuring the time of passage of a charged particle through a detector is the photomultiplier tube (PMT). (101)

2 Visible light from a scintillator liberates electrons, by the photoelectric effect, from a thin photocathode layer at the internal surface of an evacuated glass or quartz tube. The photocathodes are semiconducting alloys containing one or more metals from the alkali group and materials from group V, usually antimony (Sb). For photocathodes made with two alkali components ("bialkali cathodes"), the number of photoelectrons liberated per incident photon, the quantum efficiency, reaches a maximum value of h_q=27% at a wavelength of l_max=380 nm. (101)

Pg. 103 Material	l Range (nm)	l max (nm)	Quantum Eff. hq(lmax)	Name
AgOCs	300-1100	800	0.004	S1
BiAgOCs	170-700	420	0.068	S10
Cs3Sb-O	160-600	390	0.19	S11
Na2KSb-Cs	160-800	380	0.22	S20
K2CsSb	170-600	380	0.27	Bialkali

Scintillators

2 A scintillation counter has two functions: the conversion of the excitation of a transparent material caused by the ionizing particle into visible light and the transport of this light to the photocathode of the PMT. (107)

2 Inorganic scintillators are ionic crystals doped with activator ("color") centers. Ionizing particles produce free electrons, free holes, and electron-hole pairs (excitons). These move around in the lattice until they reach an activator center A, which they transform into an excited state A*. A* can decay back to A with emission of light. (107)

2 Inorganic scintillators are frequently used for measurement of gamma ray and X-ray energies. Since the light yield per ionization energy is much higher than that of organic scintillators, the statistical fluctuation of the number of scintillation photons is lower and the energy resolution better than for those scintillators. (108)

2 Mean decay times of scintillation light in inorganic crystals are usually larger than .2ms. In contrast to this, decay times of light in organic scintillators are much shorter, in the range of nanoseconds. (108)

2 The mechanism of scintillation here isn't a lattice effect, but proceeds through excitation of molecular levels in a primary fluorescent material which emit bands of ultraviolet light during de-excitation. This ultraviolet light is readily absorbed in most organic materials transparent in the visible wavelength region, with an absorption length of a few millimeters. The extraction of a light signal becomes possible only by introducing a second fluorescent material in which the ultraviolet light is converted into visible light ("wavelength shifter"). This second fluorescent substance is chosen in such a way that its absorption spectrum is matched to the emission spectrum of the primary fluor, and its emission should be adapted to the spectral dependence of the quantum efficiency of the photocathode. These two active components of a scintillator are either dissolved in suitable organic liquids or mixed with the monomer of a material capable of polymerization. The polymer can then be cast in any shape desired. Two parameters are used to characterize the figure of merit of a scintillator: the light yield and self-absorption length in the scintillator. (108)

2 As a bulk material for plastic scintillators, polymeric materials of aromatic compounds (polystyrene & polyvinyltoluene) or of aliphatic ones (acrylic glasses like Plexiglas) are used. The aromatic scintillators yield about twice as much light as the aliphatic ones, but the aliphatic ones are less expensive and much easier to handle mechanically. (108)

2 Plastic scintillators are used frequently in large calorimeter detectors in the shape of rectangular strips, a few meters long and with a thickness between millimeters and a few centimeters. For this application it is important to obtain a uniform light yield over its entire length even if the scintillator light is viewed by a PMT from one end only. In order to obtain a more uniform response it is therefore possible to filter out the part at short wavelengths by a yellow filter in front of the photocathode. The effect of such a filter cuts wavelengths below 430 nm. (108-110)

Structure	lmax emission (nm)	Decay time (ns)	Yield/yield (NaI)
Primary Fluorescent Material
Naphthalene	348	96	0.12
Anthracene	440	30	0.5
p-Terphenyl	440	5	0.25
PBD	360	1.2
Wavelength Shifter
POPOP	420	1.6
Bis-MSB	420	1.2	Pg. 110

Collection of Scintillator Light

2 For the transport of scintillation light from the scintillator to the photocathode usually adiabatic light guides are used. The blue scintillation light propagates in the scintillator by multiple internal total reflections at the surfaces. For polystyrene, the reflective index is n=1.581, such that light rays incident at angles larger than a_g=39° relative to the normal vector of the surface are totally reflective. The front face of the scintillator plate, usually a rectangular area of area F, is images onto the photocathode area ¦ by bent strips of transparent plastic material. If the minimal radius of curvature of the strips is large compared with their thickness, an angle of incidence smaller than the limiting angle a_g for total reflection can be avoided throughout the path of light. Because of Liouville's theorem on the phase space of light beams, the fraction of light arriving at the photocathode is less than the ratio of surfaces, ^¦/_F. (112-113)

2 The time resolution of a counter coupled in this way to the photocathode has two sources: the fluctuation of the transit time in the PMT ("jitter") and the variations of the light paths in the scintillator and light guide. This latter contribution depends on the scintillator dimensions and for sizes exceeding 2 m, it is the dominant one. For long scintillators the best time resolution achieved is s_t=200 ps. (113)

2 The wavelength shifter bar technique can be used to collect the light from very large scintillators with a few (four or less) PMTs. One example is the calorimetric neutrino detector of the Columbia-Fermilab-Rochester collaboration, in which counters with an area of 3x3 m² are viewed by four phototubes at the corners. The four pulse heights can be used to calculate the center of gravity of a hadronic shower of particles. (115) The wavelength shifter bar technique is a scintillator and a green wavelength shifter above it. Between the scintillator and the wavelength shifter is an air gap as shown below:

PMT

UV Emission

Ionizing Particle

2 A further application of the wave-shifter technique is the collection of light from a lead-scintillator sandwich counter. For rectangular counters of this kind, a fluorescent green plate mounted on the side of a counter collects the light and is viewed by a PMT behind the sandwich. If several green plates of different length cover two of more sides, the light intensity in the front and back regions of the counter can be recorded separately. This yields valuable information on the longitudinal development of an electromagnetic or hadronic shower in the sandwich counter. (117)

Cherenkov Counters

2 Cherenkov radiation is seen to be one of the manifestations of charged particles in matter interactions. It is electromagnetic radiation emitted by charged particles if their velocity v=bc exceeds the light velocity ^c/_n in the transparent medium with refractive index n traversed by the particle. The classical theory of the effect attributes this radiation to the asymmetric polarization of the medium in front of and behind the charged particle, representing a net electric dipole moment varying with time. In the same way as an acoustical shock wave generated by a body moving with supersonic velocity, the Cherenkov wave front can be constructed by the superposition of spherical elementary Huygens waves produced by the particle along its trajectory; during the time interval t the wave travels a distance ^tc/_n, and the particle moves a distance tbc. From these two distances the direction of propagation of the Cherenkov wave is obtained:

q_c is the angle of the Cherenkov radiation emitted relative to the particle trajectory. This radiation is, therefore, only emitted if b>1/n. The minimal velocity v_s=c/n at which Cherenkov emission takes place is called the threshold velocity; the angle q_c is the Cherenkov angle. This relativistic time expansion factor corresponding to the threshold velocity is:

(126)

2 A more detailed consideration of the process for radiators of finite length L shows that the radiation is not only emitted at one angle q_c, but that there is an intensity distribution around that angle q_c caused by the diffraction effects. This distribution has a maximum at q=q_c, and the distance between consecutive diffraction maxima is Dq=(l/L) sin q_c, where l is the wavelength of the Cherenkov light. The number of photons emitted per wavelength interval and angular interval is:

(126-127)

2 If the sensitivity is expanded into the ultraviolet region, the yield of photons can be increased by a factor of two or three. One way of achieving this goal is the use of quartz windows in front of the photocathode. Another method involves using normal glass windows, but coating them with a wavelength shifter sensitive to ultraviolet and emitting in the visible region. One such shifter is p-terphenyl, applied as a 0.2-mg/cm² layer on the glass window and protected by a 250 Ǻ-thick layer of MgF₂. The performance of this tube is at least the equal of the one obtained from quartz face phototubes. (127-128)

Material	n-1 (refractive index)	Threshold dilation factors gs
Glass	0.46-0.75	1.22-1.37
Scintillator (toluene)	0.58	1.29
Plexiglas (acrylic)	0.48	1.36
Water