Abstract
After reading this chapter, you should be able to manage the basics of particle detection, and to understand the sections describing the detection technique in a modern article of high-energy particle or astroparticle physics.
After reading this chapter, you should be able to manage the basics of particle detection, and to understand the sections describing the detection technique in a modern article of high-energy particle or astroparticle physics.
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Notes
- 1.
The 24-year-old Hans Bethe , Nobel prize in 1967 for his work on the theory of stellar nucleosynthesis, published this formula in 1930; the formula—not including the density term, added later by Fermi—was derived using quantum mechanical perturbation theory up to \(z_p^2\). The description can be improved by considering corrections which correspond to higher powers of \(z_p\): Felix Block obtained in 1933 a higher-order correction proportional to \(z_p^4\), not reported in this text, and sometimes the formula is called “Bethe-Block energy loss”—although this naming convention has been discontinued by the Particle Data Group since 2008.
- 2.
The classical electron radius is the size the electron would need to have for its mass to be completely due to its electrostatic potential energy, under the assumption that charge has a uniform volume density and that the electron is a sphere.
- 3.
NTP is commonly used as a standard condition; it is defined as air at 20\(\,^\circ \)C (293.15 K) and 1 atm (101.325 kPa). Density is 1.204 kg/m\(^3.\) Standard Temperature and Pressure STP, another condition frequently used in physics, is defined by IUPAC (International Union of Pure and Applied Chemistry) as air at 0\(^\circ \)C (273.15 K) and 100 kPa.
- 4.
Pavel Cherenkov (1904–1990) was a Soviet physicist who shared the Nobel prize in physics in 1958 with con-nationals Ilya Frank (1908–1990) and Igor Tamm (1895–1971) for the discovery of Cherenkov radiation, made in 1934. The work was done under the supervision of Sergey Vavilov, who died before the recognition of the discovery by the Nobel committee.
- 5.
Monte Carlo methods are computational algorithms based on repeated random sampling. The name is due to its resemblance to the act of playing in a gambling casino.
- 6.
Jerzy (“Georges”) Charpak (1924–2010) was awarded the Nobel prize in Physics in 1992 “for his invention and development of particle detectors, in particular the multiwire proportional chamber.” Charpak was a Polish born, French physicist. Coming from a Jewish family, he was deported in the Nazi concentration camp in Dachau; after the liberation he studied in Paris, and then worked since 1959 at CERN, Geneva.
- 7.
A trigger is an electronic system that uses simple criteria to rapidly decide which events in a particle detector to keep in cases where only a small fraction of the total number of events can be recorded.
- 8.
The Nobel prize for physics in 1984 was assigned to the Italian physicist Carlo Rubbia (1984 –) and to the Dutch Simon van der Meer (1925–2011) “for their decisive contributions to the large project, which led to the discovery of the field particles W and Z, communicators of weak interaction.” In short, Rubbia and van der Meer used feedback signals sent in the ring to reduce the entropy of the beam; this technique allowed the accumulation of focalized particles with unprecedented efficiency, and is at the basis of all modern accelerators.
- 9.
A synchrotron is a particle accelerator ring, in which the guiding magnetic field (bending the particles into a closed path) is time dependent and synchronized to a particle beam of increasing kinetic energy. The concept was developed by the Soviet physicist Vladimir Veksler in 1944.
- 10.
Being proportional to \((1/p_T)\) the fitted quantity by means of the radius of curvature, the accuracy on the momentum measurement can be parameterized as \(\delta (1/p_T) = \delta (p)/(p_Tp) \sim \mathrm{{constant}}\).
- 11.
Limited streamer tubes, often simply called streamer tubes, are made of a resistive cathode in the form of a round or square tube, with a thick (0.1 mm) anode wire in its axis; they operate at voltages close to the breakdown (see Sect. 4.2.1.3). Such detectors can be produced with 1–2 cm diameter, and they are cheap and robust.
- 12.
Seven detectors have been constructed at the LHC, located underground in large caverns excavated at the LHC’s intersection points. ATLAS and CMS are large, general purpose particle detectors. A Large Ion Collider Experiment (ALICE) and LHCb have more specific roles, respectively, the study of collisions of heavy ions and the study of the physics of the b quark. The remaining three are much smaller; two of them, TOTEM and LHCf, study the cross section in the forward region (which dominates the total hadronic cross section, as we shall see in Chap. 6); finally, MoEDAL searches for exotic particles, magnetic monopoles in particular.
- 13.
In the isothermal approximation, the depth x of the atmosphere at a height h (i.e., the amount of atmosphere above h) can be approximated as
$$\begin{aligned} x \simeq X e^{-h/7 \, \mathrm {km}} \, , \end{aligned}$$with \(X \simeq 1030\) g/cm\(^2\).
- 14.
The Akeno Giant Air-Shower Array (AGASA) is a very large surface array covering an area of 100 km\(^2\) in Japan and consisting of 111 surface detectors (scintillators) and 27 muon detectors (proportional chambers shielded by Fe/concrete).
- 15.
In a Schmidt telescope, a spherical mirror receives light that passed through a thin aspherical lens that compensates for the image distortions that will occur in the mirror. The light is then reflected in the mirror into a detector that records the image.
- 16.
One half of the Nobel prize in physics 2002 was assigned jointly to the US physicist Raymond Davis Jr. (Washington 1914—New York 2006) and to the leader of the Kamiokande collaboration (see later) Masatoshi Koshiba (Aichi, Japan, 1926) “for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos.”
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Appendices
Further Reading
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[F4.1] B. Rossi, “High-Energy Particles,” Prentice-Hall, New York 1952. Still a fundamental book on particle detection, in particular related to the interaction of particles with matter and to multiplicative showers.
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[F4.2] K. Kleinknecht, “Detectors for Particle Radiation” Cambridge University Press 1986.
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[F4.3] W.R. Leo, “Techniques for Nuclear and Particle Physics Experiments,” Springer Verlag 1994.
Exercises
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1.
Compton scattering. A photon of wavelength \(\lambda \) is scattered off a free electron initially at rest. Let \(\lambda '\) be the wavelength of the photon scattered in the direction \(\theta \). Compute: (a) \(\lambda '\) as a function of \(\lambda \), \(\theta \) and universal parameters; (b) the kinetic energy of the recoiling electron.
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2.
Cherenkov radiation. A proton with momentum 1.0 GeV/c passes through a gas at high pressure. The index of refraction of the gas can be changed by changing the pressure. Compute: (a) the minimum index of refraction at which the proton will emit Cherenkov radiation; (b) the Cherenkov radiation emission angle when the index of refraction of the gas is 1.6.
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3.
Nuclear reactions. The mean free path of fast neutrons in lead is of the order of 5 cm. What is the total fast neutron cross section in lead?
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4.
Photodetectors. What gain would be required from a photomultiplier in order to resolve the signal produced by three photoelectrons from that due to two or four photoelectrons? Assume that the fluctuations in the signal are described by Poisson statistics, and consider that two peaks can be resolved when their centers are separated by more than the sum of their standard deviations.
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5.
Cherenkov counters. Estimate the minimum length of a gas Cherenkov counter used in the threshold mode to be able to distinguish between pions and kaons with momentum 20 GeV. Assume that 200 photons need to be radiated to ensure a high probability of detection and that radiation covers the whole visible spectrum (neglect the variation with wavelength of the refractive index of the gas).
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6.
Electromagnetic calorimeters. Electromagnetic calorimeters have usually 20 radiation lengths of material. Calculate the thickness (in cm) for a calorimeters made of of BGO, PbWO\(_4\) (as in the CMS experiment at LHC), uranium, iron, and lead. Take the radiation lengths from Appendix B or from the Particle Data Book.
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7.
Cherenkov telescopes. Suppose you have a Cherenkov telescope with 7 m diameter, and your camera can detect a signal only when you collect 100 photons from a source. Assuming a global efficiency of 0.1 for the acquisition system (including reflectivity of the surface and quantum efficiency of the PMT), what is the minimum energy (neglecting the background) that such a system can detect at a height of 2 km a.s.l.?
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8.
Cherenkov telescopes. If a shower is generated by a gamma ray of \(E=\) 1 TeV penetrating the atmosphere vertically, considering that the radiation length \(X_0\) of air is approximately 37 g/cm\(^2\) and its critical energy \(E_c\) is about 88 MeV, calculate the height \(h_M\) of the maximum of the shower in the Heitler model and in the Rossi approximation B.
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9.
Cherenkov telescopes. Show that the image of the Cherenkov emission from a muon in the focal plane of a parabolic IACT is a conical section (approximate the Cherenkov angle as a constant).
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10.
Colliders. The luminosity at the Large Electron–Positron Collider (LEP) was determined by measuring the elastic \(e^+e^-\) scattering (Bhabha scattering) as its cross section at low angles is well known from QED. In fact, assuming small polar angles, the Bhabha scattering cross section integrated between a polar angle \(\theta _\mathrm{min}\) and \(\theta _\mathrm{max}\) is given at first order by
$$\begin{aligned} \sigma \approx \frac{1040\, \mathrm{nb}}{s\ \mathrm{[GeV^2]}} \left( \frac{1}{\theta ^2_\mathrm{max} - \theta ^2_\mathrm{min}} \right) \, . \end{aligned}$$Determine the luminosity of a run of LEP knowing that this run lasted 4 hours, and the number of identified Bhabha scattering events was 1200 in the polar range of \(\theta \in [29; 185]\) mrad. Take into account a detection efficiency of 95 % and a background of 10 % at \(\sqrt{s} = m_Z\).
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11.
Initial state radiation. The effective energy of the elastic \(e^+e^-\) scattering can be changed by the radiation of a photon by the particles of the beam (initial radiation), which is peaked at very small angles. Supposing that a measured \(e^+e^-\) pair has the following transverse momenta: \(p_1^t=p_2^t= 5\, \mathrm{GeV}\), and the radiated photon is collinear with the beam and has an energy of \(10\, \mathrm{GeV}\), determine the effective energy of the interaction of the electron and positron in the center of mass, \(\sqrt{s_{e^+e^-}}\). Consider that the beam was tuned for \(\sqrt{s}=m_Z\).
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12.
Energy loss. In the Pierre Auger Observatory the surface detectors are composed by water Cherenkov tanks 1.2 m high, each containing 12 tons of water. These detectors are able to measure the light produced by charged particles crossing them. Consider one tank crossed by a single vertical muon with an energy of \(5\,\mathrm{GeV}\). The refraction index of water is \(n \simeq 1.33\) and can be in good approximation considered constant for all the relevant photon wavelengths. Determine the energy lost by ionization and compare it with the energy lost by Cherenkov emission.
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13.
Synchrotron radiation. Consider a circular synchrotron of radius \(R_0\) which is capable of accelerating charged particles up to an energy \(E_0\). Compare the radiation emitted by a proton and an electron and discuss the difficulties to accelerate these particles with this technology.
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De Angelis, A., Pimenta, M.J.M. (2015). Particle Detection. In: Introduction to Particle and Astroparticle Physics. Undergraduate Lecture Notes in Physics. Springer, Milano. https://doi.org/10.1007/978-88-470-2688-9_4
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