1RR Oct 2001 SS Dec 2001 Physics 342 Laboratory Scattering of Photons from Free Electrons: Compton Scattering Objective: To measure the energy of high energy photons scattered from electrons in a brass rod as a function of the scattering angle. References: 1. A.H. Compton, Phys. Rev. 21, 715 (1923) and Phys. Rev. 22, 409 (1923). 2. A.C. Melissinos, Experiments in Modern Physics, Academic Press, New York, 1966, p. 252-65. 3. K. Krane, Modern Physics, 2nd Ed., Wiley and Sons, New York, 1996, p. 83-87. Apparatus: A low energy (22 keV) and weak (15µC) portable Cd109 source; a higher energy (662 keV) strong (5 mC) Cs137 source in a cylindrical lead shield; a NaI(T") scintillator mounted on a Photo-Multiplier Tube (PMT); an iron shield surrounding the PMT; a Canberra 1024-channel PC based Multi-Channel Analyzer (MCA); a high voltage (1.5 kV) power supply; a brass cylindrical rod for use as a scattering target; a carriage to rotate the scintillator and PMT assembly at a fixed distance around the target. Introduction In 1923, Compton considered the problem of high energy photons (γ-rays) scattering from solids. Experimentally, he found that low energy (few MeV γ - ray) monochromatic photons scattered by metals change their frequency and that the frequency change depends on the scattering angle. This proved to be problematic, since at that time, light scattering was understood in terms of diffraction in which the scattered (diffracted) wave does NOT change frequency. Compton’s experiments and his theoretical analysis of them came to be know as Compton scattering. Historically, his experiments are important because they provided further compelling evidence that photons do behave as particles which obey conservation of momentum and energy laws. Compton was awarded the Noble prize in 1927 for his seminal work. Compton’s experiment can be understood by considering the interaction of the incident photons with the electrons that comprise a metal. Because metals are good conductors of electricity, some fraction of the electrons associated with each atom in the metal can be considered to be free. If the quantized nature of electromagnetic radiation is taken into account (electromagnetic radiation consists of photons, each of which has the same energy E=hν), and relativistic kinematics are used to describe the scattering process, the change of wavelength is understandable as a straightforward consequence of total energy and momentum conservation during a scattering process in which an incoming photon loses some of its energy to a free electron having a mass me. The basic kinematic diagram illustrating this interaction is sketched in Fig. 1.2 Figure 1: A schematic energy diagram showing the interaction between a photon and a free electron. The incident γ has an energy E and a momentum p=h/λ. The energy of the electron before scattering is just the rest mass energy of the electron, Ee=mec2; the momentum of the electron before scattering is zero.The scattered γ has an energy E’ and a momentum p’=h/λ’. The scattered electron has an energy Ee’ and momentum ()2221’’ mcEcpee−=−. For a beam of incident photons, each of which has the same energy E=hν, there will be photons emerging at various angles θ with respect to the incident photon direction. The energy E’ of a photon emerging in a given direction can be calculated using relativistic kinematics and has a value given by ( )( )θcos1/1’2−+=cmEEEe (1) where θ is the angle between the direction of the emerging (scattered) photon and the incident photon, me is the rest mass of the electrons, and c is the velocity of light. From Eq. (1) it can be seen that in order to obtain a large Compton shift (i.e. a large value for E – E’), the incident photons should have an energy E of the same order of magnitude as the electron rest energy mec2 (mec2 = 511 keV). In this experiment 662 keV (γ - ray) photons from a Cs137 source will be Compton-scattered by a cylindrical rod made of brass. Experimental Considerations The primary source of photons in this experiment is a ∼5 mC cesium (Cs137) emitting 662 keV photons. The source is kept in a lead cylinder for shielding. When you are ready to take data, remove the end piece of the shielding cylinder. A narrow channel drilled through the center of the cylinder permits only photons which travel along it to3scatter off the target. The direction of the channel defines θ=0, the direction of the unscattered beam. This procedure of creating a parallel beam of particles from an otherwise isotropic source is called collimation. The emerging photons impinge on the target rod, and some small fraction will be scattered. Some of the scattered photons will enter the NaI(T") crystal attached to a photomultiplier tube (PMT) (see Fig. 2). Figure 2: A schematic diagram of the experimental apparatus. The energy lost in collisions with the I-atoms in the NaI crystal results in the emission of light photons from excited T" atoms which are intentionally incorporated into the NaI crystal. These photons in turn eject electrons from the photo-cathode of the PMT. The electrons are accelerated through ∼1300 volts of electrostatic potential in such a way that they produce a cascade of electrons from electrodes (called dynodes) placed inside the tube. This electron current pulse is then transformed into a voltage pulse which is pulse-shaped so that its height is proportional to the energy of the incoming γ. The pulse height is then measured and sorted by a computer using a specially designed multi-channel analysis (MCA) board. If the source is so intense that two of these pulses arrive at the same time within the PMT, a spurious overlapping signal is produced. This case must be avoided as there is no way to learn about the energy of each of these pulses. The time separation between two pulses must be larger than certain value (called dead time) in order for these two pulses to be resolved separately. In order to avoid this problem, you will be measuring the energy distribution of the source at a scattering angle of 5° instead of the normally chosen angle of 0°, By moving the detector slightly off-center from the source, the intensity of the γ beam greatly reduced to ensure that the probability