COMPTON SCATTERING. Phys 2010 Brown University March 13, 2009

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1 COMPTON SCATTERING Phys 00 Brown University March 3, 009 Purpose The purpose of this experiment is to verify the energy epenence of gamma raiation upon scattering angle an to compare the ifferential cross section obtaine from the ata with those calculate using the Klein-Nishina formula an classical theory. Introuction Scattering of photons on atomic electrons, first measure by Arthur Compton in 9, was one of the funamental experiments that helpe to establish the valiity of quantum theory. In Compton scattering the conservation of energy an momentum in the two-boy interaction leas to the relation among the energy of the scattere photon, E, the energy of the incient photon, E, an the scattering angle,, given by: cos, E E mec where m e c = 5.0 KeV is the energy of the electron at rest. The ifferential scattering cross section (the ratio of the scattere energy per unit soli angle to the incient energy per unit area) epens both on the photon energy an scattering angle. It is given by an expression, known as the Klein-Nishina formula, r 0 cos cos cos cos where r 0 = (e /4 m e c ) =.8 0 cm is the classical electron raius an = E /m e c. This formula takes into account the relativistic effects an aitional quantum corrections, erive in quantum electroynamics., Funamentals of Experiment The experiment, shown in Fig., consists of a -ray source, a scattering material (the PMMA scintillator) an a etector (the NaI scintillator) capable of measuring the energy an rate of scattering events as a function of angle between the incient an scattere photons. The source within its lea housing poses absolutely no health risk. Therefore, you are not require to wear raiation bages in the lab.

2 A scintillator is use as the scattering material to provie a signal that can be use to ientify an select in the NaI etector only those events that are coincient with a scattering event in the PMMA. This coincient etection is important in rejecting backgroun signals. In the absence of this aitional backgroun rejection the experiment woul be much more ifficult to perform. Question: Explain, why ifferent scintillating materials are use for scattering an etecting the -rays. Figure : Block iagram of the scheme of the experiment. Description of Electronics A photomultiplier tube requires only a high DC voltage to operate. In this experiment the DC voltage is provie by a Canberra 30D power supply. The tubes use in this experiment each have two outputs. The output pulse from the connector marke DYNODE is use to measure the energy eposite in the scintillator an that from the connector marke ANODE is use for timing an etermining coincience between events in the two scintillators. A block iagram of the electronics is shown in Fig.. Pulses from the ynoe are fe into a preamplifier/amplifier combination (Ortec moel 3 an Canberra moel 0) an then into the analog-to-igital converter (ADC) input of the multi-channel analyzer (MCA), a boar in the computer. The MCA consists of 4096 channels, the channels sequentially being associate with a increasing pulse height. The MCA is controlle by the computer using the software MAESTRO.

3 Pulses from the anoes of the PMT's are fe into constant fraction iscriminators (CFD), Canberra moel 6. A CFD prouces a logic output pulse if the input pulse excees a fixe value that can be set with the THRESHOLD ial. The logic output pulse starts a fixe time after the input pulse has risen to a certain fraction (for moel 6 this fraction is 0.4) of its peak value. If the pulses have the same shape but ifferent amplitues, as is the case in this experiment, then the time elay between the event that prouce the input pulse an the logic output pulse from the CFD will be a constant, inepenent of pulse size. The magnitue of the time elay can be ajuste by the WALK control, a screw on the front panel. Pulses from the positive outputs of the two CFD's are fe into a coincience analyzer (Canberra moel 040), which prouces a logic output pulse when the two input pulses are about 0.5 s or less of each other. The output pulses of the coincience analyzer are then fe into the START input of a gate generator moule (LeCroy moel ), which prouces an output pulse suitable for controlling the MCA. The TTL (transistor-transistor logic) output of the gate generator is connecte to the GATE input of the MCA. The MCA has a toggle switch with three positions. If the switch is in its mile position the MCA recors all pulses into the ADC without reference to the gate pulse. If the switch is in the own position, the MCA only recors a pulse into the ADC if there is a simultaneous gate pulse (coincience). Conversely, when the switch is in the up position, a pulse into the ADC is recore only when there is not a simultaneous gate pulse (anticoincience). Raioactive Calibration Sources To ajust the electronics, prior to performing the Compton scattering measurements, you will nee to use several stanar raioactive sources. These sources are encapsulate in plastic an are all below 0 Ci in activity. They can be hanle with impunity, but when not in use they shoul be store in a lea container. They shoul not be remove from Room. Among several provie -sources you might fin the following most useful (check Melissinos for the -ray energies from these sources): 37 Cs, 33 Ba, Na. Using the calibration feature in MAESTRO one can either accumulate spectra from the calibration sources one at a time (each taken separately but in the same file) then calibrating after each spectra, or by taking spectra of several sources at the same time. Note: use KeV as the calibration unit or MEASTRO will not work properly. Ajustments of Electronics Check that the port hole in the lea shieling of the main 37 Cs source is covere. a) Set up to measure energy spectrum

4 Turn on the power to the NIM (Nuclear Instrument Moule) bin. Place 37 Cs calibration sources a few centimeters in front of the NaI scintillator. Apply a voltage of 800V to 000V to the PMT an look at the ynoe output with an oscilloscope. You shoul see pulses varying in amplitue with a group ranging from +400 to +800 mv an having withs in the range of ns. The important criteria here is that the pulses have about the right amplitue an with If the pulses o not have these characteristics try ajusting the voltage on the PMT. DO NOT APPLY MORE THAN 000V. Note that the electronics has 50 output impeance; therefore the electronics you use to look at the signal (i.e. the oscilloscope) must have 50 input impeance. On some oscilloscopes you can select high input-impeance or 50 input-impeance. If you cannot select the input impeance on the oscilloscope two 50 input-impeance matchers are provie. What happens if you try to look at 50 output-impeance signal with a high-impeance input evice? Connect the ynoe output to the Ortec preamplifier (set the input capacitance to 500 pf for the NaI PMT an 000 pf for the PMMA PMT) an the output of the preamplifier to the Canberra amplifier. Look at the output of the Canberra with the oscilloscope. The amplifier reshapes the pulses so that at the output they have a with of about 5 s. You shoul ajust the gain of the amplifier so that the vast majority of the pulses have amplitue of less than 8 V. Note the change in pulse rate on moving the position of the source. Turn on the computer an familiarize yourself with the operation of the Maestro software. Connect the output of the Canberra amplifier to the ADC input of the MCA (labele IN on the car) an with the coincience switch off (this switch is set in the software) observe the spectrum of the 37 Cs calibration source. Ajust the gain of the amplifier so that the main peak is about 80% of the maximum energy measurable with the MCA. Question: What are the structures seen at the high an low ens of the spectrum? Repeat the process outline above with the PMMA scintillator an PMT. The average voltage from the ynoe for the PMMA photomultiplier shoul be about +00 mv, an the pulses at the output of the amplifier shoul mostly be less than 5 V. Explain the results. Calibrate the NaI etector using several calibration sources - the calibration sources can be use iniviually or simultaneously. Use the MCA in the non-coincience moe an employ the features of Maestro such as region of interest (ROI), peak information, etc. to perform the calibration. The ifference between real time an live time is calle ea time. Ajust the istance between the source an the PMT or the high-voltage on the PMT to keep the counting rate low enough to achieve a ea time of.5% or less. Save your calibration ata for future reference but o not close the file. If a file is close an a new one create, the new file will not contain the calibration from the close file. To preserve your calibration throughout the experiment, when an exercise has been

5 complete, save the file but o not close it, instea, o a save as an enter a name that escribes the next exercise an clear the screen. Make a plot of energy versus channel number an keep a recor of the settings on the electronic components. You may have to reo the calibration if someone changes the settings. It is essential to check the calibration occasionally even if no one else uses the apparatus. b) Set up of coincience circuit Move the NaI scintillator so that it is no more than a few centimeters from the PMMA. Place a Na source (use source fabricate in 988) irectly between the two. The Na ecays via + (positron) emission. The annihilation in the source of a positron with an electron, both at rest, occurs in about 0. s proucing two 5 KeV -rays traveling in opposite irections, as require to conserve energy an momentum. These simultaneous photons traveling in opposite irections can be use to test an ajust the coincience circuits of the etection system. Observe pulses from the anoes of the two PMT's on separate channels of an oscilloscope. The NaI pulses shoul have amplitues of about 00 mv an withs of 00 ns. PMMA pulses shoul have amplitues of about 300 mv an withs of ~5 ns. Now connect the anoes of the PMT's to the inputs of the CFD's. Make sure that the CFD's are set in the constant fraction iscrimination moe! Set the THRESHOLD ial of the CFD's to zero. Observe pulses from the positive outputs of the CFD's. The pulses shoul have amplitue of about V an a with of ~500 ns for the NaI an ~50 ns for the PMMA scintillator. Trigger the scope on pulses in one channel but isplay both channels simultaneously (chop moe). With the Na source in place there shoul be an observable number of pulses in the two channels that appear coincient. Note the pulse rate with the Na source temporarily remove. Now connect the positive outputs of the CFD's to the A an B inputs of the coincience analyzer. Coincience is etermine by the arrival times of the leaing ege of the pulses, not by overlap of the pulse envelopes. Set the range of resolving time to s an the associate variable ial to mi-range. Fee the output of the coincience analyzer into the scaler (Ortec moel 484) mounte in the NIM bin. The scaler counts the number of pulses it receives. With the Na source remove the count rate shoul be or 3 per secon. With the source between the scintillators the pulse rate shoul increase to ~00 per secon. The pulses out of the coincience analyzer shoul be +4 V in amplitue an s long. These are fe into the LeCroy gate generator that prouces a pulse of 4 V at a selectable gate with. A gate with of at least 0.5 s beyon the peak of the pulse you are measuring is require for gating the MCA (about 6 s). The with of the pulse prouce by the gate generator can be selecte with the Full Scale With control. For fine ajustment use a screw river to ajust the small screw uner this control. If the gate pulse is not wie enough you will have trouble etecting coincience at lower energies.

6 Measurement of the Total Cross Section for Compton Scattering In the experiments that follow you will use the high activity 37 Cs source in the lea housing. The source is alreay aligne with the hole in the lea housing. With the port still covere, move the PMMA scintillator an its support out of the -ray beam. Place the NaI scintillator irectly across the circle, i.e., about 0 cm) from the source. Remove the brick covering the hole to the source. Determine the beam profile by counting events in the photo-peak as a function of angle. Use steps. Plot your results. Place the NaI etector in the center of the beam. Measure the counting rate in the 66 KeV photo-peak with nothing in the beam path an then with varying thickness of PMMA plastic sheets. Use at least three ifferent values of thickness. Measurement of the Energy of the Scattere Photon an the Differential Scattering Cross Section With the -rays from the source blocke by a brick, reposition the PMMA scintillator irectly in the path of the beam. Reopen the beam port. Measure the energy an the rate of the scattere -rays etecte by the NaI scintillator coincient with a scattering event in the PMMA scintillator. Do you nee to measure the total number of events in both structures in the spectrum, or just the main peak to obtain the correct results? This measurement shoul be performe at a number of angles between 0 an 60. Count for sufficiently long at each angle, perhaps three hours, to obtain goo statistics. Analysis a) Total Cross Section for Compton Scattering Determine linear attenuation coefficient in the PMMA from the results of the measurements with ifferent thickness of the scintillator. Assuming that this attenuation is entirely ue to the Compton scattering, calculate total Compton scattering cross section, given the ensity of the PMMA of.8 g/cm 3. Compare the results of your measurement with the theoretical value: comp sin r 0 b) Energy of Scattere Photon ln ln 3.

7 With an appropriate plot compare the measure epenence of the energy of the scattere photon to that given by the Compton formula. What is the value of the rest mass of the electron you obtain from the experimental results? c) Differential Scattering Cross Section Compare your angular epenence measurements of the count rate, C( ), with the ifferential cross section preicte by the Klein-Nishina formula. The ifference between the two is ue to a number of corrections that one nees to apply to the ata. Consier the following: ) The efficiency of etecting a photon in the NaI scintillator is epenent upon the photon energy an hence on the scattering angle. This can have a significant influence on the angular epenence of the counting rate an must be aresse. ) There is a certain probability that a photon scattere in the PMMA will scatter a secon time before exiting the plastic, a process of multiple Compton scattering. Given the size of the PMMA, the effect of multiple scattering cannot be ismisse as unimportant. To hanle this problem accurately woul require going to numerical methos an employing Monte Carlo simulations. This is beyon the scope of our laboratory experiment. Instea we will escribe the phenomenon below an make a number of simplifying approximations. 3) For a fixe position of the NaI etector there is a range of scattering angles for the photon. The PMMA target an the NaI etector both have a finite size. Show that the effect of the resulting istribution of scattering angles is small in this experiment an coul be neglecte. 4) Not all events in the PMMA are the result of Compton scattering. How important is this correction?

8 Figure. Attenuation coefficient in NaI scintillator. ) Correction for the efficiency of the NaI scintillator We consier, first, the energy epenence of the efficiency of the NaI. The linear attenuation coefficient of NaI, shown in Fig., can be expresse empirically, between 00 an 700 kev, as (E) = 5.8 E E cm -, where E, the photon energy, is expresse in units of 00keV. The first term on the right is the contribution of the photoelectric absorption an the secon term is the Compton component. Then the probability that a scattere photon of energy E will be recore by the NaI is given by: ( ) = e t, where t is the length of the NaI crystal (5.cm). The quantity is a function of since is epenent upon E, which in turn epens upon. e) Correction for multiple scattering in the PMMA scintillator

9 The phenomenon of multiple Compton scattering in the target PMMA has the property of both increasing an ecreasing the counting rate in the NaI. Consier a photon that is first scattere at an angle such that it woul be incient on the NaI. If it is scattere a secon time an consequently oes not arrive at the NaI, then the event rate measure by the etector is ecrease. The situation is reverse for a photon that is scattere initially at angle such that it is not incient upon the NaI but on being scattere again an possesses a scattering angle to reach the etector, in this case the measure rate is increase. Figure 3: Scintillator geometry. The ecrease in count rate ue to the scattering of photons that woul otherwise be incient upon the NaI can be approximate as follows. A uniform, parallel beam of photons is incient on the PMMA cyliner perpenicular to its axis of symmetry. (Check that this is a reasonable assumption base on the measure beam profile.) Suppose an incient photon scatters at point P in the material, an the angle the scattere photon makes with the irection of the incient beam is ; see Fig. 3. The probability that the incient photon will reach point P having traverse a istance x in the PMMA is exp( ix) where i is the linear attenuation coefficient of PMMA at the incient photon energy, E = 66keV. The photon scattere through the angle must travel a istance y to emerge from the PMMA. The probability that it will o so without further scattering is exp( sy) where s is the linear attenuation coefficient at the scattere photon energy, E. The istances x an y can be expresse in terms of variables in cylinrical coorinates. x = R((-q sin ) / -q cos ), where q = r/r an y = R((-q sin ) / -q cos ), The probability that an incient photon, Compton scattere by the angle will arrive at the etector, is obtaine by taking the integral over the volume of the PMMA target:

10 e i e x s y e V. ix V The enhancement of the etector signal as a consequence two sequential Compton scattering events yieling a final photon propagating at the angle is much more ifficult to estimate. It involves, at the least, a ouble integral over the target volume, which we will not pursue here. Instea we make a very crue approximation. Since Compton scattering is peake in the forwar irection ( / is largest for small ), the linear attenuation coefficient reflects primarily small angle scattering. (The fact that / must be multiplie by sin in the integral to obtain the number propagating with angle weakens the argument.) The ecrease in intensity of the incient beam with istance x in the PMMA is compensate by a comparable increase in number of photons with somewhat lower energies propagating in close to the same irection. The crue approximation is to remove the exp( ix) terms from the expression for an write: s y e V. V It is straightforwar to obtain ( ) by numerical integration using for the energy epenence of in PMMA the expression (E) = 0.05E cm, where E is expresse in units of 00 KeV. f) Calculations With these corrections in min we now return to the relation between C( ) an / The correcte count rate is: C. C corr This correcte count rate is proportional to / A C corr. The proportionality constant A can be obtaine from: A Ccorr comp Compute an plot its angular epenence. Calculate by numerical integration an graph it as well. Calculate C corr ( ) an numerically integrate to obtain the coefficient A. Plot your result for A C corr an compare with / obtaine from the Klein-Nishina formula. References. R. A. Dunlap, Experimental Physics: Moern Methos, New York: Oxfor University Press, 988. (QC33.D86 988) Chapters an.

11 . A. Melissinos, Experiments in Moern Physics, New York: Acaemic Press, 966. (QC33.M45) Chapters 5 an W. R. Leo, Techniques for Nuclear an Particle Physics Experiments, n rev e., New York: Springer, 994. (QC L46 994) Parts of chapters, 3, 7, 8, 9,, 4 an W. Heitler, The Quantum Theory of Raiation, 3r e, Oxfor: Clarenon Press, 960. (QC475.H43 960) P. 9.