Muon Decay - Brown University Wiki
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1. MCA Bin Calibration To calibrate the MCA we will use the Gate Generator and the TAC however in this cases we will reverse the configuration of the direct and delayed pulses The direct pulse will go to the Start input and the delayed pulse will go to the Stop input This way every pulse entering the scintillator will generate an output pulse from the TAC and all of the pulses will have the same width the delay between the pulses as measured on the scope and set with the Gate Generator This will generate a column on the MCA that identifies the bin associated with that time interval Before calibrating you need to determine the longest time interval you want to record on the MCA and set the Time Range on the TAC accordingly The Time Range sets the maximum time the TAC will measure before timing out and also sets the voltage per time scaling of the TAC Once a column appears on the MCA enter the delay measured on the scope and enter this time difference in Maestro s calibration routine see the Maestro manual Do a minimum of 3 different pulse widths one near the shortest time one in the middle and one near the longest time Doing but more calibration points is better It is good practice to record your time vs bin information in case something happens and the calibration in Maestro fails This way you can calibrate the raw data after the fact if needed Note In this configuration all muons passing through the main scintill2. of photons in the plastic material of the scintillator Because of the low intensity of the emitted photons a photomultiplier tube PMT is used to amplify the signal and convert it to a detectable electric pulse Naturally the scintillator PMT combination must be free from any light leaks See Melissinos for a discussion of a scintillation counter If a PMT signal exceeds the threshold voltage the discriminator outputs a square pulse Gate Generator gt START DELAY Main So E MCA scintillator a START HV Bea LeCroy 4 fold Logic Unit our TAC Fig 1 Basic Experimental Setup Determining Discriminator Thresholds View the PMT signals by connecting the output from the PMT to an oscilloscope remember to impedance match Notice some pulses have large amplitudes likely muon events however others have much smaller amplitudes and could be a muon event but could also be noise To reduce the noise component you need to set the input signal threshold on the discriminator This value is to distinguish between noise and muon events The trigger setting on the scope can be used to simulate the effect of setting the threshold Note setting this value too high will significantly lengthen the data collection time while setting it too low will distort your data with noise The threshold value depends on the HV applied to the PMT DO NOT APPLY MORE THAN 1 1 kV TO THE PMT S Turn the HV control knob slowly when approaching 1
3. BROWN BE PHYSICS Muon Decay Edited 10 2 13 by DGH amp Stephen Albright Purpose The purpose of this experiment is to determine the mean lifetime of the muon A muon is a weakly interacting particle similar to an electron but differing in lepton number and mass roughly 207 times as massive Note This experiment requires long data collection times so start early Also this manual is not intended to be all inclusive You are expected to reference the equipment manuals and technical resources provided in the lab on the lab wiki etc You may not consult with students who have done this lab before or refer to their write ups Introduction There are three fundamental forces in particle physics the strong force which holds nuclei together the electromagnetic force which holds atoms together and the weak force which is responsible for two seemingly unrelated phenomena beta decay and supernovas The fourth force gravity is so weak that it can be neglected for particles with small rest energies Before quarks were understood to be the fundamental units of matter particles were classified into four groups based on how they interact and on their spin These four groupings are photon lepton meson and baryon Quarks leptons and force mediating particles such as gluons and photons are now understood to be more fundamental yet the four group classification remains an important way of grouping subatomic particles The photon forms a c
4. decay which generates an electron e muon neutrino v and electron antineutrino Ve All subatomic particles are characterized by a constant probability of decay per unit time This probability is an intrinsic property of a particle and like the particle s mass or spin helps identify the particle It is standard to denote the decay per unit time as A Now we consider some of the statistical aspects of particle decay First consider a sample of N t muons at time The infinitesimal change in the number of muons in a time dt is given by dN N t dt N t N t Adt 2 The last equality follows from considering the definition of while the minus sign comes from the fact that dN must be negative if muons are decaying From this differential relation we have dN t N HA a t 3 N t N e 4 No is a constant which we interpret as the initial number of muons by requiring as a boundary condition to our differential equation N t 0 No Another important statistical concept for this experiment is the probability density function P t P t has the following property P t dt is the probability that a muon will not decay for a time t after its creation or capture in the scintillator but will decay within the interval dt after t That is P t dt probability of non decay from 0 to ft x probability of decay from to t dt To find an expression for P t first we divide the time interval into n discrete subint
5. here you can print the plot Printing to a file in Maestro may provide you with a useful data format Questions 1 Give a brief summary of how a scintillator and a photomultiplier work 2 What factors go into choosing the delay time How does this delay time affect your data 3 Ifthe Start pulse generated by the arrival of a muon is delayed by 1 usec and the Stop pulse from the associated decay is not delayed why isn t the mean lifetime of the muon measured to be 1 2 usecs in this setup 4 Calculate the error in your determination of the mean lifetime of the muon Use the method in Bevington What is the flux of cosmic muons at sea level 6 Measure the average rate of pulses from the main scintillator Assuming a random time distribution calculate the expected number of muon pairs that will enter the scintillator close enough time to be falsely measured as a decay 7 Make the required measurements and estimate the fraction of the background that was eliminated by using the coincidence anti coincidence setup Discuss why the coincidence anti coincidence setup reduces background counts n Maestro BH MUON MOH 25 Oct O1 Che Fis Acqure Calodite Sarcas ROI Dupisy Window sa ollk lx GED fa elole fi n srnu wes 2 7 Mch 3 BH MUON MCB 25 Oct O1 Chn Maker 8149 HLI 0 Cris D start E Macstro OH MUON r Removable Disk E _ Doct Micresolt Word Bake 10saM Fig 5 Typical MCA Output
6. References 1 Arya Elementary Modern Physics 2 Bevington Data Reduction amp Error Analysis for the Physical Sciences 3 Frisch and Smith Measurement of Relativistic Time Dilation Using Mu Mesons Am J Phys 31 342 4 A Melissinos Experiments in Modern Physics Academic Press 1966 5 A Das and T Ferbel Introduction to Nuclear and Particle Physics World Scientific 2003
7. ator are being recorded Since the rate of decaying muons is very small compared to the total number of muons passing through the scintillator this is a good opportunity to check out the detectors etc buy measuring the total muon flux Reducing Coincidental Background In the Basic configuration it is possible for two muons to enter the main scintillator close enough in time that they would be counted as a decayed muon The Alternative setup shown in Fig 3 uses two additional scintillators and a combination of coincidence anti coincidence configurations to significantly reduce this coincidental background rate without excessively reducing the overall counting rate In this setup a Start pulse is generated when the pulses from the top and two main PMTs are coincidence and a pulse from the bottom PMT is not coincidence This signifies that a particle has passed through the top scintillator entered the main but not passed through to the bottom scintillator Most of these particles have stopped in the main scintillator A Stop pulse is produced when a second pulse the decay signal comes from both of the main scintillator PMTs but not from the bottom The count rates of the top and bottom PMTs should be set approximately the same and they should have the same discriminator threshold The pulse width of the top and bottom discriminators should be longer than the pulse width of the main discriminator and should overlap to insure proper coincide
8. ervals The probability that a muon will decay in one subinterval is approximately At n so the probability that the muon will not decay in this subinterval is J t n Thus the probability that a muon will not decay within n subintervals is J 2 t n and the probably that the muon will decay from to t dt is Adt Thus P t dt A 1 My dt 5 n In this calculation the muon only considers decaying n times before time t In reality it could decay at any time Thus we should take the continuous limit At n P t dt Lim 0 dt 6 Noting that l Lim e 7 we obtain P t dt Ae dt 8 Since the muon must decay P t satisfies the normalization condition below which can be checked P at 1 0 0 Muon lifetime to is defined as to 1 A The current world average puts the muon lifetime at to 2 19 us Equipment e Oscilloscope Tektronix DPO 2012 High Voltage Power Supply Canberra 3102D Constant Fraction Discriminator Canberra 2126 4 Fold Logic Unit LeCroy 364AL or 365AL Dual Gate Generator LeCroy 222 TAC SCA Canberra 2145 Computer w MCA card Dell Computer w Ortec TRUMP PCI card The Experiment You are to setup and take data for the Basic setup and the Alternative setup If configured correctly the Basic setup should yield at least 5000 counts in 24 hrs and the Alternate setup should yield at least 2000 counts in 24 hrs Allow 3 days for data collection with the Basic setup a
9. kV Setting Up Coincidence Though PMTs are generally quiet devices they do generate some electrical noise To keep this and noise from other sources from being recorded as signal we put two PMTs on the main scintillator We compare the coincidence of their outputs and if they occur within a small tolerance of time the Logic Unit outputs a square wave You will determine and set this tolerance time Starting and Stopping the TAC From the Logic Unit the signal goes to the TAC But the TAC needs a Start pulse and a Stop pulse but we only have one pulse at a time and we do not know which pulse is which Notice in Fig 1 that a pulse from the Logic Unit goes straight into the Stop input of the TAC A different but identical and simultaneous pulse from the Logic Unit goes into the Gate Generator where it is delayed From there this delayed pulse goes to the Start input of the TAC So for every pulse that comes from the Logic Unit a direct pulse goes into the Stop port of the TAC and a delayed pulse goes into the Start port Here is the cleverness of this arrangement when a muon enters the scintillator a pulse stops the TAC and resets it making it to take a new measurement A short time later determined by the delay setting a pulse starts the TAC which is just a fancy stopwatch If the muon decays a second pulse stops the TAC and if all is set correctly the TAC sends a pulse with a time depended height to the MCA where it is recorded Of cou
10. lass of its own It is a boson that is it has integral spin and does not obey the Pauli exclusion principle It interacts electromagnetically strongly and weakly Massive particles that interact strongly weakly and electromagnetically when charged are called hadrons Hadrons with integral spin are called mesons and are composed of two quarks those with half integral spin are baryons and are composed of three quarks The proton and neutron are two famous baryons the pion is a meson Four and five quark combinations have been predicted but experimental evidence remains inconclusive The final group of particles leptons contains such particles as the electron muon and neutrinos All leptons are fermions that is they have half integral spin and do obey the Pauli exclusion principle They interact weakly electromagnetically when charged but do not interact strongly Evidence of the muon s existence was discovered in 1934 by Anderson and Neddermeyer while studying cosmic rays For historical reasons muons were called u mesons until the 1960 s when the definition of the word meson was made more specific Theory In this experiment we will investigate muon decay that takes place according to the following reactions PPS e t 7 EVs W gt e Vy T 1 The first reaction is antimuon w decay which generates a positron e muon antineutrino Va and electron neutrino ve The second reaction of our interest is muon w
11. nce and vetoing see Fig 4 Note that the listed times are not necessarily optimal HV 1 Gate Generator scintillator PMT E 1N He HV OUT gt START scintillator ine PMT Y i START x z HV H o OUT STOP z scintillator PMT fosc HV TAC LeCroy 4 fold Logic Unit Fig 3 Alternative setup with coincidence and anticoincidence configurations Main Discriminator Top Discriminator Bottorn Discriminator 50 ns 75 ns 75 mv 100 ns Pulse width and pulse relationship for the signals coming from the three discriminators Fig 4 Timing Information for the Coincidence Anti coincidence Setup Data Analysis Your MCA output should look something like Fig 5 Calculate the mean lifetime of the muon using a semi log plot of decays versus channel number In practice the number of decays in a group of about 50 channels versus time is plotted in order to ensure that each point on the plot has a reasonable statistical weight Use least squares to determine the slope of both the time calibration and the semi log plots as described in Bevington Also fit known functions to the data to determine the lifetime For the determination of to statistically weighted figures should be used Printing from Maestro Do not print directly from Maestro you will get pages and pages of numbers in a column To print out a data plot save your data and close the window Then open WinPlot and recall the spectrum From
12. nd 7 days for the Alternative setup Compare the results from these two setups in your write up Note We do occasionally have power outages and computers do crash so to avoid losing data and time save your data 2 or 3 times a day Also after collecting data for the first 12 24 hrs inspect it and make sure it looks reasonable Equipment and Experiment Details Impedance Matching Since this experiment measures time on the order of secs impedance matching is very important Since most of this equipment has an input amp output impedance of 50Q it may be necessary to use an impedance matcher on the inputs of the scope However this will not always be true Also using a T in the cables impacts the impedance and must be considered when determining the proper matching Failure to properly match impendences will result in signal distortion NIM Bins amp Modules Most of the equipment in this lab is NIM electronics NIM stands for Nuclear Instrumentation Module and is a mechanical and electrical standard used by experimentalists in particle and nuclear physics In the equipment rack are two NIM bins these are standardized power supplies that can power a wide assortment of NIM modules The modules are inserted in the bin Each bin has a power switch on its right side This switch controls the power to the modules in the bin The upper bin contains pulse shaping timing and data collecting modules The lower bin contains 4 HV Power supplie
13. rse there is another Start pulse sent to the TAC but since it is unlikely there will be a stop pulse within the set time window nothing of merit happens Creating Delays with the Gate Generator To generate a time delayed Start pulse one could use a sufficiently long cable rg58 u has a delay of 5 nsec meter however we will use the LeCroy 222 Dual Gate Generator see Fig 2 To set the delay time an oscilloscope will be used Set the scope to trigger on a direct pulse out of the Logic Unit Connect the Delay output of the Gate to the other channel of the scope There should be two similar signals on the scope with a small time shift between them Use the Full Scale Width knob and the small adjustment screw under the knob to set the desired delay time Remember to consider impedance matching Start Stop O From Logic Unit Or Nim Nim O O O To TAC O O O Blank TTL DEL Fig 2 LeCroy Gate Generator Used to Delay the Start pulse Using the MCA Maestro amp the TRUMP PCI Card The MCA is composed of the Maestro program and the TRUMP PCI card Cables are plugged into the card at the back of the computer and the software interfaces with the card to collect data and do data analysis The user s manual is on the lab wiki https wiki brown edu confluence download attachments 29406 MAESTRO V6 User Manual pdf version 1 amp modificationDate 1380592747664 Before the data from the MCA can be trusted it must be calibrated
14. s High Voltage Power Supply To power on the HV power supplies always power the bin on first then turn on the individual power supplies When powering them down do the opposite turn the power supplies off first then turn off the power to the bin When HV is applied to a PMT it must be increased slowly to prevent damaging the PMT or making it unnecessarily noisy 30 yrs ago this was done by hand but modern NIM HV power supplies are smart and ramp the voltage up at the appropriate rate Due to this feature the output of the supply responds slowly to rotations of the control knob This maks it possible to overshoot the desired output voltage So when setting the HV near the maximum recommended voltage of 1KV turn the control knob small amounts and wait for the output voltage to stabilize before proceeding The good news is once the desired voltage has been selected it does not need to be readjusted the power supplies may simply be switched off and on only by their individual switches as desired because the automatic feature takes care of the rest Scintillator Photomultiplier Tube and Discriminator The setup for the basic experiment is shown in Fig 1 Many cosmic ray muons pass through the main scintillator per minute and a fraction of them having lost sufficient energy will come to rest in the scintillator and will soon decay Both the muon arrival and the electron produced in the decay of the muon will give rise to the emission
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