TeachSpin Muon Physics Manual
Contents
1. u u Charge Ratio at Ground Level Our measurement of the muon lifetime in plastic scintillator is an average over both negatively and positively charged muons We have already seen that s have a lifetime somewhat smaller than positively charged muons because of weak interactions between negative muons and protons in the scintillator nuclei This interaction probability is proportional to Z where Z is the atomic number of the nuclei so the lifetime of negative muons in scintillator and carbon should be very nearly equal This latter lifetime is measured to be T 2 043 0 003 usec Reiter 1960 It is easy to determine the expected average lifetime t obs of positive and negative muons in plastic scintillator Let be the decay rate per negative muon in plastic scintillator and let A be the corresponding quantity for positively charged muons If we then let N and N represent the number of negative and positive muons incident on the scintillator per unit time respectively the average observed decay rate A and its corresponding lifetime t obs are given by tXFIN A A N BAT AT 1 p 07 Tore E 4 1 0 5 where N N T A is the lifetime of negative muons in scintillator and T is the corresponding quantity for positive muons Due to the Z effect for plastic scintillator and we can set equal to the free space lifetime value t since positive muons are not capt2. EM F SUPA ls UP ee CQ e AOS TIAS SN A 4 T 1 PIDE AAA PS i AL ij r E 11 gt Alten N TET ART M EN x d NAT a bg s MESES Y u M I Ue f hy L qM E Wo nas TM yi i he El M M nt an M M M ann Viii A tt it e o FUIT SS p epe2il aov Pe VE 2 L nnm s Pe s ne DIE 7 m z VIS IPEA awe eae gt o a A wt cda 17 rg DITA AL emi e Lee PAL unm AM aw ae y a 3 A Th Em 2 r Lj ween 3 lic rii ras rien sim mn Al ere rta 74 phys4211 an sa to vor s Hu El esien Los drver Seu alu MY 2ocu an r My locos My Foru ber Figure 11 Muon Physics Folders All of the software can be run from either the CD or copied to disk The muon decay simulation software can be run without any of the detector electronics present You should copy all six folders on the CD to a convenient directory Table2 lists the folders and describes the software they contain Table 2 Important Folders Folder name muon data muon simu muon uti sample data The program you will probably use the most is muon located in the folder muon data This is the principal data acquisition program used to collect real data This program
3. v 5 A Gis Rat EINEN e At i a was to teal PEG A E i x 1 Fabel o TA 1 mer ee 1 xcim Ue Tao P TAN M Aufl wt t 7 A in 5 her Y Mh A AL TELLS M vuv c WS H SW TIR Y A LAC 2 PES 1 i e A k n NL TEN f N IV t D LVS c SN od di AL 5 i Getting Started You cannot break anything unless you drop the detector on the floor or do something equally dramatic Every cable you need is provided along with a 500 terminator The black aluminum cylinder detector can be placed in the wooden pedestal for convenience The detector will work in any orientation Cable types are unique Connect the power cable and signal cable between the electronics box and the detector Connect the communication cable between the back of the electronics box and your PC or laptop Use either the USB connection or the serial port but not both Turn on power to the electronics box Switch is at rear The red LED power light should now be steadily shining The green LED may or may not be flashing Set the HV between 1100 and 1200 Volts using the knob at the top of the detector tube The exact setting is not critical and the voltage can be monitored by using the multimeter probe connectors at the top of the detector tube If you are curious you can look directly at the output of the PMT using the PMT Output on the detector
4. ameasguremenit 18 T Ra 42 Muon Di CSV TIL Figure 12 User Interface There are 5 sections to the main display panel Control Muon Decay Time Histogram Monitor Rate Meter Muons through detector Control The Configure sub menu is shown in figure 13 This menu allows you to specify which communications port com1 com2 com3 or com4 that you will connect to the electronics box Select either com or com2 if you will use a serial port for communication Typically you will have only a single serial port on your PC so in this case you would select com The serial port on your PC is the D shaped connector with 9 pins If you select the wrong port an error message will eventually appear after you try 21 SL J yA Ni y IMMUOIn EIVSICS to start the data acquisition see below telling you that the port you selected cannot be opened If you wish to use the USB port then connect to the USB port on your computer select com2 and follow the instructions below for starting the program If your PC cannot find the USB port then com2 is not the correct port selection or you lack the USB driver in the first place To correct the first situation examine the folder system hardware devices communications and find out what port other than com exists Choose this port If you need to install the USB driver then the Windows operating system will inform you of such and ask you where it can find
5. IN Click on Start You should see the rate meter at the lower left hand side of your computer screen immediately start to display the raw trigger rate for events that trigger the readout electronics The mean rate should be about 6 Hz or so 30 Muon Physics Suggested Student Exercises 1 Measure the gain of the 2 stage amplifier using a sine wave Apply a 100kHz 100mV peak to peak sine wave to the input of the electronics box input Measure the amplifier output and take the ratio Vour Vin Due to attenuation resistors inside the electronics box inserted between the amplifier output and the front panel connector you will need to multiply this ratio by the factor 1050 50 z 21 to determine the real amplifier gain Q Increase the frequency How good is the frequency response of the amp Q Estimate the maximum decay rate you could observe with the instrument 2 Measure the saturation output voltage of the amp Increase the magnitude of the input sine wave and monitor the amplifier output Q Does a saturated amp output change the timing of the FPGA What are the implications for the size of the light signals from the scintillator 3 Examine the behavior of the discriminator by feeding a sine wave to the box input and adjusting the discriminator threshold Monitor the discriminator output and describe its shape 4 Measure the timing properties of the FPGA a Using the pulser on the detector measure the time between succ
6. Instruments Designed for Teaching MUON PHYSICS MP1 A USER S MANUAL 4 A Product of TeachSpin Inc Written by Thomas Coan amp Jingbo Ye Southern Methodist University TeachSpin Inc 2495 Main Street Suite 409 Buffalo NY 14214 2153 716 885 4701 or www teachspin com Muon Physics T E Coan and J Ye v090505 0 Contents INTRODUCTION ze ine namen iii c 3 OUR MUON SOURCE aca AA er 3 MUON DECAY TIME DISTRIBUTION eene 5 DIETER TGR PHYSICS eier aria 5 INTERACTION OF M S WITH MATTER csi nn 7 Vil CHARGE RATIO AT GROUND LEVEL nee 9 BACKGROUNDS can A A ux DU FERMI COUPLING CONSTANT Grz in Q TRIER 10 TIME DILATION EFFECT TRE Y 11 ELECTRONICS scorie ia oe E nn anna TE SOFTWARE AND USER INTERFACE ENS ERR YER MARE A sun 19 CORRO einen GN dnd cia mnl MN DDR ERR E 21 Data file TORA see sconti EN 23 MOn OT asd siu aliad 24 R te MERIBF iioii ana RARAS ZA Muons through Detector eee vas 24 Muon Decay Time Histogram eee PP 24 TEE LIFEFIME FITTER susana Mn 25 MUON DECAY SIMA ATION cease opea aU RELIER Con T o 25 UTILITY SOFTWARE eno Sime Roe AAAS
7. To measure the muon s lifetime we are interested in only those muons that enter slow stop and then decay inside the plastic scintillator Figure 2 summarizes this process Such muons have a total energy of only about 160 MeV as they enter the tube As a muon slows to a stop the excited scintillator emits light that is detected by a photomultiplier tube PMT eventually producing a logic signal that triggers a timing clock See the electronics section below for more detail A stopped muon after a bit decays into an electron a neutrino and an anti neutrino See the next section for an important qualification of this statement Since the electron mass is so much smaller that the muon mass m m 210 the electron tends to be very energetic and to produce scintillator light essentially all along its pathlength The neutrino and anti neutrino also share some of the muon s total energy but they entirely escape detection This second burst of scintillator light is also seen by the PMT and used to trigger the timing clock The distribution of time intervals between successive clock triggers for a set of muon decays is the physically interesting quantity used to measure the muon lifetime Figure 2 Schematic showing the generation of the two light pulses short arrows used in determining the muon lifetime One light pulse is from the slowing muon dotted line and the other is from its decay into an electron or positron wavey line Table 1
8. FAR E 23 REFERENCES wsssssssssosssssssssssesssssnssones anemias dod Instrumentation and Technique 27 Cosmio Rays ESS 27 General Ae TI Muon Lifetime in Matter essers 28 GETTING STARTED isn 9 On 29 SUGGESTED STUDENT EXERCISES een 51 HOW TO GET HELP A AAEE A A o Introduction The muon is one of nature s fundamental building blocks of matter and acts in many ways as if it were an unstable heavy electron for reasons no one fully understands Discovered in 1937 by C W Anderson and S H Neddermeyer when they exposed a cloud chamber to cosmic rays its finite lifetime was first demonstrated in 1941 by F Rasetti The instrument described in this manual permits you to measure the charge averaged mean muon lifetime in plastic scintillator to measure the relative flux of muons as a function of height above sea level and to demonstrate the time dilation effect of special relativity The instrument also provides a source of genuinely random numbers that can be used for experimental tests of standard probability distributions Our Muon Source The top of earth s atmosphere is bombarded by a flux of high energy charged particles produced in other parts of the universe by mechanisms that are not yet fully understood The composition of these pr
9. stores its data in one of two files the file named data or a file named with the date on which the data was collected derived from the year month day and time in that order when the date is written in numerical form For example the file 03 07 15 39 corresponds to a data file written 15 July 2003 at 3 39pm Minutes and hours are written in 24 hour notation Real data files are automatically written to the folder muon data Files with the extension tcl and dll are support programs that you do not need to modify for normal running The Tcl files are however useful to read if you want to see how the user interface and our curve fitter are written in the Tcl Tk scripting language The program muon is the main data acquisition program After you launch it you will first see the user interface shown in figure 12 The interface allows you to set port settings on your PC to observe various data rates to control how data is displayed on the PC and to fit the collected data 20 Un SILET Yi Jl A 1 u i A E pM HAM v vM it AP E ATI j ir AA wit We ir nG H MEER ERKENNEN e Pin Kleine 181 1 4 Val ps i i OnImol s r UU CIIM P je wp dpa ORN i je UMD OM Decay Time Hi LORTAITIT a SI DD i PM AB d a
10. Designed fex Teaching US and C an ada Do not attempt to repair this instrument while it is under warranty This instrument is warranted for a period of two 2 years from the date it is delivered For breakdowns due to defects in components workmanship or ordinary use TeachSpin will pay for all Jabor and parts to repair the instrument to original working specifications For the first year of the warranty TeachSpin will also pay all shipping costs This warranty is void under the following circumstances 1 The instrument has been dropped mutilated or damaged by impact or extreme heat 2 Repairs not authorized by TeachSpin Inc have been attempted 3 The instrument has been subjected to high voltages plugged into excess AC voltages or otherwise electrically abused TeachSpin Inc makes no expressed warranty other than the warranty set forth herein and all implied warranties are excluded TeachSpin Inc s liability for any defective product is limited to the repair or replacement of the product at our discretion TeachSpin Inc shall not be liable for 1 Damage to other properties caused by any defects damages caused by inconvenience loss of use of the product commercial Joss or loss of teaching time 2 Damage caused by operating the unit without regard to explicit instructions and warnings in the TeachSpin manual Tri Main Center Suite 409 2495 Main Street Buffalo NY 14214 2153 Phone 716 885 4701 www tea
11. IM AST d E o IN ZED m M AEA DE PUES ESO 5 Pant MUT SH amp U SM I 4 607 A it T1 1 4 baw 4 j SM n I e nm ur MUT V 1n n E ex TE nq 14 i MEM TA Wb Mnt TU YMIO Im v 1 2 fi DX A 15 e LY i I AA ia am M AM et a MU A m ae y q tt yf MAMI yl ns nr NL M hg i US REN N eid oe NP ze IN BEA ASE R eio od es m MP us ven e lt OS N triggers can be adjusted using the Threshold control knob The threshold voltage is monitored by using the red and black connectors that accept standard multimeter probe leads The toggle switch controls a beeper that sounds when an amplifier signal is above the discriminator threshold The beeper can be turned off The back panel of the electronics box is shown is figure 7 An extra fuse is stored inside the power switch Figure 8 shows the top of the detector cylinder DC power to the electronics inside the detector tube is supplied from the electronics box through the connector DC Power The high voltage HV to the PMT can be adjusted by turning the potentiometer located at the top of the detector tube The HV level can be measured by using the pair of red and black connectors that accept standard multimeter probes The HV monitor output is 1 100 times the HV applied to the PMT A pulser inside the detector tube can drive a light emitting diode LED imbedded in
12. The fit curve drawn through the data points disappears once a new data point is collected but results of the fit remain The View Raw Data button opens a window that allows you to display the timing data for a user selected number of events with the most recent events read in first Here an event is any signal above the discriminator threshold so it includes data from both through going muons as well as signals from muons that stop and decay inside the detector Each raw data record contains two fields of information The first is a time indicating the year month day hour minute and second reading left to right in which the data was recorded The second field is an integer that encodes two kinds of information If the integer is less than 40000 it is the time between two successive flashes in units of nanoseconds If the integer is greater than or equal to than 40000 then the units position indicates the number of time outs instances where a second scintillator flash did not occur within the preset timing window opened by the first flash See the data file format below for more information Typically viewing raw data is a diagnostic operation and is not needed for normal data taking The Quit button stops the measurement and asks you whether you want to save the data Answering No writes the data to a file that is named after the date and time the measurement was originally started i e 03 07 13 17 26 data Answering Yes appends the d
13. WEN AMO O a es e E noc We enjoyed showing our Muon Physics apparatus in the workshop mode at the Topical Conference on Advanced Labs held in July at Ann Arbor While there we devised a teaching method that we think you and your students will both enjoy and appreciate It will show them the cause and effect relationships that lie between the muons and the computer screen in this experiment and along the way it will teach them a lot about pulse electronics and event processing All you need is a digital scope and not even an expensive one Recall how the Muon Physics apparatus works There s a big plastic scintillator inside the black aluminum cylin der through which muons are passing frequently The muons passing through or the lower energy muons that come to rest inside the plastic all deposit some energy in the plastic And of course the scintillator material is opti mized to convert some of that energy into a very brief pulse of light A fraction of that light reaches the photocathode of a photomultiplier tube PMT attached to the scintillator where it ejects photoelectrons Inside the PMT those initial photoelectrons are multiplied via a cascade process to yield a macroscopic charge pulse delivered to the PMT s anode That charge pulse emerges from the scintillator unit via a BNC cable and is conveyed over to the electronics unit Inside the electronics box there is a linear amplifier which shapes that charge p
14. is an average over both charge species so the mean lifetime of the detected muons will be somewhat less than the free space value T 2 19703 0 00004 usec The probability for nuclear absorption of a stopped negative muon by one of the scintillator nuclei is proportional to Z where Z is the atomic number of the nucleus Rossi 1952 A stopped muon captured in an atomic orbital will make transitions down to the K shell on a time scale short compared to its time for spontaneous decay Wheeler Its Bohr radius is roughly 200 times smaller than that for an electron due to its much larger mass increasing its probability for being found in the nucleus From our knowledge of hydrogenic wavefunctions the probability density for the bound muon to be found inside the nucleus is proportional to Z Once inside the nucleus a muon s probability for encountering a proton is proportional to the number of protons there and so scales like Z The net effect is for the overall absorption probability to scale like 7 Again this effect is relevant only for negatively charged muons E ww e 9 microsec Figure 3 Disintegration curves for positive and negative muons in aluminum The ordinates at t 0 can be used to determine the relative numbers of negative and positive muons that have undergone spontaneous decay The slopes can be used to determine the decay time of each charge species From Rossi p168 Muon Physics e
15. is the number of seconds as measured by the PC from the beginning of 1 January 1970 i e 00 00 00 1970 01 01 UTC a date conventional in computer programming Monitor This panel shows rate related information for the current measurement The elapsed time of the current measurement is shown along with the accumulated number of times from the start of the measurement that the readout electronics was triggered Number of Muons The Muon Rate is the number of times the readout electronics was triggered in the previous second The number of pairs of successive signals where the time interval between successive signals is less than the maximum number of clock cycles of the timing circuit is labeled Muon Decays even though some of these events may be background events and not real muon decays Finally the number of muon decays per minute is displayed as Decay Rate Rate Meter This continuously updated graph plots the number of signals above discriminator threshold versus time It is useful for monitoring the overall trigger rate Muons through Detector This graph shows the time history of the number of signals above threshold Its time scale is automatically adjusted and is intended to show time scales much longer than the rate meter This graph is useful for long term monitoring of the trigger rate Strictly speaking it includes signals from not only through going muons but any source that might produce a trigger The horizontal axis is
16. measurement at the new altitude distinguishes between competing predictions A comparison of the muon stopping rate at two different altitudes should account for the muon s energy loss as it descends into the atmosphere variations with energy in the shape of the muon energy spectrum and the varying zenith angles of the muons that stop in the detector Since the detector stops only low energy muons the stopped muons detected by the low altitude detector will at the elevation of the higher altitude detector necessarily have greater energy This energy difference AE h will clearly depend on the pathlength between the two detector positions Vertically travelling muons at the position of the higher altitude detector that are ultimately detected by the lower detector have an energy larger than those stopped and detected by the upper detector by an amount equal to AE h If the shape of the muon energy spectrum changes significantly with energy then the relative muon stopping rates at the two different altitudes will reflect this difference in spectrum shape at the two different energies This is easy to see if you suppose muons do not decay at all This variation in the spectrum shape can be corrected for by calibrating the detector in a manner described below Like all charged particles a muon loses energy through coulombic interactions with the matter it traverses The average energy loss rate in matter for singly charged particles traveling c
17. the scintillator It is turned on by the toggle switch at the tube top The pulser produces pulse pairs at a fixed repetition rate of 100 Hz while the time between the two pulses comprising a pair is adjusted by the knob labeled Time Adj The pulser output voltage is accessible at the connector labeled Pulse Output For reference figure 9 shows the output directly from the PMT into a 502 load Figure 10 shows the corresponding amplifier and discriminator output pulses rro PA UAR 4 iyi i ul nn yo pa S RD Vv hal CTA ANE Figure 6 Front of the electronics box ANA n aem W e TUR EU Ln FALL RT EAT Vu mmm MAA Yo Te MERE j 47 mw I Ai PT DR Wh WT SN SET y A AA d PAL UNITA y n e VIA die AU Ae d DENT Sr Lu MI B5 nv NEN 76s A Th di 15704 DAY Sea MI win TET Pob UR va n y a T Anm RN Car ns gt A VE wi TO MERI A a ee Ln rl vas rt P ACE Ft 9 Ay ENS i n H I Ad EIN A a 1 Ps i 18 79 LEA 7 Y IA dal JU TC PAL E r de ME 1t ADA Ys RM UA Nm UN uM A 1L gt f wv d Figure 7 Rear of electronics box The communications ports are on the left Use only one Figure 8 Top view of the detector lid The HV adjustment potentiometer and monitoring ports for the PMT are located here Ly yn f yay E 1 ENT e Kalt Vt Figure 9
18. to learn in and from our Muon Physics apparatus
19. to the column lying between the 1 and 2 labels of the histogram With only one example of a successor event in hand it is impossible to decide between hypotheses A and B above for its origin If however we continue watching for perhaps 20 to 30 minutes with the scope set as in Fig 3 we ll get a lot more instances of these successor events all of them lying on the same scope face display It s the distribution in time of a sample of such events across the scope s face that differs according to the two hypotheses as follows A successor events due to a separate unrelated muons are as likely to fall near the us mark as they are to land at any other time say 8 us since the muons involved under this hypothesis are independent and uncorrelated B successor events due to the decay of stopped muons will not be uniformly distributed in time across the scope s face Instead they will be more concentrated at short times and exponentially fewer at long times because of the exponential decay of muons in the scintillator EEE EN TA BER EB Ee 8 5 amp E iS 7 Sakis a b CO E Eek O xw d 5 RR DB x QV Qo o Ce A A V oy Vd 5 oy c 0343 ne dd 54 8 x 4 4 5 P 42 871 Ot 9 AREA EBD s 9 E 5 Bog A LET Xo 9 o x 85 6 Us Here cw VAT eA y amp AL GN 0 0 5 MR 0 XS Oe we 9 E DEAN es
20. General Scintillator Properties Mass density Refractive index Base material Wavelength of 423 nm Maximum Emission Interaction of u 5 with matter The muons whose lifetime we measure necessarily interact with matter Negative muons that stop in the scintillator can bind to the scintillator s carbon and hydrogen nuclei in much the same way as electrons do Since the muon is not an electron the Pauli exclusion principle does not prevent it from occupying an atomic orbital already filled With electrons Such bound negative muons can then interact with protons E pon vy before they spontaneously decay Since there are now two ways for a negative muon to disappear the effective lifetime of negative muons in matter is somewhat less than the lifetime of positively charged muons which do not have this second interaction mechanism Experimental evidence for this effect is shown in figure 3 where disintegration curves for positive and negative muons in aluminum are shown See Rossi 1952 The abscissa is the time interval t between the arrival of a muon in the aluminum target and its decay The ordinate plotted logarithmically is the number of muons greater than the corresponding abscissa These curves have the same meaning as curves representing the survival population of radioactive substances The slope of the curve is a measure of the effective lifetime of the decaying substance The muon lifetime we measure with this instrument
21. Once the muon lifetime is determined compare the theoretical binomial distribution with an experimental distribution derived from the random lifetime data of individual muon decays For example let p be the success probability of decay within 1 lifetime p 0 63 The probability of failure q 1 p Take a fresh data sample of 2000 good decay events For each successive group of 50 events count how many have a decay time less than 1 lifetime On average this is 31 5 Histogram the number of successes This gives you 40 experiments to do The plot of 40 data points should have a mean at 50 0 63 with a variance 0 Npq 50 0 63 0 37 11 6 Are the experimental results consistent with theory How to get help If you get stuck and need additional technical information or if you have physics questions you can contact either Thomas Coan coanQ mail physics smu edu or Jingbo Ye yejb mail physics smu edu We will be glad to help you 35 ry rwn i i Wa Pee IA OSA A eser y ra C i 3 jM 4 Riga AA NS E Lye u 9 HAN 159 ri vol Ew FS AUI XA I X ah Pe Rage 12 T 3 ue UT u ahah Perl Tr ut tM ANA ee Y 5 B WE na LO P A Y 1 tH tS y due UN uad AD TN is en A1 HT 4 NET UR AAA A LL Me es Q A T Ad I PHP t E meta 997 gt PSA iy y MET u A ys Meat ote 7 e EN tae bi da it f 4 i Warranty for Instruments
22. Output pulse directly from PMT into a 500 load Horizontal scale is 20 ns div and vertical scale is 100 mV div Wm i cde zz Aa Figure 10 Amplifier output pulse from the input signal from figure 9 and the resulting discriminator output pulse Horizontal scale is 20 ns div and the vertical scale is 100 mV div amplifier output and 200 mV div discriminator output wt rong de me es q j yee aqui u Ay As N ahs ea T I ol Y 2 2 rU LEE ty i 4 Abi oe n 18 TE 2 ded 5 1 YA 10 ri gt Physics i Ao ud NU ps x eV Software and User Interface Software is used to both help control the instrument and to record and process the raw data There is also software to simulate muon decay data All software is contained on the CD that accompanies the instrument and can also be freely downloaded from www muon edu Both Microsoft and Linux operating systems are supported Source code for the user interface and the data fitting software is written in the Tcl Tk scripting language and is provided You should find the folders directories shown in figure 11 on the supplied CD e phys 1211 VET L no vk RARI VIS A ev B tr M CURT i x q d ILOX d td 1 MU ir wc 4 z we 3 i SORTED AA tae ae Lt vi M 2 CIE Tr rin
23. and assume that on average stopped muons travel halfway into the scintillator corresponding to a distance s 10 g cm The entrance muon momentum is then taken from range momentum graphs at the Particle Data Group WWW site and the corresponding y computed The lower limit of integration is given by y E mc where E E AE with E 2160 MeV The integral can be evaluated numerically See for example Internet site http people hofstra edu faculty Stefan_Waner RealWorld integral integral html Hence the ratio R of muon stopping rates for the same detector at two different positions separated by a vertical distance H and ignoring for the moment any variations in the shape of the energy spectrum of muons is just R exp t t where t is the muon proper lifetime When comparing the muon stopping rates for the detector at two different elevations we must remember that muons that stop in the lower detector have at the position of the upper detector a larger energy If say the relative muon abundance grows dramatically with energy then we would expect a relatively large stopping rate at the lower detector simply because the starting flux at the position of the upper detector was so large and not because of any relativistic effects Indeed the muon momentum spectrum does peak at around p 500 MeV c or so although the precise shape is not known with high accuracy See figure 4 o Differential Intensity cm s s
24. ata to the file muon data The file muon data is intended as the main data file Data file format Timing information about each signal above threshold is written to disk and is contained either in the file muon data or a file named with the date of the measurement session Which file depends on how the data is saved at the end of a measurement session The first field is an encoded positive integer that is either the number of nanoseconds between successive signals that triggered the readout electronics or the number of timeouts in the one second interval identified by the corresponding data in the second column An integer less than 40000 is the time measured in nanoseconds between successive signals and background aside identifies a muon decay Only data of this type is entered automatically into the decay time histogram An integer greater than or equal to 40000 corresponds to the situation where the time between successive signals exceeded the timing circuit s maximum number of 40000 clock cycles A non zero number in the units place indicates the number of times this timeout situation occurred in the particular second identified by the data in the first field For example the integer 40005 in the first field indicates that the readout circuit was triggered 5 times in a particular second but that each time the timing circuit reached its maximum number of clock cycles before the next signal arrived 23 WM X The second field
25. chspin com Fax 716 836 1077 convenielice for its customers Those m a e to the individual manufacturer warranties and any problems should de re m ferres 7 16 those manufacturers k punte d 4 Any other tenens whether incidental consequential or obere pt y t e bod g Aie wt ps A n es 1 4 a m 1 i E AE A s m d LI boy T 2 5 er P 4 e yo xr omg 1 I ofa 4 i ets d 5 Cato Y A A Main Center Sulte 409 2495 Main S Street Buffalo NY 14214 2153 Phone 716 885 4701 ww 716 836 1077 BOX ____ of Muon Physics MP1 A PACKING LIST Date Purchased by Serial Faculty Name Purchase Orders Comments Thank You for Your Order ITEM Muon Physics Detector with HV amp Variable Double Pulser Muon Physics Readout Unit BNC Cable BNC 50 OHM Terminator Low Voltage Cable USB A B Cable Software CD with User Manual in PDF User s Manual QTY QTY 3475 Il GG6C Warranty USA amp Canada 2 years on parts amp labor Packed by Forecast 2495 Main Street It s Raining T R Buffalo NY 14214 e Relaxation Times gt www teachspin com fax 716 836 1077 VOL III No 6 NEWSLETTER OF TEACHSPIN INC AUGUST 2009 More About Muons Sa Y an i 24 m Nec eL Mes ri E IS a 2 A AN vtr wa WEA HAN We WAN
26. e surviving population of muons Again what we call the muon lifetime is 1 A Because the muon decay time is exponentially distributed it does not matter that the muons whose decays we detect are not born in the detector but somewhere above us in the atmosphere An exponential function always looks the same in the sense that Whether you examine it at early times or late times its e folding time is the same Detector Physics The active volume of the detector is a plastic scintillator in the shape of a right circular cylinder of 15 cm diameter and 12 5 cm height placed at the bottom of the black anodized aluminum alloy tube Plastic scintillator is transparent organic material made by mixing together one or more fluors with a solid plastic solvent that has an aromatic ring structure A charged particle passing through the scintillator will lose some of its kinetic energy by ionization and atomic excitation of the solvent molecules Some of this deposited energy is then transferred to the fluor molecules whose electrons are then promoted to excited states Upon radiative de excitation light in the blue and near UV portion of the electromagnetic spectrum is emitted with a typical decay time of a few nanoseconds A typical photon yield for a plastic scintillator is 1 optical photon emitted per 100 eV of deposited energy The properties of the polyvinyltoluene based scintillator used in the muon lifetime instrument are summarized in table 1
27. ence ICRC 2001 927 2001 Neddermeyer S H and Anderson C D Phys Rev 51 884 1937 Rasetti F Phys Rev 89 706 941 60 198 1946 Simpson J A Elemental and Isotopic Composition of the Galactic Cosmic Rays in Rev Nucl Part Sci 33 p 330 Thorndike A M Mesons a Summary of Experimental Facts 1952 McGraw Hill New York 21 General http www pdg lbl gov http people hofstra edu faculty Stefan Waner RealWorld integral integral html http aero stanford edu StdAtm html Bevington P R and D K Robinson Data Reduction and Error Analysis for the Physical Sciences 2ed 1992 McGraw Hill New York Evans R D The Atomic Nucleus 1955 McGraw Hill New York chapter 18 Perkins D H Introduction to High Energy Physics 4ed 2000 Cambridge University Press Cambridge Rossi B High Energy Particles 1952 Prentice Hall Inc New York Taylor J R An Introduction to Error Analysis 2ed 1997 University Science Books Sausalito CA Weissenberg A O Muons 1967 North Holland Publishing Amsterdam Muon Lifetime in Matter Bell W E and Hincks E P Phys Rev 88 1424 1952 Eckhause M et al Phys Rev 132 422 1963 Fermi E et al Phys Rev 71 314 1947 Primakoff H Rev Mod Phys 31 802 1959 Reiter R A et al Phys Rev Lett 5 22 1960 Wheeler J A Rev Mod Phys 21 133 1949 TEYU wet P y i
28. entative lifetime and fit again that part of this new distribution that have times greater than 5t The tentative background level is subtracted from the previous distribution to produce a new distribution and the whole process is repeated again for a total of 3 background subtraction steps Muon Decay Simulation Simulated muon decay data can be generated using the program muonsimu found in the muon simu folder Its interface and its general functionality are very similar to the program muon in the muon data folder The simulation program muonsimu lets you select the decay time of the muon and the number of decays to simulate Simulated data is stored in exactly the same format as real data Utility Software The folder muon util contains several useful programs that ease the analysis of decay data The executable file sift sifts through a raw decay data file and writes to a file of your 25 choosing only those records that describe possible muon decays It ignores records that describe timing data inconsistent with actual muon decay The executable file merge merges two data files of your choosing into a single file of your choosing The data records are time ordered according to the date of original recording so that the older the record the earlier it occurs in the merged file The executable file ratecalc calculates the average trigger rate per second and the muon decay rate per minute from a data file of your choo
29. essive rising edges on an oscilloscope Compare this number with the number from software display b Measure the linearity of the FPGA Alter the time between rising edges and plot scope results v FPGA results Can use time between 1 us and 20 us in steps of 2 us c Determine the timeout interval of the FPGA by gradually increasing the time between successive rising edges of a double pulse and determine when the FPGA no longer records results Q What does this imply about the maximum time between signal pulses d Decrease the time interval between successive pulses and try to determine bound the FPGA internal timing bin width Q What does this imply about the binning of the data Q What does this imply about the minimum decay time you can observe 31 5 Adjust or misadjust discriminator threshold Increase the discriminator output rate as measured by the scope or some other means Observe the raw muon count rate and the spectrum of decay times This exercise needs a digital scope and some patience since the counting rate is slowish 6 What HV should you run at Adjust misadjust HV and observe amp output We know that good signals need to be at about 200 mV or so before discriminator so set discriminator before hand With fixed threshold alter the HV and watch raw muon count rate and decay spectrum 7 Connect the output of the detector can to the input of the electronics box Look at the amplifier output using a
30. ew corrected theoretical prediction for the stopping rate ratio Ry Ro R 1 6exp We find t 1 067 and R 0 52 0 06 The raw measurements yield Ryay 0 56 0 01 showing good agreement For your own time dilation experiment you could first measure the raw muon stopping rate at an upper and lower elevation Accounting for energy loss between the two elevations you first calculate the transit time t in the muon s rest frame and then a naive theoretical lower elevation stopping rate This naive rate should then be multiplied by the muon spectrum correction factor 1 5 0 2 before comparing it to the measured rate at the lower elevation Alternatively you could measure the lower elevation stopping rate divide by the correction factor and then account for energy loss before predicting what the upper elevation stopping rate should be You would then compare your prediction against a measurement Again the correction factor is relevant for elevations separated by 2000 3000 meters or so 14 Electronics A block diagram of the readout electronics is shown in figure 5 The logic of the signal processing is simple Scintillation light is detected by a photomultiplier tube PMT whose output signal feeds a two stage amplifier The amplifier output then feeds a voltage comparator discriminator with adjustable threshold This discriminator produces a TTL output pulse for input signals above threshold and this TTL output
31. g muon decay times are exponentially distributed along with the chi squared per degree of freedom ratio a standard measure of the quality of the fit See Bevington for more details A Screen capture button allows you to produce a plot of the display Select the button and then open the Paint utility in Windows and execute the Paste command under the Edit pull down menu The Lifetime Fitter The included muon lifetime fitter for the decay time histogram assumes that the distribution of times is the sum of an exponential distribution and a flat distribution The exponential distribution is attributed to real muon decays while the flat distribution is attributed to background events The philosophy of the fitter is to first estimate the flat background from the data at large nominal decays times and to then subtract this estimated background from the original distribution to produce a new distribution that can then be fit to a pure exponential The background estimation is a multi step process Starting with the raw distribution of decay times we fit the distribution with an exponential to produce a tentative lifetime 7 We then fit that part of the raw distribution that have times greater than 57 with a straight line of slope zero The resulting number is our first estimate of the background We next subtract this constant number from all bins of the original histogram to produce a new distribution of decay times Again we fit to produce a t
32. g pulse from the PMT amplifier that is larger than a given voltage pre selected by the experimenter This pre selected value is called the threshold voltage There is a knob on the front panel that sets the threshold voltage CONTROL and a set of pin jacks THRESHOLD that can be used with a voltmeter to read a DC voltage proportional to the threshold To see the results of that discrimination criterion its time to use the additional output labeled DISCRIMINATOR on the electronics box With Channel 1 still devoted to the amplifier output pulse we now trigger the scope on the falling edge of the discriminator s output To accomplish this we put another 50 Q termination on a BNC tee at the discriminator s output and convey its signal via a second short BNC cable to the oscilloscope s Channel 2 input The results are shown in Fig 2a amp 2b rrr try er te EEVA ee y wd 4 e T v B4 ot 7 Nur c v X box cue om vg co ew TEE TT s e Lr a f h J 7 T v XU A M m Pd ARA AD 1 7 NTF TY Cy TT P i rS y i A T3 y n IRR A ET get Fig 2a Lower trace Channel 1 the amplifler output upper trace Channel 2 the discriminator output Discriminator control is set at 2 on Its 0 10 scale i ie do dl iiidid ibid DES TTUT narra nad n n ni rn naf i ren nn n
33. ger point that one of these many overlaid traces included a second muon event We can offer two possible hypotheses for this Successor event A the scope was triggered by one muon s passage through the scintillator and the successor pulse was due to the passage of another separate unrelated muon B on one of the many traces the scope was triggered by a muon coming to rest in the scintillator and the visible successor pulse was due to the decay of this very muon producing either a positron or an electron in the scintillator Now if the computer was connected to the electronics box and it was executing the Muon program with a Start that coincided with the beginning of the persistence interval shown in Fig 3 you d get to learn another valuable concep tual connection After perhaps a minute s wait just as you saw the first successor event appear at 1 4 us on the Scope s face you would also see one event one count one occurrence appear for the first time in the main histogram in the computer s display window That s because the electron ic stopwatch in the electronics unit starts its clock at every muon event and in this pioneer case has stopped that stopwatch at a successor event only 1 4 us later This pair of events of 1 4 us spacing corresponds to one occurrence of an interpulse spacing lying between and 2 us This is just what the computer tabulates It adds of one instance or one unit
34. imary cosmic rays is somewhat energy dependent but a useful approximation is that 98 of these particles are protons or heavier nuclei and 2 are electrons Of the protons and nuclei about 87 are protons 12 helium nuclei and the balance are still heavier nuclei that are the end products of stellar nucleosynthesis See Simpson in the reference section for more details The primary cosmic rays collide with the nuclei of air molecules and produce a shower of particles that include protons neutrons pions both charged and neutral kaons photons electrons and positrons These secondary particles then undergo electromagnetic and nuclear interactions to produce yet additional particles in a cascade process Figure 1 indicates the general idea Of particular interest is the fate of the charged pions produced in the cascade Some of these will interact via the strong force with air molecule nuclei but others will spontaneously decay indicated by the arrow via the weak force into a muon plus a neutrino or antineutrino T H vy T H Vu The muon does not interact with matter via the strong force but only through the weak and electromagnetic forces It travels a relatively long instance while losing its kinetic energy and decays by the weak force into an electron plus a neutrino and antineutrino We will detect the decays of some of the muons produced in the cascade Our detection efficiency for the neutrinos and antineutrinos is utterly negligib
35. it In this case just enter data into the pop up window pointing to the location of the driver contained in the USB driver folder on the included CD The Windows operating system will then automatically assign a port name that you can determine by examining the folder system hardware devices communications The maximum x axis value for the histogram of the muon decay times and the number of data bins is also set here There are also controls for reading back all ready collected data The blue colored Save Exit switch is used to finalize all your communication and histogramming selections Figure 13 Configure Sub Menu The Start button in the user interface initiates a measurement using the settings selected from the configure menu After selecting it you will see the Rate Meter and the Muons through detector graphs show activity The Pause button temporarily suspends data acquisition so that the three graphs stop being updated Upon selection the button changes its name to Resume Data taking resumes when the button is selected a second time 22 eS LE ua Muon Physics A i s A e ei u 4 o The Fit button when selected will prompt the user for a password The instructor can change the password If the correct password is entered the data displayed in the decay time histogram is fit and the results displayed in the upper right hand corner of the graph Data continues to be collected and displayed
36. le p T 4 T 7 V V Y y _ ul et _ e e e Figure 1 Cosmic ray cascade induced by a cosmic ray proton striking an air molecule nucleus Not all of the particles produced in the cascade in the upper atmosphere survive down to sea level due to their interaction with atmospheric nuclei and their own spontaneous decay The flux of sea level muons is approximately 1 per minute per cm see http pdg 1b1 gov for more precise numbers with a mean kinetic energy of about 4 GeV Careful study pdg 1b1 gov shows that the mean production height in the atmosphere of the muons detected at sea level is approximately 15 km Travelling at the speed of light the transit time from production point to sea level is then 50 usec Since the lifetime of at rest muons is more than a factor of 20 smaller the appearance of an appreciable sea level muon flux is qualitative evidence for the time dilation effect of special relativity K Var ETA ER XX 2 A v1 y y em Tg NY Zu US TZ CAE C f NJ 26 urn o u m 4 MANN h Muon Physics VU RATES MATT i Stra ig J l j ds Ue B x ER DEM WAIE Irt AY n 1 H Seton gt P Muon Decay Time Distribution The decay times for muons are easily described mathematically Suppose at some time t we have N t muons If the probability that a muon decays in some small time interval dt is Adt whe
37. lose to the speed of light is e artery 2 MeV g cm where we measure the thickness s of the matter in units of g cm Here s px where p is the mass density of the material through which the particle is passing measured in g cm and the x is the particle s pathlength measured in cm This way of measuring material thickness in units of g cm allows us to compare effective thicknesses of two materials that might have very different mass densities A more accurate value for energy loss can be determined from the Bethe Bloch equation 11 f LS dE _ _ E ome _ MeV Z 1 af a 0 3071 SZ Z i T y 6 Here N is the number of electrons in the stopping medium per cm e is the electronic charge z is the atomic number of the projectile Z and A are the atomic number and weight respectively of the stopping medium The velocity of the projectile is D in units of the speed c of light and its corresponding Lorentz factor is y The symbol denotes the mean excitation energy of the stopping medium atoms Approximately J AZ where A 13 eV More accurate values for J as well as corrections to the Bethe Bloch equation can be found in Leo p26 A simple estimate of the energy lost AE by a muon as it travels a vertical distance H is AB 2 MeV g cm p air where p air is the density of air possibly averaged over H using the density of air according to the standard atmosphere Here the atmosphere i
38. nn nenas gt HE VI EE RM EF 15 40 7 A do 9 Lent ER NI Fig 2b Same as 2a except discriminator set at 8 Notice that the discriminator s output sits quiescently at 160 mV and drops briefly to zero for a standardized duration if and only if the discriminator fires The fact that the discriminator pulse occurs after the amplifier pulse reflects the fact that the amplifier output pulse is the cause and the discriminator output pulse is the effect TEACH Sd Tri Main Center Suite 409 2495 Main Street Buffalo NY 14214 2153 9 F sit ga Ww 45 0 Mu p RO HO B Gr 08979 9 9 9T 9 9 9 5 9 99 a 9 VEN Ww M la 329 d TT T 2v M mE t Yo 2 gt 4 an gt de 4 r 24 Te to oe 5 am ar FIA I che PE Ww m oo ae de CQ Wr epe FAP EA PS ep m PUn E 1 er Y LA cedes b o ote gt gt Amis NETUS yia 2 aiite 4 LI LI LI UI m UU US Fig 4 Another infinite persistence view as In Fig 3 but this one showing 20 minutes worth of accumulation of events occurring in the 9 us after triggering events Fig 4 clearly shows that hypothesis B is the one strongly supported by the data Of the 24 events visible 15 fall with in the first 2 us while only 5 fall in the next block of 2 us width and only 3 fall in the ne
39. pulse triggers the timing circuit of the FPGA A second TTL output pulse arriving at the FPGA input within a fixed time interval will then stop and reset the timing circuit The reset takes about 1 msec during which the detector is disabled The time interval between the start and stop timing pulses is the data sent to the PC via the communications module that is used to determine the muon lifetime If a second TTL pulse does not arrive within the fixed time interval the timing circuit is reset automatically for the next measurement Discriminator erla Amplifler PMT O Output Input gt gt Discriminator LLL EPA Timer bc Two Stage USB Amplifier E aller uhr EN Port Monitor Ref Monitor Adjust Y pr ILL LED Pulser 0 LED Varlable Monitor Time Delay t Figure 5 Block diagram of the readout electronics The amplifier and discriminator outputs are available on the front panel of the electronics box The HV supply is inside the detector tube The front panel of the electronics box is shown in figure 6 The amplifier output is accessible via the BNC connector labeled Amplifier output Similarly the comparator Output is accessible via the connector labeled Discriminator output The voltage level against which the amplifier output is compared to determine whether the comparator PM d pr gt Sis 15 1 Vll ERA MU A NER T AIRES ANA HAVIA i ws Ks FILZ ay ies vu i
40. r GeV c 10 10 10 Muon Momentum GeV c Figure 4 Muon momentum spectrum at sea level The curves are fits to various data sets shown as geometric shapes Figure is taken from reference Greider p399 CN n f A LS 4 UT Tes me ty i NASRA uum Bia fut pii nysics o 13 lt momentums s 120 MeV c 790 MeV c We do this by first measuring the muon stopping rate at two different elevations Ah 3008 meters between Taos NM and Dallas TX and then computing the ratio R aw of raw stopping rates Rray Dallas Taos 0 41 0 05 Next using the above expression for the transit time between the two elevations we compute the transit time in the muon s rest frame t 1 324 for vertically travelling muons and calculate the corresponding theoretical stopping rate ratio R exp t t 0 267 We then compute the double ratio Ro Ryaw R 1 5 0 2 of the measured stopping rate ratio to this theoretical rate ratio and interpret this as a correction factor to account for the increase in muon flux between about E 7160 MeV and E 600 MeV This correction is to be used in all subsequent measurements for any pair of elevations separated by 2000 3000 meters or so To verify that the correction scheme works we take a new stopping rate measurement at a different elevation h 2133 meters a s l at Los Alamos NM and compare a new stopping rate ratio measurement with our n
41. re is a constant decay rate that characterizes how rapidly a muon decays then the change dN in our population of muons is just dN N t dt or dN N t Adt Integrating we N t No exp A t where N t is the number of surviving muons at some time t and No is the number of muons at t 0 The lifetime of a muon is the reciprocal of A t 1 This simple exponential relation is typical of radioactive decay Now we do not have a single clump of muons whose surviving number we can easily measure Instead we detect muon decays from muons that enter our detector at essentially random times typically one at a time It is still the case that their decay time distribution has a simple exponential form of the type described above By decay time distribution D t we mean that the time dependent probability that a muon decays in the time interval between t and t dt is given by D t dt If we had started with No muons then the fraction dN N that would on average decay in the time interval between t and t dt is just given by differentiating the above relation dN NoAexp A t dt dN No Aexp A t dt The left hand side of the last equation is nothing more than the decay probability we seek so D t A exp A t This is true regardless of the starting value of No That is the distribution of decay times for new muons entering our detector is also exponential with the very same exponent used to describe th
42. s that are used inside the electronics box to start and stop the electronic stopwatch And that stopwatch is the source of all the muon timing information sent on to the computer There s still more you can do learn and teach using the scope The next opportunity 1s to use the scope to see what happens soon after a typical triggering event For this purpose we widen the time base say to lus div move the trigger point to the left to give a view of 9 Lis of time after each triggering event and use the peak detect mode Here we can get a bit quantitative muon events happen at a rate of about 5 per second so there s a typical waiting time of 1 5th of a second until the next one That s 200 ms or 200 000 us so typically the successor muon event will not appear in the scope s 9 us field of view But if you set up this display and wait a minute or two you ll see the first occurrence of a successor event one is N b wih be 6 009 SE Kee aS A Ee 495 os ox to 5 po s X x v c 7 2 deles TELE TED TM sgl OPERE CHT i mW CH2 1 0mv M100us CHA Fig 3 Traces as in Fig 2 of amplifier pulses below and discriminator pulses above but with time base set to 1 us div and persistence time set to Infinite Here you see at the scope s trigger point the overlapping record of hundreds of trigger events and you can also see at 1 4 us after the trig
43. s assumed isothermal and the air pressure p at some height h above sea level is parameterized by p po exp h ho where 1030 g cm is the total thickness of the atmosphere and hy 8 4 km The units of pressure may seem unusual to you but they are completely acceptable From hydrostatics you will recall that the pressure P at the base of a stationary fluid is P pgh Dividing both sides by g yields P g ph and you will then recognize the units of the right hand side as g cm The air density p in familiar units of g cm is given by p dp dh If the transit time for a particle to travel vertically from some height H down to sea level all measured in the lab frame is denoted by t then the corresponding time in the particle s rest frame is t and given by O A dh LAN Here D and y have their usual relativistic meanings for the projectile and are measured in the lab frame Since relativistic muons lose energy at essentially a constant rate when travelling through a medium of mass density p dE ds Co so we have dE pCo dh with Co 2 MeV g cm Also from the Einstein relation E ymc dE mc dy so mc pCo dy Hence pl Ta dy Y A pCo x Here y is the muon s gamma factor at height and yz is its gamma factor just before it enters the scintillator We can take 1 5 since we want muons that stop in the 12 o Sdn e LPS UE NM Muon Physics SR dio scintillator
44. scope A digital scope works best Be sure that the scope input is terminated at 500 What do you see Now examine the discriminator output simultaneously Again be certain to terminate the scope input at 502 What do you see 8 Set up the instrument for a muon lifetime measurement Start and observe the decay time spectrum Q The muons whose decays we observe are born outside the detector and therefore spend some unknown portion of their lifetime outside the detector So we never measure the actual lifetime of any muon Yet we claim we are measuring the lifetime of muons How can this be 9 Fitting the decay time histogram can be done with the included fitter or with your own 10 From your measurement of the muon lifetime and a value of the muon mass from some trusted source calculate the value of Fermi coupling constant Gr Compare your value with that from a trusted source 11 Using the approach outlined in the text measure the charge ratio p of positive to negative muons at ground level or at some other altitude 12 Following the approach in the manual measure the muon stopping rate at two different elevations and compare predictions that do and do not assume the time dilation effect of special relativity 32 Wt mH y pon ue i M t ERE Y a MW n mp 18 s 1 MA tty S Ln NENA Muon Physics Wi o pe VAI Da NDS ID ER LAA LARUM E ATA A e n asta 4 M 1 M ru NT NN 13
45. sing The returned errors are statistical The executable freewrap is the compiler for any Tcl Tk code that your write or modify If you modify a Tcl Tk script you need to compile it before running it On a Windows machine you do this by opening a DOS window and going to the muon util directory You then execute the command freewrap your script tcl where your script tcl is the name of your Tcl Tk script Do not forget the tcl extension 26 TH MM AAA q a ALO LE wr A Muon Physics References Instrumentation and Technique Leo W R Techniques for Nuclear and Particle Physics Experiments 1994 Springer Verlag New York Owens A and MacGregor A E Am J Phys 46 859 1978 Ward T et al Am J Phys 53 542 1985 Ziegler J F Nuclear Instrumentation and Methods 191 1981 pp 419 424 Zorn C in Instrumentation in High Energy Physics ed F Sauli 1992 World Scientific Singapore pp 218 279 Cosmic Rays Friedlander M W A Thin Cosmic Rain Particles from Outer Space 2000 Harvard University Press Cambridge USA Gaisser T K Cosmic Rays and Particle Physics 1990 Cambridge University Press Cambridge Greider P K F Cosmic Rays at Earth 2001 Elsevier Amsterdam Kremer J et al PAys Rev Lett 83 4241 1999 Longair M S High Energy Astrophysics vol 1 1992 Cambridge University Press Cambridge Motoki M et al Proc of International Cosmic Ray Confer
46. t eae o8 7 sm ae ee km Er ee 9 Y 1 H1 ch Tom A Y ROS 1 Fig 1 Amplifier output pulses viewed using 10 mV div vertically 25 ns div horlzontally triggering on upward slopes at a level of 15 mV and using 5 seconds persistence time The high voltage monitor on the PMT reads 11 068 V Notice that multiple pulses have occurred during that five seconds of persistence and note also that the pulses differ in amplitude Why so Mostly because muons aren t aimed at the scintillator so some of them pass through its center and others just catch a corner of it As a result the amount of energy deposition naturally varies accordingly Notice too that these pulses we re attributing to the pas sage of muons lie atop a voltage baseline which itself is noisy Some of that is noise generated in the electron ics box and some is due to genuine scintillation everfts Those scintillations however are produced by the rela tively low energy events associated with ambient radioactivity The presence of that noise brings up an important question what shall we count as a real muon event and what signals do we want to reject This is an issue in all pulse processing experiments and here too we ll deal with it using an electronic pulse height discriminator The electronics of our pulse height discriminator are set to fire to give an output pulse whenever there is an incomin
47. time indicated down to the second The scale is sliding so that the far left hand side always corresponds to the start of the measurement session The bin width is indicated in the upper left hand portion of the plot Muon Decay Time Histogram This plot is probably the most interesting one to look at It is a histogram of the time difference between successive triggers and is the plot used to measure the muon lifetime The horizontal scale is the time difference between successive triggers in units of microseconds Its maximum displayed value is set by the Configure menu All time differences less than 20 usec are entered into the histogram but may not actually be displayed due to menu choices You can also set the number of horizontal bins using the same menu The vertical scale is the number of times this time difference occurred and is adjusted automatically as data is accumulated A button Change y scale Linear Log allows you to plot the data in either a linear linear or log linear fashion The horizontal error bars for the data points span the width of each timing bin and the vertical error bars are the square root of the number of entries for each bin 24 The upper right hand portion of the plot shows the number of data points in the histogram Again due to menu selections not all points may be displayed If you have selected the Fit button then information about the fit to the data is displayed The muon lifetime is returned assumin
48. tion the relationship between the muon lifetime and Gr is particularly simple 19277 Gg mc T where m is the mass of the muon and the other symbols have their standard meanings Measuring with this instrument and then taking m from say the Particle Data Group http www pdg lbl gov produces a value for Gr 10 iwl EC Nie n ls diu ws Da eL Mr vv LANE Sic HAW IW AES RE VERTUS A C N i H 1 y E me tT L y ma MI A Time Dilation Effect A measurement of the muon stopping rate at two different altitudes can be used to demonstrate the time dilation effect of special relativity Although the detector configuration is not optimal for demonstrating time dilation a useful measurement can still be preformed without additional scintillators or lead absorbers Due to the finite size of the detector only muons with a typical total energy of about 160 MeV will stop inside the plastic scintillator The stopping rate is measured from the total number of observed muon decays recorded by the instrument in some time interval This rate in turn is proportional to the flux of muons with total energy of about 160 MeV and this flux decreases with diminishing altitude as the muons descend and decay in the atmosphere After measuring the muon stopping rate at one altitude predictions for the stopping rate at another altitude can be made with and without accounting for the time dilation effect of special relativity second
49. tube and an oscilloscope A digital scope works best Be certain to terminate the scope input at 50 or you signal will be distorted You should see a signal that looks like figure 9 The figure shows details like scope settings and trigger levels Connect the BNC cable between PMT Output on the detector and PMT Input on the box Adjust the discriminator setting on the electronics box so that it is in the range 180 220 mV The green LED on the box front panel should now be flashing You can look at the amplifier output by using the Amplifier Output on the box front panel and an oscilloscope The scope input impedance must be 500 Similarly you can examine the output of the discriminator using the Discriminator Output connector Again the scope needs to be terminated at 50Q Figure 10 shows typical signals for both the amplifier and discriminator outputs on the same plot Details about scope time settings and trigger thresholds are on the plot Insert the software CD into your PC and copy all the folders directories into a convenient folder directory on your PC Open the folder directory muon data and launch the program muon exe Windows may hide the exe extension You should now see user interface as shown in figure 12 Configure the port on your PC See the material above under Control in the Software and User Interface section for details Choose your histogramming options Click on the Save Exit button 29 i SPP
50. ulse into a brief positive going analog voltage pulse This is the first place along the cause and effect chain where the pulse is easy to see with an oscilloscope Using a 50 0 termination on a BNC tee at the output labeled AMPLIFIER a short cable to a scope s input and setting the scope for a five second persistence we see pulses like those in Fig 1 The only amplifier pulses that appear on the scope screen are those that fire the discriminator and thus subsequently trig ger the scope In particular one can see in Fig 2a that the smallest amplitude pulse is about 15 mV high for the discrim inator setting of 2 whereas Fig 2b shows that the smallest amplitude pulse is 30 mV high for a setting of 8 Instead of reading the dial on the discriminator students can measure the DC voltage provided at the test points It turns out the voltage at the test points is not the threshold voltage but is proportional to it It is a useful exercise for the students to measure the proportionality constant It turns out to be 50 mV threshold Volt at test points With this understanding of the role of the discriminator students can now choose a proper setting for accumulating data The result of a good choice for threshold level is the success ful transformation of analog information the muon pulses of varying heights to digital information the standardized shape giving a yes no indication of a muon event It s these event pulse
51. ured by the scintillator nuclei Setting p 1 allows us to estimate the average muon lifetime we expect to observe in the scintillator We can measure p for the momentum range of muons that stop in the scintillator by rearranging the above equation As 117 f AA ln ical Mi Y DOREM Ln d Backgrounds The detector responds to any particle that produces enough scintillation light to trigger its readout electronics These particles can be either charged like electrons or muons or neutral like photons that produce charged particles when they interact inside the scintillator Now the detector has no knowledge of whether a penetrating particle stops or not inside the scintillator and so has no way of distinguishing between light produced by muons that stop and decay inside the detector from light produced by a pair of through going muons that occur one right after the other This important source of background events can be dealt with in two ways First we can restrict the time interval during which we look for the two successive flashes of scintillator light characteristic of muon decay events Secondly we can estimate the background level by looking at large times in the decay time histogram where we expect few events from genuine muon decay Fermi Coupling Constant Gr Muons decay via the weak force and the Fermi coupling constant Gr is a measure of the strength of the weak force To a good approxima
52. xt bin of time of 2 us width Now once the idea of accumulating evidence of successor events on a scope s face has been attached to the emergence of instances of addition to the histogram it should be clear that the histogram is the method of choice for accumulating and viewing lots of data And with a few hours or a few days of data accumulation students will see the emergence of a fine exponential decay curve due to type B processes PRSRT STD US POSTAGE PAID Buffalo NY Permit No 2 The sharper students will also see underlying that exponential and continuing for the full 20 us width of the histogram a flat background called accidental coinci dences attributable to type A processes In fact the best of your students will even be able to predict how many such events ought to appear in each time bin of the histogram They ll need only some careful reasoning and numbers for the muon event rate r say 5 second the histogram s bin width t typically 1 us and the duration T of data accumulation say 1 day 86 400s The mean number of accidental coincidences per bin for this case is predicted to be N 7 r T r x F T t 5 s 86 400 s 1 x 10 s 2 Think of all that a student can learn in this investigation including all these electronic instrumental statistical and reasoning skills that extend far beyond the particular though interesting case of muons and you ll see why we think there s a lot
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